SELF-ASSEMBLY BEHAVIOR OF MODULATED ELEMENTAL REACTANTS 
 
 
 
 
 
 
 
 
 
 
 
 
 
by 
 
DMITRI LEO M. CORDOVA 
 
 
 
 
 
 
 
 
 
 
 
 
 
A DISSERTATION 
 
Presented to the Department of Chemistry and Biochemistry 
and the Graduate School of the University of Oregon 
in partial fulfillment of the requirements 
for the degree of 
Doctor of Philosophy  
 
June 2020 
 
  
DISSERTATION APPROVAL PAGE 
 
Student: Dmitri Leo M. Cordova 
 
Title: Self-assembly Behavior of Modulated Elemental Reactants 
 
This dissertation has been accepted and approved in partial fulfillment of the 
requirements for the Doctor of Philosophy degree in the Department of Chemistry and 
Biochemistry by: 
 
Dr. Mark C. Lonergan Chairperson 
Dr. David C. Johnson Advisor 
Dr. Christopher H. Hendon Core Member 
Dr. Richard Taylor Institutional Representative 
 
and 
 
Kate Mondloch Interim Vice Provost and Dean of the Graduate School  
 
Original approval signatures are on file with the University of Oregon Graduate School. 
 
Degree awarded June 2020 
  
ii 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
© 2020 Dmitri Leo M. Cordova  
  
iii 
  
DISSERTATION ABSTRACT 
 
Dmitri Leo M. Cordova 
 
Doctor of Philosophy 
 
Department of Chemistry and Biochemistry 
 
June 2020 
 
Title: Self-Assembly Behavior of Modulated Elemental Reactants 
 
 
Diverse bulk-derived layered structures have been made via Modulated Elemental 
Reactants (MER) synthesis despite only superficial understanding of its mechanism. The 
premise behind this approach is that an elemental multilayer precursor self-assembles in 
an almost diffusionless process if it has the correct number of atoms per layer and its 
nanoarchitecture closely resembles the target product. The work presented here is 
concentrated on developing a deeper understanding of the reaction mechanism of 
Modulated Elemental Reactants, prompted by developments in analysis methods for thin 
films. 
A new method for analyzing X-ray Florescence (XRF) data was developed to 
measure the number of atoms per square Angstrom (areal density) in a thin film with sub-
monolayer accuracy. With this advancement, precursors can be made so that the two 
conditions set by the simple MER mechanism are satisfied. The crystallographic alignment 
of thick PbSe layers on VSe2 demonstrated a strong non-epitaxial relationship between the 
two constituents, suggesting that compatibility of two layered constituents in a 
heterostructure can be determined by testing for preferred alignment. A new class of charge 
density wave containing heterostructures, [(PbSe)1+d]m(VSe2)1, where m = 1-4 and the 
number of PbSe bilayers, was synthesized by precisely controlling the element areal 
iv 
  
density and nanoarchitecture of the precursor. Alternate reaction pathways were explored 
when the areal density of the precursor was modified. Next, a similar class of 
heterostructures, [(PbSe)1+d]1(VSe2)1, where q = 1-11 and the number of PbSe monolayers, 
was investigated. When a small odd number of PbSe monolayers (q = 1, 3, and 5) was 
targeted for synthesis, the precursors exhibited unexpected long range lateral surface 
diffusion during the deposition process, uncovering a new aspect of MER synthesis. 
Computational studies confirmed that the low temperature rearrangement is driven by the 
stability of PbSe bilayers compared to monolayers. Lastly, the growth mechanism of a new 
heterostructure, [(SnSe2)1+d]1(VSe2)1 was elucidated from Laue oscillations in x-ray 
reflectivity data and in-plane x-ray diffraction and precursor nanoarchitecture, and was 
used as a guide to direct reaction pathways toward the synthesis of a new alloy, SnxV1-xSe2. 
This dissertation contains previously published and unpublished coauthored 
material. 
 
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CURRICULUM VITAE 
 
NAME OF AUTHOR:  Dmitri Leo M. Cordova 
 
 
GRADUATE AND UNDERGRADUATE SCHOOLS ATTENDED: 
 
 University of Oregon, Eugene 
 
 University of the Philippines, Manila 
 
 
DEGREES AWARDED: 
 
 Doctor of Philosophy, Chemistry, 2020, University of Oregon 
 
 Bachelor of Science, Biochemistry, 2013, University of the Philippines Manila 
  
 
AREAS OF SPECIAL INTEREST: 
 
 Solid State Chemistry 
 
 Materials Chemistry 
 
 
PROFESSIONAL EXPERIENCE: 
 
 Graduate Employee, University of Oregon, September 2016 - December 2018 
 
 Instructor III, University of the Philippines Manila, June 2013 - July 2016 
  
 
GRANTS, AWARDS, AND HONORS: 
 
 Merit Scholarship, Science Education Institute, Department of Science and 
 Technology, Republic of the Philippines, 2013  
 
 Cum laude, University of the  Philippines, Manila, 2013 
 
  
PUBLICATIONS: 
 
Cordova, D. L. M.; Kam, T. M.; Gannon, R. N.; Lu, P.; Johnson, D. C.; 
Controlling the self-assembly of new metastable tin vanadium selenides 
vi 
  
using composition and nanoarchitecture of precursors, J. Am. Chem. Soc., 
Submitted. 
 
Cordova, D. L. M.; Johnson, D. C.; Synthesis of Metastable Inorganic Solids 
with Extended Structures. ChemPhysChem, Accepted. DOI 
10.1002/cphc.202000199 
 
Hamann, D. M.; Rudin, S; Asaba, T.; Ronning, F.; Cordova, D. L. M.; Lu, P.; 
Johnson, D. C.; Emergent Structure and Properties in Interface Stabilized 
2D-Layers. ACS Nano. Submitted. 
 
Cordova, D. L. M.; Fender, S. S.; Kam, T. M.; Seyd, J.; Albrecht, M.; Lu, P.; 
Fischer, R.; Johnson, D. C. Designed Synthesis and Structure-Property 
Relationships of Kinetically Stable [(PbSe)1+d]m(VSe2)1 (m = 1, 2, 3, 4) 
Heterostructures. Chem. Mater. 2019, 31 (20), 8473–8483.  
 
Cordova, D. L. M.; Kam, T. M.; Fender, S. S.; Tsai, Y. H.; Johnson, D. C. Strong 
Non-Epitaxial Interactions: Crystallographically Aligned PbSe on VSe2. 
Phys. Status Solidi 2019, 1800896, 1800896.  
 
Choffel, M. A.; Hamann, D. M.; Joke, J. A.; Cordova, D. L. M.; Johnson, D. C. 
The Reaction between Mn and Se Layers. Zeitschrift fur Anorg. und Allg. 
Chemie 2018, 644 (24), 1875–1880.  
  
Hamann, D. M.; Bardgett, D.; Cordova, D. L. M.; Maynard, L. A.; Hadland, E. 
C.; Lygo, A. C.; Wood, S. R.; Esters, M.; Johnson, D. C. Sub-Monolayer 
Accuracy in Determining the Number of Atoms per Unit Area in Ultrathin 
Films Using X-Ray Fluorescence. Chem. Mater. 2018, 30 (18), 6209–
6216. 
 
Cordova, D. L. M.; Abuel, R. J. D.; Galingana, M. O.; Villanueva, L. A.; 
Billones, J. B. Piggyback Drug Development: (Molecular Docking of 
Entacapone Analogues as Direct M. Tuberculosis InhA Inhibitors). J. 
Chem. Pharm. Res. 2015, 7 (5), 636–642. 
 
 
 
vii 
  
ACKNOWLEDGMENTS 
 
I wish to express my sincere appreciation to Dr. David Johnson, for welcoming me 
into his lab and allowing me make mistakes and learn from them. I am forever grateful for 
the advice and encouragement you have given me and for affording me the freedom to 
pursue research paths that truly interests and challenges me. I am thankful to the members 
of my committee, Dr. Mark Lonergan, Dr. Chris Hendon, and Dr. Richard Taylor, for the 
words of encouragement they have given me along the way. I am especially thankful to Dr. 
Cathy Page, for introducing me to the wonderful world of solid state chemistry and for 
serving as an inspirational educator. I am thankful for the kindness of the staff at the 
Chemistry offices, Janet Macha, Kathy Noakes, Christi Mabinuori, and Jim Rasmussen, 
for the tiny things they do that make student's lives easier amidst the chaos of doing science.  
My colleagues from the Johnson lab have been absolutely essential during my time 
in Oregon, I am forever grateful for them. Dr. Dani Hamann has been a valuable part of 
my journey, she is a trusted friend, mentor, and like a big sister to me. I am glad to have 
experienced both the highs and lows of science alongside her. I have had the distinct 
pleasure of working with incredible undergraduates who always inspire me to do better. I 
am glad that Shannon Fender, Taryn Kam, Mina Buchanan, and Terence Tsai have been 
part of the team for the past three years. I am thankful for the other members of the Johnson 
lab, Marisa Choffel, Renae Gannon, Alex Lygo, Dylan Bardgett, Jake Logan, Jordan Joke, 
Dr. Erik Hadland, Dr. Marco Esters, Aaron Miller, Alex Skochko, and Coleman Johnson 
for the fruitful conversations and fond memories.  
My work would not have been possible without the help of the talented people from 
the UO TSA Machine Shop. Jeffrey Garman, Cliff Dax, Julien McAdams, and Kris 
viii 
  
Johnson have gotten us out of dire situations more than I can remember. I am thankful to 
the CAMCOR staff for making it possible to pursue high quality research; namely Steve 
Weimholt, Kurt Langworthy, Becky Beach, Mark Adams, and Robert Fischer. 
I am glad to have forged valuable connections with different collaborators from all 
over the world whose insight have opened my eyes to different facets of solid state 
chemistry. I am thankful to Dr. Kirsten Jensen and her group at Copenhagen for helping 
me collect and analyze total scattering data. I am thankful to Dr. Ping Lu from Sandia for 
collecting HAADF-STEM data that literally adds another dimension to how we visualize 
our materials. I am thankful to Dr. Mark Asta, Dr. Ben Hanken, and Dr. Shahriar 
Hooshmand from UC Berkeley for the insightful calculations that explained the 
experimental phenomena we were observing. I am thankful for Dr. Vedran Vonk from 
DESY for discovering interesting structural correlations in our materials and Jenia 
Karapetrova from APS for making our beamline experience quite memorable. I am 
thankful for collaborators with the finest instrumentation that have made our materials 
more interesting by uncovering interesting properties; Dr. Manfred Albrecht and Johannes 
Seyd from Augsburg, Dr. Dietrich Zahn and Fabian Gohler from TU Chemnitz, Dr. 
Stephen Cronin and Yu Wang from USC, Dr. Matt Beekman from Cal Ply SLO, Dr. Sage 
Bauers and Dr. Dennice Roberts from NREL, and Dr. Wolfgang Bensch from Kiel. 
Finally, I am thankful for my family and friends for being there to hold me up when 
I think nothing else can. I am thankful for my parents, Chie and Leo, and sister, Hannah, 
for the never-ending support. I am thankful for my family here in the US, Tita Iah, Lola, 
Tito Jay, Tito Abong, and families, who have made the transition for me quite easy and 
have been a constant source of inspiration for me.   
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For my family, friends, and teachers 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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TABLE OF CONTENTS 
Chapter Page 
 
 
I. SYNTHESIS OF METASTABLE SOLIDS 
   WITH EXTENDED STRUCTURES .......................................................................  1 
 
 I.1 Introduction ......................................................................................................  1 
 I.2 Selected Overview of Selected Solid State Synthesis Tecnhiques ..................  4 
 
       I.2.1 Direct Solid State Reaction of Elements or Compounds ........................  4 
 
 I.2.2 Synthesis in a Fluid Phase .......................................................................  7 
 I.2.3 The Experimental Procedure to Discover New Compounds ..................  9 
 I.3 Energy Landscape Description of Synthetic Pathways ....................................  10 
       I.3.1 Molecular Synthesis ................................................................................  11 
 I.3.2 Synthesis Using a Fluid Phase ................................................................  13 
 I.3.3 Synthesis Using Molecular Beam Epitaxy ..............................................  17 
 I.3.4 Synthesis via Topotactic Reactions .........................................................  21 
 I.3.5 Synthesis via Amorphous Intermediates .................................................  24 
      I.4 Predicting Undiscovered Compounds ..............................................................  33 
      I.5 Modulated Elemental Reactants - An Approach 
           to Control Reaction Pathway using Designed Precursors ................................  37 
 
 I.5.1 More Complex Precursors - Composition Modulation ...........................  41 
 I.5.2 Ideas Concerning the Reaction Mechanism of the Self-Assembly 
         of Precursors into Products ......................................................................  49 
 
      I.6 Next Steps in Materials Synthesis ....................................................................  58 
 I.6.1 Pair Distribution Function Analysis ........................................................  59 
 
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Chapter Page 
 
 
 I.6.2 In-situ Studies ..........................................................................................  61 
 I.6.3 EDX and other STEM Techniques .........................................................  63 
      I.7 Conclusions....................................................................................................... 64 
      I.8 Dissertation Overview  .....................................................................................  64 
II. STRUCTURAL, COMPOSITIONAL, AND ELECTRICAL 
    CHARACTERIZATION TECHNIQUES ...............................................................  67 
 
 II.1 Structural Characterization via X-ray Diffraction ..........................................  67 
 II.1.1 X-ray Reflectivity ..................................................................................  72 
 II.1.2 Specular X-ray Diffractions ...................................................................  74 
 II.1.3 Grazing Incidence In-plane X-ray Diffraction .......................................  75 
      II.2 X-ray Fluorescence .........................................................................................  76 
 II.2.1 X-ray Fluorescence Analysis of Thin Films ..........................................  77 
 II.2.2 X-ray Fluorescence Calibration Methods ..............................................  80 
      II.3 Electrical Transport Measurements ................................................................  82 
 II.3.1 Van der Paw Method for Measuring Resistivity ...................................  83 
 II.3.2 Van der Paw Method for Measuring Carrier Density ............................  84 
III. STRONG NON-EPITAXIAL INTERACTION:  
      CRYSTALLOGRAPHICALLY ALIGNED PbSe on VSe2 .................................  86 
 
 III.1 Introduction ...................................................................................................  86 
 III.2 Experimental ..................................................................................................  91 
 III.3 Results and Discussion ..................................................................................  91 
 III.4 Conclusions ...................................................................................................  101 
 III.5 Bridge ............................................................................................................  102 
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Chapter Page 
  
IV. DESIGNED SYNTHESIS AND STRUCTURE-PROPERTY  
      RELATIONSHIPS OF KINETICALLY STABLE 
      [(PbSe)1+d]m(VSe2)1 (m = 1, 2, 3, 4) HETEROSTRUCTURES ............................  104 
 
 IV.1 Introduction ...................................................................................................  104 
 IV.2 Experimental .................................................................................................  107 
 IV.3 Results and Discussion ..................................................................................  109 
 IV.4 Conclusions ...................................................................................................  131 
 IV.5 Bridge ............................................................................................................  131 
V. THE INSTABILITY OF MONOLAYER THICK PbSe on VSe2 .........................  133 
 V.1 Introduction ....................................................................................................  133 
 V.2 Experimental ...................................................................................................  136 
 V.3 Results and Discussion ...................................................................................  137 
 V.4 Conclusions ....................................................................................................  158 
 V.5 Bridge .............................................................................................................  159 
VI. CONTROLLING THE SELF-ASSEMBLY OF NEW METASTABLE TIN  
      VANADIUM SELENIDES USING COMPOSITION AND     
      NANOARCHITECTURE OF PRECURSORS ....................................................  160 
 VI.1 Introduction ...................................................................................................  160 
 VI.2 Experimental .................................................................................................  162 
 VI.3 Results ...........................................................................................................  164 
 VI.4 Discussion .....................................................................................................  179 
 VI.5 Conclusions ...................................................................................................  181 
VII. CONCLUSIONS AND SUMMARY ..................................................................  183 
VII.1 Concluding Remarks ....................................................................................  183 
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Chapter Page 
 
 
 VII.2 Outlook ........................................................................................................  185  
APPENDICES .............................................................................................................  187 
 A. SUPPLEMENTAL MATERIAL TO CHAPTER IV .......................................  187 
 B. SUPPLEMENTAL MATERIAL TO CHAPTER V ........................................  189 
REFERENCES CITED ...............................................................................................  190 
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LIST OF FIGURES 
 
Figure Page 
 
 
I.1     The number of known compounds and possible combinations of the elements  
     plotted versus the number of elements in the compound. .................................  1 
 
I.2     Free energy surface with a number of local minima and a global minimum.  
     Shown are two different starting points resulting in two different reaction  
     trajectories and two different products. .............................................................  3 
 
I.3     Schematic of the reaction of elements to form a ternary compound showing  
     the formation of binary compounds before the nucleation of the first  
     ternary phase ......................................................................................................  4 
 
I.4     A schematic illustration of the evolution of crystalline phases from a flux  
     reaction due to the changes in concentration of different species in solution. 
     The initial product (A) is the easiest to nucleate from the flux given the species  
     and their respective concentrations. The growth of phase A depletes the  
     concentration of some species in solution and the species continue to evolve  
     with time. This can lead to the nucleation and growth of a second phase (B),  
     which again depletes the concentration of some species in solution.  This can  
     lead to phase A dissolving. This process can continue forming phase T.  
     Typically the density of the compounds increase during the reaction, with the  
     density of T greater than B, which has a density greater than A. ......................  8 
 
I.5     The C-H-O ternary phase diagram showing the thermodynamically stable  
     binary compounds. A select few ternary compounds are shown on tie lines 
     between binary compounds. They are all metastable with respect to a mixture  
     of the binary compounds ...................................................................................  10 
 
I.6     Reaction coordinate diagram for a molecule containing two sites with the same          
     functional group. This results in very similar reaction energies for either site (6a). 
     If a protecting group is installed at one site, then this favors the reaction at the  
     other site (6b) .....................................................................................................  12 
 
I.7     A schematic diagram showing solids A and B dissolving in a flux. The major  
     species in solution are A, B and A2. As the concentration of A and B increase, the         
     solution becomes supersaturated with respect to solid AB, which then nucleates  
     and grows. As the concentration of A2 increases, decreasing the concentration of  
     A, solid AB begins to dissolve. Eventually the solution becomes supersaturated  
     with respect to solid A2B, which nucleates. ......................................................  14 
 
 
 
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Figure Page 
 
 
I.8     A schematic free energy landscape showing the trajectory of an initial  
     system (the star) through the free energy landscape as a function of time.  
     The system initially lands in a basin where the saddle point to the crystalline 
     phase AB is the lowest energy path.  From this basin the system nucleates the     
     compound A2B through the lowest energy pathway to a lower free energy  
     state of the system .............................................................................................  15 
 
I.9     A schematic diagram of an MBE growth chamber.  Several deposition sources           
     provide fluxes of different elements aimed towards a heated substrate. In-situ  
     analysis tools (reflection high-energy electron diffraction and deposition rate       
     monitors) are used to control the process ..........................................................  18 
 
I.10    Schematic of MBE growth, showing arriving atoms, evaporating atoms, a  
     growing epitaxial island and atoms moving on the growth surface ..................  19 
 
I.11    Schematic of idealized model of intercalation-deintercalation topochemical  .             
     reactions where the layered moiety is preserved ...............................................  23 
 
I.12    Schematic of a series of sequential topochemical reactions where the addition 
     of reactants results in the formation of products that are higher in energy than  
     the precursor ......................................................................................................  24 
 
I.13    Schematic of a binary diffusion couple of A and B after annealing for  
     sufficient time at the temperature of the dashed horizontal line. The phase  
     diagram for A and B is shown above the diffusion couple   .............................  25 
 
I.14    Schematic of thin film diffusion couples of A and B shown as a function of          
     annealing time. The top case is where B is the limiting reagent. The bottom  
     case is where A is the limiting reagent. The hypothetical phase diagram for  
     A and B is shown in Figure I.13 ........................................................................  26 
 
I.15    Schematic of an ultra thin film diffusion couple. The system progresses  
     through a homogenous amorphous intermediate before nucleation  
     occurs .................................................................................................................  27 
 
I.16    Schematic of the two different reaction pathways taken by precursors with  
     layer sequences ABC and ABCB ......................................................................  29 
 
I.17    Schematic of the free energy reaction pathway taken by a precursor with  
     thick elemental layers of A and B .....................................................................  29 
 
I.18    Schematic of the free energy reaction pathway taken by a precursor with thin     
     elemental layers of A and B ..............................................................................  30 
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Figure Page 
 
 
I.19    Schematic of the free energy reaction pathway taken by a precursor of  
     ultrathin elemental layers of A and B at a 1 to 2 ratio of the elements. An           
     amorphous intermediate is formed from which the metastable compound AB2      
     nucleates first.  This compound decomposes at higher temperatures to form  
     the equilibrium mixture of AB and B ................................................................  31 
 
I.20    Schematic of a free energy diagram in a binary system of elements showing the     
     energy of thermodynamically stable compounds, with lines showing the energy  
     of physical mixtures of adjacent compounds.  If the free energy of a compound  
     is above this line, it is thermodynamically unstable with respect to                        
     disproportionation.  If below the line, it is thermodynamically stable ..............  34 
 
I.21    Schematic of a free energy diagram in a binary system of compounds showing  
     the energy of thermodynamically stable compounds, with lines showing the  
     energy of physical mixtures of adjacent compounds.  If the free energy of a 
     compound is above this line, it is thermodynamically unstable with respect to    
     disproportionation.  If below the line, it is thermodynamically stable ..............  36 
 
I.22.   Schematic of the free energy reaction pathway taken by a precursor designed  
     to form Fe3Si5 ....................................................................................................  38 
 
I.23    The Fe-Sb phase diagram with the metastable compound FeSb3 shown in red.    
     FeSb3 decomposes exothermically to a mixture of FeSb2 and Sb .....................  40 
 
I.24    The increase in the number of possible homologous compounds as the number  
     of layers in the unit cell is increased. The increase is much greater as the  
     number of distinct constituent layers increases .................................................  42 
 
I.25    HAADF-STEM images of structural isomers containing four bilayers of PbSe  
     and four TiSe2 trilayers. The notation on the bottom of the images provides the    
     number of PbSe bilayers in bold and the number of TiSe2 layers in normal font.    
     The sequence of numbers matches the sequence of layers in each isomer .......  45 
 
I.26   The different layered constituents that can be used as building blocks to  
     prepare heterostructures via designed precursors ..............................................  46 
 
I.27   The ternary phase diagram of Pb-V-Se. The three elements do not have a  
     ternary thermodynamically stable compound. However, using designed  
     precursors, metastable heterostructures containing PbSe and VSe2 have been  
     made and are contained as red circles in the ternary phase diagrams. For two 
     constituent heterostructures, the metastable heterostructures lie on the tie line 
     (black line) connecting the two building blocks ................................................  48 
 
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Figure Page 
 
 
I.28    The ternary phase diagram of Bi-Ti-Se. A three-component heterostructure  
     containing BiSe, Bi2Se3, and TiSe2 will be contained in an area enclosed by  
     the tie lines connecting Bi2Se3 and TiSe2, and BiSe and TiSe2. Shown as a red  
     circle in that area is metastable three-component heterostructure 
     (BiSe)1+δ(Bi2Se3)1+γ(BiSe)1+δ(TiSe2)1, first synthesized by Lygo et al.  
     via MER .............................................................................................................  48 
 
I.29    The quaternary phase diagram of Pb-Sn-Ti-Se. Each phase in the tetrahedron  
     represents a ternary phase diagram containing 3 elements. The three-component  
     heterostructure is contained in the area defined by the tie lines connecting the  
     three components in three different ternary phase diagram ..............................  49 
 
I.30    A schematic representation of the a|x and b|x bilayers interdiffusing to form  
     amorphous layers of a-x and b-x before nucleation and growth of crystalline  
     A and B layers (top). The density of the nucleation sites determines the lateral  
     grain sizes and the random orientation of the different nucleation sites results  
     in the turbostratic disorder found in the self-assembled product ......................  50 
 
I.31    Differences in structure between crystalline and ferecrystalline phases from  
     HAADF-STEM. Crystalline VSe2 have the same orientation across several  
     layers. Ferecrystalline TaSe2 exhibits multiple zone axes across multiple layers. 
     The ferecrystalline heterostructure [(PbSe)1+d]1(VSe2)1 exhibits different  
     zone axes across adjacent repeat units ...............................................................  53 
 
I.32    The structural coherence of between planes of atoms in different  
     crystallographic layers depends on their crystal structure and the structure  
     of the layers adjacent to them. In (a), the adjacent rock salt structured bilayers  
     of PbSe have the same crystallographic orientation. In (b) the adjacent layers  
     of VSe2, TISe2 and NbSe2 with the same block have the same crystallographic 
     alignment while the alignment of the MoSe2 layers in the same block  
     are different .......................................................................................................  54 
 
I.33.   Synthesis of CuCr2Se4 can be accomplished without the formation of CuSe  
     as a reaction intermediate by controlling the sequence of Cu, Cr, and  
     Se layers .............................................................................................................  56 
 
I.34    Local minima within the energy landscape of an Sn|Se|V|Se precursor can be 
     determined by constraining Sn and Se atoms between layers of VSe2.  
     Calculations demonstrate that the formation of CdI2-structured SnSe2 is  
     favored while MoSi2-structured SnSe2 is not ....................................................  62 
 
II.1     Schematic of an atomic lattice describing the conditions required for  
     Bragg's law ........................................................................................................  68 
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Figure Page 
 
 
II.2     (a) A simulated x-ray diffraction pattern of powder PbSe. (b) Atomic planes  
     and their Miller indices represented in the simulated x-ray diffraction  
     pattern ................................................................................................................  70 
 
II.3     Schematic of the geometry for x-ray reflectivity ...............................................  72 
II.4     X-ray reflectivity patterns of V|Se precursors annealed in different conditions     
     demonstrating changes in film structures during self-assembly ........................  73 
 
II.5     Schematic of the geometry for specular x-ray diffraction .................................  74 
 
II.6     X-ray diffraction patterns of VSe2 with various orientations. (red) powder  
     simulation, (blue) specular MER film, (red) in-plane MER film ......................  75 
 
II.7     Schematic of the geometry for grazing incidence in-plane x-ray  
     diffraction ..........................................................................................................  75 
 
II.8     Schematic of x-ray fluorescence analysis ..........................................................  77 
II.9     The linear relationship of amount of material deposited and intensity for  
     different elements deposited on Si substrate. All linear fits pass through  
     zero ....................................................................................................................  78 
 
II.10  Background correction (dashed line) using pre-installed software ....................  78 
II.11  Manual background correction using the data from a blank substrate ..............  79 
II.12  The linear relationship between the total number of Sn atoms per square  
     Angstrom and background corrected integrated intensity .................................  80 
 
II.13  Calibration curve for Pb obtained using thin film and dropcast samples. The  
     linear fits for both methods agree with each other with 10% error ...................  81 
 
II.14  Thin film sample shape, and current and voltage contact configuration for a  
     van der Pauw resistivity measurement ..............................................................  83 
 
II.15  Thin film sample shape, and current and voltage contact configuration for a  
     van der Pauw carrier density measurement .......................................................  85 
 
 
 
 
 
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Figure Page 
 
 
III.1   (a) Specular x-ray diffraction and (b) x-ray reflectivity patterns of various 
      thicknesses of PbSe films on SiO2 as deposited (black) and annealed at 300°C  
     for 30 minutes (red). The presence of non-00l reflections in the specular  
     diffraction patterns indicate that PbSe is randomly oriented. Kiessig fringes  
     that extend only up to ~2° suggest that the film is rough ..................................  93 
 
III.2   Specular x-ray diffraction of representative V|Se precursors after annealing  
     at each of the indicated temperatures for 30 minutes. The prominent 00l  
     reflections appearing in the as deposited sample indicates that  
     crystallographically aligned VSe2 forms upon deposition and becomes more 
     ordered as the film is annealed ..........................................................................  95 
 
III.3   (a) Specular x-ray diffraction of [(PbSe)1.11]1(VSe2)1, (b) in-plane diffraction  
     of [(PbSe)1.11]1(VSe2)1, and (c) x-ray reflectivity patterns of of  
     [(PbSe)1.11]1(VSe2)1 after annealing at the indicated temperatures for 30  
     minutes. Since the film is crystallographically aligned to the substrate, only  
     00l reflections are observed in the specular scans. The higher order 00l  
     reflections observed in the as deposited film suggest crystallization of the 
     superlattice taking place upon deposition. Reflections for independent lattices  
     of PbSe and VSe2 are observed in the in-plane diffraction pattern show that  
     both constituents are present starting at the as deposited state. Kiessig fringes  
     are retained in the x-ray reflectivity pattern even after multiple steps of  
     annealing suggest that the film remains smooth throughout the self-assembly 
     process ...............................................................................................................  97 
 
III.4   (a) Specular x-ray diffraction and (b) x-ray reflectivity patterns of 20 layers of  
     PbSe on 4 layers of VSe2 (20:4) and 82 layers of PbSe on 8 layers of VSe2  
     (82:8) films as deposited (black) and annealed at 300°C for 30 minutes (red).  
     The thicker (82:8) film has weak non-00l reflections implying that there is a  
     small fraction of randomly oriented grains. Annealed film samples have very  
     strong 00l reflections indicating crystallographic alignment to the substrate due  
     to the presence of the intervening layers of smooth VSe2. The films are  
     exceptionally smooth compared to PbSe on SiO2 because the Kiessig fringes 
     extending to higher angles .................................................................................  100 
 
III.5   Grazing incidence in-plane diffraction patterns of 82 layers of PbSe on SiO2, 20  
     layers of PbSe on 4 layers of VSe2, and [(PbSe)1.11]1(VSe2)1. The PbSe films  
     have reflections that can be indexed to rock salt PbSe. All possible hkl  
     reflections are observed in PbSe in SiO2 film, indicating that the grains are 
     randomly oriented. The absence of hkl reflections in the 20:4 film indicates  
     that grains are parallel to the substrate ..............................................................  102 
 
 
xx 
  
Figure Page 
 
 
IV.1   The calculated number of atoms per square Angstrom for V, Pb, and Se based  
     on bulk lattice parameters are shown as solid lines. The measured amounts of  
     each element in the precursors are shown as filled circles.  The deviations  
     from the calculated number reflect the experimental challenges of controlling  
     the deposition process to fractions of a monolayer. AD: as-deposited  
     precursor ............................................................................................................  110 
 
IV.2   The x-ray reflectivity patterns of the precursors designed to form the targeted  
     [(PbSe)1+δ]m(VSe2)1 compounds. The modulation length of the (Pb|Se)mV|Se  
     layer sequence determined from the position of the first order Bragg reflection  
     is graphed versus the number of Pb|Se layers (m) in the repeating layer  
     sequence in the inset ..........................................................................................  111 
 
IV.3   X-ray reflectivity and specular x-ray diffraction patterns collected as a function  
     of increasing temperature after annealing a 4(Pb|Se)(V|Se) precursor at the 
     indicated temperatures for 1 hour ......................................................................  112 
 
IV.4   In-plane X-ray diffraction patterns collected as a function of increasing 
     temperature after annealing a (V|Se) + 4(Pb|Se) precursor at the indicated  
     temperatures for 1 hour .....................................................................................  113 
 
IV.5   Proposed reaction pathway for the formation of products from a 3(Pb|Se)  
     + 1(V|Se) precursor. The pathway depends on the absolute number of atoms  
     per repeat unit of the precursor. The thermodynamic product is a  
     disproportionation of the precursor into isolated regions of PbSe and VSe2 ....  115 
 
IV.6   Specular x-ray diffraction patterns of [(PbSe)1+δ]m(VSe2)1 (m = 1, 2, 3, 4) 
     heterostructures ..................................................................................................  117 
 
IV.7   Low angle x-ray reflectivity patterns of [(PbSe)1+δ]m(VSe2)1 (m = 1, 2, 3, 4) 
     heterostructures ..................................................................................................  118 
 
IV.8   Grazing incidence in-plane diffraction of self-assembled [(PbSe)1+δ]m(VSe2)1  
     (m = 1, 2, 3, 4) heterostructures .........................................................................  120 
 
IV.9   (a) HAADF-STEM image of the [(PbSe)1+δ]3(VSe2)1 heterostructure showing  
     the film consists of PbSe (bright rows) and VSe2 .............................................  122 
 
IV.10 Results of a Rietveld refinement of the corresponding specular x-ray diffraction  
     of the heterostructure and a comparison of the structural model refined to the 
     HAADF-STEM-derived atomic positions .........................................................  123 
 
 
xxi 
  
Figure Page 
 
 
IV.11 Room temperature Seebeck coefficients and resistivity graphed as a function  
     of the number of PbSe bilayers in the respective compounds ...........................  124 
 
IV.12 (a) Temperature dependence of resistivity and (b) carrier concentrations  
     calculated from Hall coefficients assuming a single band model for 
     [(PbSe)1+δ]m(VSe2)1 (m = 1, 2, 3, 4) heterostructures. Inset of top plot shows  
     a comparison of the CDW transition temperatures for [(PbSe)1+δ]m(VSe2)1 and 
     [(SnSe) 1+δ]m(VSe2)1 compounds .......................................................................  126 
 
IV.13 Calculated (a) resistivity and (b) carrier concentrations for a monolayer of  
     VSe2 using Equation 1 and the data in Figure IV.11. If Equation1 is valid,  
     the resistivity and carrier concentration calculated from each of the compounds 
     should be the same .............................................................................................  128 
 
V.1    The targeted number of atoms per square Angstrom for each element per repeat 
     unit for each of the designed precursors are shown as lines. The circles are the  
     amounts determined using XRF data ................................................................  138 
 
V.2    X-ray reflectivity patterns show that all precursors are smooth and the  
     modulation is retained upon deposition .............................................................  139 
 
V.3    X-ray diffraction patterns of all precursors show two different groups based  
     on the relationship of the high angle peaks with the precursor modulation  
     length .................................................................................................................  140 
 
V.4    The dependence of the precursor modulation length on the number targeted  
     number of PbSe monolayers per RU .................................................................  141 
 
V.5    X-ray reflectivity data collected after annealing the q = 7 precursor at the 
     designated temperatures. The blue dashed lines (---) are the expected peak 
     positions for a [(PbSe)1+d]7(VSe2)1 heterostructure ...........................................  143 
 
V.6    Specular x-ray diffraction data collected after annealing the q = 7 precursor  
     at the designated temperatures. The blue dashed lines (---) are the expected  
     peak positions for  [(PbSe)1+d]7(VSe2)1 .............................................................  144 
 
V.7    In-plane x-ray diffraction pattern of a q = 7 precursor annealed at 300ºC ........  145 
 
V.8    The c-lattice parameters of even and odd samples with q ≥ 7 monolayers as a  
     function of q ......................................................................................................  145 
 
V.9    Representative HAADF-STEM image of an annealed q = 7 precursor ............  147 
 
xxii 
  
Figure Page 
 
 
V.10  X-ray reflectivity data collected after annealing the q = 3 precursor at the 
      designated temperatures. The blue dashed lines (---) are the expected peak  
     positions for a [(PbSe)1+d]3(VSe2)1 heterostructure and the red solid lines are  
     the expected positions for twice the unit cell size of the aforementioned .........  148 
 
V.11  Specular x-ray diffraction data collected after annealing the q = 3 precursor  
     at the designated temperatures. The blue dashed lines (---) are the expected  
     peak positions for a [(PbSe)1+d]3(VSe2)1 heterostructure and the red solid lines  
     are the expected positions for twice the unit cell size of the aforementioned ...  149 
 
V.12  Representative HAADF-STEM image of an annealed q = 3 precursor ............  150 
 
V.13  (a) Specular x-ray diffraction and x-ray reflectivity patterns of the as-deposited 
     (gray) and annealed (black) ‘2141’ precursor (b) HAADF-STEM image of the 
     annealed precursor film .....................................................................................  151 
 
V.14  X-ray reflectivity data collected after annealing the q = 1 precursor at the 
     designated temperatures. The blue dashed lines (---) are the expected peak 
     positions for the calculated modulation length and the red solid lines are the 
     expected positions for a [(PbSe)1+d]2(VSe2)1 heterostructure ............................  152 
 
V.15  Specular x-ray diffraction data collected after annealing the q = 1 precursor  
     at the designated temperatures. The blue dashed lines (---) are the expected  
     peak positions for the calculated modulation length and the red solid lines are  
     the expected positions for a [(PbSe)1+d]2(VSe2)1 heterostructure ......................  153 
 
V.16  Representative HAADF-STEM image of an annealed q = 1 precursor ............  154 
 
V.17  DFT calculated energies and structures of PbSe blocks in vacuum with varying    
     numbers of monolayers (q). Shown above are visual representations of the  
     relative Pb and Se atom positions in the z-axis direction ..................................  156 
 
VI.1  Evolution of Sn|Se|V|Se precursor annealed at different temperature steps. 
    (a) The number of atoms per Å2 of each element measured by XRF at each  
    temperature step and calculated from number of unit cells and a-lattice  
    parameters at RT, 250°C, and 400°C. (b) X-ray reflectivity patterns showing 
    the evolution of the overall film structure (c) Specular x-ray diffraction 
    showing the evolution of the structure perpendicular to the substrate 
    (d) Grazing incidence in-plane x-ray diffraction showing the evolution of 
    the structure in the plane parallel to the substrate. .............................................  166 
 
 
 
xxiii 
  
Figure Page 
 
 
VI.2  (a) Laue oscillations coming from the coherent film thickness at different  
    temperatures. (b) Kiessig (black circles) and Laue (red circles, left axis) 
    film thickness, and the number of unit cells (red circles, right axis) formed 
    at each annealing temperature. The size of the coherent domain in the 
    as deposited sample (filled red circle) is estimated from the line width 
    of the 002 reflection. ...........................................................................................  169 
 
VI.3  Proposed formation and growth mechanism for [(SnSe2)1+d]1(VSe2)1.... ...........  170 
 
VI.4  (a) XRR modelling of the optimized [(SnSe2)1+d]1(VSe2)1 heterostructure.  
    (b) Electron density profile and schematic of the film based on the model. ......  173 
 
VI.5  Rietveld refinement result of the specular x-ray diffraction of  
    [(SnSe2)1+d]1(VSe2)1 and the atomic z-plane model of the average structure. ....  174 
 
VI.6  LeBail fit of the grazing incidence in-plane x-ray diffraction pattern of the  
    optimized [(SnSe2)1+d]1(VSe2)1 heterostructure. .................................................   175 
VI.7  HAADF-STEM image of the  (a) entirety and (b) large section of the film 
    shows that it consists of [(SnSe2)0.80]1(VSe2)1. ...................................................  176 
 
VI.8  EDX elemental analysis of a section of the film showing atomic plane  
    position of the elements. .....................................................................................  177 
 
VI.9  Synthesis of a new SnxV1-xSe2 alloy. (a) Specular x-ray diffraction of  
    a precursor with half the number of required atoms per layer  
    (b) In-plane x-ray diffraction of the tin and vanadium diselenide alloy 
    showing the presence of alloys with two different values of x. .........................  179 
 
VI.10 Schematic of the free energy landscape of tin vanadium 
     selenides ............................................................................................................  180 
A.1    Plot of c-lattice parameter of the [(PbSe)1+δ]m(VSe2)1 heterostructures and m,  
     showing that the lattice parameter increases linearly as a PbSe bilayer is  
     added to the repeat unit. .....................................................................................  187 
 
B.1     In plane x-ray diffraction patterns of the annealed q = 1 and 3 precursors. .....  189 
 
 
 
xxiv 
  
LIST OF TABLES 
 
Table Page 
 
 
II.1     Comparison of the proportionality constants of different elements ..................  82 
 
III.1   The number of Pb and Se atoms in the different PbSe precursors determined by  
     x-ray fluorescence. The target composition to obtain a bilayer of PbSe is: Pb  
     and Se: 0.107 atoms per Å2 ...............................................................................  94 
 
III.2   Lattice parameters calculated from specular x-ray diffraction patterns of PbSe  
     on SiO2. AD = as deposited, AN = annealed .....................................................  94 
 
III.3   The number of V and Se atoms in the different VSe2 precursors determined by  
     x-ray fluorescence. The target composition to obtain a trilayer of VSe2 is:  
     V = 0.103 atoms per Å2 and Se = 0.205 atoms per Å2 .......................................  94 
 
III.4   Structural parameters (c and a lattice constants) calculated from specular and  
     in-plane x-ray diffraction patterns of VSe2 on SiO2. AD = as deposited, AN =  
     annealed 350°C for 30 minutes .........................................................................  96 
 
III.5   The total number of Pb, V, and Se atoms in the different Pb|Se|V|Se precursors 
     determined by x-ray fluorescence .....................................................................  96 
 
III.6   Structural parameters (superlattice d-spacing and a-lattice consants) calculated 
     from specular and in-plane x-ray diffraction patterns of Pb|Se|V|Se precursor 
     annealed at various temperatures. AD = as deposited .......................................  98 
 
III.7   The total number of Pb, V, and Se atoms in the different PbSe precursors on  
     VSe2 determined by x-ray fluorescence. Exact composition ratio of Pb/Se  
     cannot be determine because of the presence of Se in both constituents ..........  100 
 
III.8   Lattice constants calculated from specular x-ray diffraction PbSe on VSe2.  
     AD = as deposited, AN = annealed ...................................................................  101 
 
IV.1   Structural parameters calculated from the x-ray reflectivity and specular x-ray 
     diffraction patterns .............................................................................................  119 
 
IV.2   In-plane lattice parameters derived from the diffraction patterns via LeBail  
     fitting. Misfit lattice parameters were calculated using the lattice parameters  
     and the stoichiometric coefficients of each constituent .....................................  120 
 
VI.1   Number of atoms per unit area determined using XRF compared to target  
     values based on the lattice constants of bulk SnSe2 and VSe2 ..........................  165 
 
xxv 
  
LIST OF TABLES 
 
Table Page 
 
 
VI.2   Thin film layer parameters obtained from XRR modelling (FOM = 0.141) .....  173 
A.1    Rietveld refinement results from GSAS analsysis of the  
     [(PbSe)1+δ]3(VSe2)1 heterostructure  ..................................................................  188 
 
 
 
xxvi 
  
CHAPTER I 
 
SYNTHESIS OF METASTABLE SOLIDS WITH EXTENDED STRUCTURES 
 
Authorship Statement 
 At the time of writing, this chapter has been accepted as a review article to 
ChemPhysChem (DOI 10.1002/cphc.202000199). Dr. David C. Johnson is my advisor and 
group leader, and I am the primary author. 
 
 
I.1. Introduction 
 The number of known inorganic compounds with extended structures is 
dramatically less than the number predicted based on the number of potential systems of n 
elements out of the 86 known stable elements.1 In Figure I.1, the number of known 
compounds, estimated based on databases of known compounds, is plotted versus the 
number expected for each value of n, which was estimated based on the number of possible  
 
Figure I.1. The number of known compounds and possible combinations of the elements 
plotted versus the number of elements in the compound. 
1 
  
elemental combinations. The large difference between them results from the constraints of 
traditional approaches to prepare inorganic compounds with extended structures. There 
have been many proposed compounds predicted to be thermodynamically stable and 
structural homologies suggest many other potential compounds.2–4 The challenge is the 
synthesis of these unknown compounds, as many of these compounds cannot be prepared 
using classical synthesis approaches.5 The synthetic challenge is especially difficult if the 
unknown compounds are metastable with respect to mixtures of known thermodynamically 
stable phases.6 Chemists and material scientists have historically not been able to design 
synthetic routes that avoid thermodynamic traps, limiting the ability to prepare compounds 
with desired structures.7 Indeed the holy grail of solid-state synthesis is a design and 
mechanism based approach to the synthesis of targeted compounds.8   
 The concept of an energy landscape on which a reactant moves as it lowers its free 
energy in the process of eventually forming the thermodynamic product is a useful, but 
underutilized tool to discuss synthetic approaches to metastable compounds.9 An energy 
landscape describes the complex relationship between the stability of different atomic 
configurations as a function of a variety of system parameters such as temperature, 
pressure, and overall composition. The energy landscape provides a framework where the 
relationships between different compounds and the reaction trajectories between them can 
be discussed.10 There are two types of energy minima in energy landscapes, local and 
global free energy minima. There are, of course, many more local free energy minima, 
defined here as a position in the free energy landscape that requires an activation energy 
for the system to move to a different state of lower free energy. Reaction barriers inherent 
in the energy landscape pertinent to the synthesis of inorganic compounds with extended 
2 
  
structures include nucleation energies and the activation energy required for diffusion. This 
is schematically illustrated in Figure I.2, where two different starting points on an energy  
 
 
Figure I.2. Free energy surface with a number of local minima and a global minimum. 
Shown are two different starting points resulting in two different reaction trajectories and 
two different products. 
 
landscape are chosen, resulting in two different reaction pathways. The two starting points, 
while taking different reaction pathways, both lower the free energy as rapidly as possible. 
The system moves into different free energy basins and passes through saddle points in the 
landscape that are associated with reaction barriers.  
 Nucleation is the self-assembly of atoms or molecules to form a new 
thermodynamically more stable phase. The interface between the new phase and the prior 
phase is typically higher in free energy, resulting in an initially higher energy for the new 
phase when it is small in physical size. This increase in free energy for small nuclei creates 
an activation energy for the new phase even though the bulk phase is thermodynamically 
more stable. 
3 
  
 Diffusion is the movement of atoms in a solid, typically driven by concentration 
gradients. It is an activated process, as atoms typically move out of a locally stable bonding 
environment through a less stable bonding state before arriving in another stable bonding 
site. The rate of diffusion typically depends on the concentration of defects, with each 
specific defect having a different activation energy for diffusion.  
 The small number of known compounds shown in Figure I.1 reflects the state of 
the art: researchers have not discovered how to move across the energy landscape in a 
controlled manner. Each local free energy minima is a potential new compound, which is 
kinetically stable but thermodynamically unstable relative to the known compounds in the 
phase diagram. Two key questions for chemists are "Where are the minima?" and "How 
can the metastable compounds at these minima be synthesized?".  
 
I.2. Selective Overview of Solid State Synthesis Techniques 
I.2.1 Direct Solid State Reaction of Elements or Compounds 
 Probably the most common technique to synthesize new solids with extended 
structures is the direct reaction of solid reactants at elevated temperatures, shown 
schematically in Figure 3. These reaction conditions involve a complicated mixture of  
 
 
Figure I.3. Schematic of the reaction of elements to form a ternary compound showing the 
formation of binary compounds before the nucleation of the first ternary phase. 
 
4 
  
atomic configurations as reactants convert to products via heterogeneous intermediate 
mixtures containing elements and binary compounds.11 The reaction rates are typically 
limited by slow solid state diffusion. To increase diffusion rates, high temperatures are 
typically used. Consequently, all phases in the relevant phase diagram can form as reaction 
intermediates. The relative amounts of each compound during the reaction process is 
related to the diffusion rates of the different elements through or around the different phases 
formed. Binary compounds typically form as reaction intermediates on the way to ternary 
compounds. Since products form at the interfaces between reactants, reaction rates slow as 
the thickness of the product layer increases. 
 To obtain reasonable reaction rates in traditional solid state synthesis one needs to 
increase diffusion rates and/or decrease diffusion distances. There are two general 
approaches to increasing diffusion rates. One is to increase temperature, as mentioned 
earlier, because diffusion is an activated process. However, long reaction times are still 
needed due to long diffusion lengths and the need to diffuse through product layers. This 
typically results in the formation of thermodynamic products. A second approach to 
increase diffusion rates is to add a flux so atoms can move through a fluid phase. Adding 
a flux changes the reacting system, sometimes making compounds thermodynamically 
stable that would be metastable without the flux.  Reactions in a fluid phase will be 
discussed more in subsequent paragraphs.  
 There are also several approaches to decrease reaction time by decreasing the 
distance atoms need to diffuse during the reaction. The simplest approach is the physical 
grinding or ball milling of the reacting mixture, before and/or during a sequence of 
annealing steps, to decrease particle size and pulverize the product layers on the outside of 
5 
  
particles. A second approach is to prepare precursor in which the atoms of the desired 
product are already intimately mixed. An example would be preparing an alloy to react 
with a third element rather than reacting the three elements directly. Ideally the atoms in 
the precursor are bound to one another via strong bonding interactions, such that they 
remain bonded during the reaction to form products. With many molecular precursors, 
there is still the challenge of removing atoms present in the precursor but not in the desired 
product. The excess atoms will typically have long range diffusion path lengths to get out 
of the solid as the precursor converts to product. A third approach is to prepare a 
homogenous amorphous phase with a composition that matches that of the targeted 
compound, which will be discussed in section I.3.5. 
 An important aspect of solid state reactions is the choice of starting reactants, which 
will impact reaction times, reaction pathway and the temperatures required for conversion 
of reactants into products. An elegant example of this is the formation of pyrite, FeS2 from 
the reaction between Na2S and FeCl2 explored by Neilson and coworkers.12 Pyrite is 
thermodynamically stable and can be formed directly from the elements via a high 
temperature reaction. Gaseous sulfur reacts with iron to form a surface skin of FeS2 around 
the metallic iron particles. The reaction rate depends on the diffusion of species through 
the surface layer of FeS2, and the reaction must be done carefully to prevent high pressures 
of sulfur vapor at the high reaction temperatures required for diffusion. Neilson and 
coworkers showed that NaFeS2 forms as a reaction intermediate at low temperature (100-
175°C) as Na2S reacts with FeCl2. The thermodynamic products, NaCl and FeS2, form as 
NaFeS2 decomposes at higher temperatures. The temperatures and times required are less 
than needed for the direct reaction of the elements. Attempts to make metastable pyrites 
6 
  
via using this approach as a synthetic pathway were unfortunately unsuccessful. The 
increased use of in situ and operando probes will result in the discovery of many other 
unexpected reaction intermediates in solid state reactions.13 These reaction pathways may 
enable the synthesis of targeted metastable compounds. 
 
I.2.2 Synthesis in a Fluid Phase 
 It is very common in solid state synthesis to use a fluid phase to increase diffusion 
rates and lower reaction temperatures. The fluid phase goes by a variety of different names, 
including a melt, a solvent, a flux, a mineralizer, a eutectic flux or a reactive flux, as 
researchers adjust the fluid phase's composition and resulting properties to hopefully obtain 
desired products. A fluid phase could also be a supercritical fluid by raising the temperature 
and pressure above the critical point, such as in hydro- and solvothermal syntheses. A 
common property of all fluid phases is a much higher diffusion rate than found in solids, 
and potentially further enhanced diffusion rates due to convection effects or active stirring. 
The net result is that these systems can explore large areas of the free energy landscape. 
The rate-limiting step in forming a solid crystalline phase from a fluid phase is typically 
nucleation. Since the compound that will nucleate is one with the lowest activation energy 
for nucleation, what nucleates is not necessarily the thermodynamically most stable phase. 
In contrast to the typical reaction between bulk elements, the fluid phase approach can 
directly form ternary compounds without forming binary compounds as reaction 
intermediates.  
 Phase evolution often occurs in fluid reactions, as initial products react with flux to 
make more stable compounds.14,15 In situ studies have found kinetically stable compounds 
7 
  
that form at short times (Figure I.4), presumably because they are easier to nucleate.16 A 
sequence of nucleation events can occur as more stable compounds nucleate and grow at 
the expense of earlier compounds. During the growth of new phases, the concentration of 
some species in solution drops. This can result in previously formed compounds dissolving 
in the flux. Understanding what factors influence the sequence of nucleation events or the 
time required for the next compound to nucleate from a mixture  
 
FLUX B
A A
B
B
T T  
Figure I.4.  A schematic illustration of the evolution of crystalline phases from a flux 
reaction due to the changes in concentration of different species in solution. The initial 
product (A) is the easiest to nucleate from the flux given the species and their respective 
concentrations. The growth of phase A depletes the concentration of some species in 
solution and the species continue to evolve with time. This can lead to the nucleation and 
growth of a second phase (B), which again depletes the concentration of some species in 
solution.  This can lead to phase A dissolving. This process can continue forming phase T. 
Typically the density of the compounds increase during the reaction, with the density of T 
greater than B, which has a density greater than A. 
 
at a specific temperature is challenging.17 There is unfortunately little understanding of 
speciation in the complex mixtures and solvents used synthetically and hardly any 
knowledge of speciation in fluxes.18 How species evolve in the reaction mixtures is also 
not known. An additional challenge in fluid phase synthesis is that most often there is no 
knowledge of the relative solubility of the various potential products or what the likely 
potential products are. In general, the composition of the system, temperature and time are 
8 
  
the main parameters used to steer reaction towards a desired product. Fast diffusion rates 
mean that the system can explore many configurations as it proceeds towards the 
thermodynamic minimum. The net result is that serendipity plays a large part in what 
compounds form.19 
 
I.2.3. The Experimental Procedure to Discover New Compounds 
 Solid state reaction and fluid phase synthesis approaches are by far the most 
common techniques used to prepare new solid state compounds as they are experimentally 
relatively easy to perform. Additional synthesis approaches, such as “soft” chemistry and 
topochemical approaches, will be discussed in the following section. The products of initial 
reactions in all of these synthetic approaches are typically examined via powder x-ray 
diffraction, looking for "new" reflections that cannot be explained by existing compounds. 
Reaction conditions are then varied to try to increase the intensity of the "new" reflections 
at the expense of "known" reflections, indicating that more of the new product is being 
formed. Since both solid state and fluid phase synthesis approaches suffer from the inability 
to understand how to control the reaction pathway, the changes made in the reacting 
systems depend mainly on experience and intuition. There are typically a limited number 
of experimental parameters that can be varied to either steer the reaction down a particular 
pathway or to change the relative free energies to make a desired product more stable than 
a competing phase. Without the ability to avoid binary compounds as reaction 
intermediates, any multinary compound has to be more stable than a mix of the binary 
compounds to be discovered (see Figure I.3). This is a tremendous limitation on what can 
9 
  
be prepared and probably the underlying reason for the difficulty in preparing new ternary 
and higher order compounds. 
 
I.3. Energy Landscape Description of Synthetic Pathways.  
 The energy landscape concept is a useful platform to compare and contrast different 
solid state synthesis approaches. It is instructive to introduce the energy landscape by using 
it to describe the synthesis of organic compounds. Chemists are used to graphs of energy 
along a reaction coordinate linking reactants to products, which is a line along a particular 
trajectory in the energy landscape. The maxima on an energy versus reaction 
 
 
Figure I.5. The C-H-O ternary phase diagram showing the thermodynamically stable binary 
compounds. A select few ternary compounds are shown on tie lines between binary 
compounds. They are all metastable with respect to a mixture of the binary compounds. 
 
coordinate plot is a saddle point between two adjacent minima on the energy landscape. To 
focus this discussion toward the synthesis of compounds in local free energy minima - 
kinetically stable compounds - Figure I.5 contains a ternary phase diagram for the elements 
10 
  
C, H and O. In addition to the thermodynamically stable compounds (shown as red unfilled 
circles) there are an enormous number of kinetically stable compounds that have been 
made. We show only a couple on tie lines between two stable binary compounds. The 
amount of energy that would be released by the decomposition of the ternary compound to 
a mix of binary compounds is shown underneath the chemical formula. Most, if not all. of 
the ternary compounds in this phase diagram are metastable. A key to chemists preparing 
these metastable compounds has been the development of reaction mechanisms to 
understand the rate limiting steps in product formation and the discovery of different 
reagents and reaction sequences that enable a desired kinetic product to be formed. While 
many of the specifics of these reaction mechanisms are not directly translatable into the 
synthesis of extended solids, the underlying principles are, and the concept of an energy 
landscape is a useful common platform for this comparison. After the synthesis of 
molecules, we will discuss four solid state chemistry approaches to metastable solids in the 
context of energy landscapes, focusing on what makes them work, what limits their more 
general implementation and what key features need to be combined in new synthesis 
approaches. 
 
I.3.1. Molecular Synthesis  
 Organic chemists have developed a number of concepts and tools used to control 
chemical reactions to obtain specific products.20 They have developed "protecting groups" 
that are used to control the reaction pathway by limiting diffusion of reactant molecules to 
the sites blocked by the protecting group.21 We attempt to show this schematically in Figure 
I.6, which shows a probably energy landscape for a system containing two sites that could 
11 
  
a. b.
R R
FG1 FG2 FG1+PG FG2  
Figure I.6. Reaction coordinate diagram for a molecule containing two sites with the same 
functional group. This results in very similar reaction energies for either site (6a). If a 
protecting group is installed at one site, then this favors the reaction at the other site (6b). 
 
react with the same reagent. If they are similar (I.6a), there will be two nearly equivalent 
saddle points in energy, one towards the reaction of each of the groups leading to different 
products. Attaching a protecting group raises the energy of one of the saddle points relative 
to the other one (I.6b), as diffusional access to the reacting bond by reactants is blocked. 
With the protecting group in place, therefore, the majority of the reactant molecules will 
react at the site without the protecting group if the reaction temperature is adjusted to be 
above that required to form the product without the protecting group and below that 
required for the site with the protecting group to react. Chemists have also developed 
catalysts for specific reactions, which lower the activation energy for one reaction while 
leaving other activation energies unaffected. Catalysts and the manipulation of the identity 
and concentration of chemical species in the system permit molecular chemists to favor 
reaction of one functional group over another. Organic chemists have also learned how to 
use concentration to favor inter- versus intra-molecule reactions. These and other 
approaches enable chemists to steer molecular reactions across the energy landscape, 
avoiding unwanted molecules by favoring a particular reaction pathway instead of another. 
The reactions in general preserve most of the structure of the reactants, with changes only 
occurring at specific locations. It is important to note that controlling molecular reactions 
is different than forming an extended structure. Organic chemists, like solid state chemists, 
still cannot control the crystal structure of the product formed.22,23 
12 
  
 A second key to the success of organic chemistry is the ability to predict potential 
free energy minima in the energy landscape via a set of local coordination rules for 
elements: carbon needs four bonds, oxygen two and hydrogen one.24 Given a formula, say 
C4H8O2, undergraduate chemists are expected to be able to use these rules to come up with 
the structures of all of the compounds - isomers of one another - that follow these rules. 
This ability to predict structures of compounds does not exist in extended inorganic 
systems. The reasons include elements in the rest of the periodic table existing in several 
possible oxidation states, being stable in a number of different local coordination 
environments, and having several different possible coordination numbers. This situation 
is even more complex because many  elements can exist in different oxidation states, even 
in the same compound, and extended inorganic compounds can be non-stoichiometric 
and/or have a composition range due to vacancies. As DiSalvo pointed out for intermetallic 
compounds, there are no general rules that predict or make understandable the 
stoichiometries, although ideas by Zintl and others make the composition of subsets of 
these materials reasonable if their structures are examined.25  
 
I.3.2 Synthesis Using a Fluid Phase 
 It is useful to begin our discussion of solid state synthesis with respect to the energy 
landscape by focusing on fluid phase synthesis and how this approach is able to prepare 
metastable compounds. The initial system in fluid phase synthesis typically involves one 
or more solids that dissolve and react in the liquid phase as temperature is raised.26 As the 
concentration of species in solution increase as A and B dissolve, the solution can become 
supersaturated with respect to a solid compound, which will nucleate and grow. This is 
13 
  
shown schematically in Figure I.7. As the solution evolves, the concentration of species 
evolves, potentially forming one or  more complex fluid phase species (for example A2). 
The increases in concentration of these species as a function of time can result in the 
solubility limits for another compound to be exceeded. If this occurs, then a second phase 
will nucleate and grow. As the amount of the second phase increases, the amount of the 
first phase may decrease as it either dissolves as concentrations decrease due to the growth 
of the second phase or is a reactant in the formation of the second phase. The evolution of 
the solution as a function of time, the species formed and the solid compounds that might 
nucleate are typically not known. A hypothetical set of chemical equilibria and the resulting 
concentration changes as a function of time corresponding to the schematic are also shown  
 
Figure I.7. A schematic diagram showing solids A and B dissolving in a flux. The major 
species in solution are A, B and A2. As the concentration of A and B increase, the solution 
becomes supersaturated with respect to solid AB, which then nucleates and grows.  As the 
concentration of A2 increases, decreasing the concentration of A, solid AB begins to 
dissolve. Eventually the solution becomes supersaturated with respect to solid A2B, which 
nucleates. 
 
in Figure I.7. This sequential formation of solid phases, each typically more dense than the 
preceding phase, is known as the Ostwald step rule.27,28  
 Viewing this reaction in the context of an energy landscape (Figure I.8) involves 
the system continuously decreasing its free energy as a function of time as species in the  
14 
  
fluid react to form intermediates and the concentrations of different species in solution 
evolve. The high diffusion rates in the solution allow the system to explore a large fraction 
of the energy landscape in the local basin in which it resides. To form a solid compound, 
the system needs to move though a saddle point in the energy landscape where the saddle 
point is related to the activation energy required to nucleate the solid phase.29 There are 
typically more than one saddle point in any free energy basin with different activation 
energies with respect to the state of the system at each point in time. Each saddle point 
corresponds to a different solid compound that could form. What nucleates first depends 
on the activation energies, which depend on the concentration of different species, the 
solubility constants of the different compounds and the size of the critical nucleus required.  
 
 
Figure I.8. A schematic free energy landscape showing the trajectory of an initial system 
(the star) through the free energy landscape as a function of time. The system initially lands 
in a basin where the saddle point to the crystalline phase AB is the lowest energy path.  
From this basin the system nucleates the compound A2B through the lowest energy 
pathway to a lower free energy state of the system. 
 
The system needs to become supersaturated in order to nucleate a compound. The location 
of the saddle points, the activation energy for the system to exit through the different saddle 
points, and the location of the system in the free energy landscape all change as a function 
15 
  
of time as species and their concentrations evolve and experimental parameters such as 
temperature are varied. 
 A key point is that the first phase to nucleate is the easiest to nucleate, not 
necessarily the thermodynamically most stable compound that could form. In the free 
energy landscape, the first compound typically forms by the system moving through the 
lowest energy saddle point. After the first phase nucleates, the free energy of the system 
decreases as the volume of the first phase to nucleate increases to eliminate the 
supersaturation. This causes the concentrations of other species in solution evolve and 
remaining solid reactants to dissolve. The evolving concentrations may lead to a second 
phase nucleating if the solution becomes supersaturated. As the amount of the second phase 
increases, the concentration of species in solution again evolves. The amount of the first 
phase may decrease as it dissolves in response to the concentration changes or if it is a 
reactant in the formation of the second phase. 
 The major challenge in planning a fluid phase synthesis is that the concentration of 
different species as a function of temperature and time, the solubility constants of the 
different compounds and the effect of adding different species to the system on the 
concentrations of all of the different species are typically not known.30 The structure of the 
products is often unrelated to the structure of the reactants. Structural motifs in the solids 
state structure of reactants may not exist in the solution. It is a complicated problem. The 
ability to change concentrations and add additional species to the solution provide 
experimental parameters that can be used to influence the reaction pathway by changing 
the concentration and species in solution, which will impact the relative energies of the 
saddle points and the free energy minima. This has enabled chemists to prepare compounds 
16 
  
with amazingly complex structures containing elements with a wide range of bond lengths, 
bond angles, and coordination environments. The lack of knowledge about the 
intermediates and relationships between them and potential products, however, has resulted 
in the synthesis of novel solids being described as being "as much an art as a science".25 
 
I.3.3. Synthesis Using Molecular Beam Epitaxy 
 Molecular beam epitaxy (MBE), initially developed by Cho and Arthur at Bell 
Laboratories, is an interesting contrast to synthesis in a fluid phase for the production of 
kinetically stable products.31 Briefly MBE involves bombarding a surface, held at a specific 
temperature, with controlled fluxes of a number of different elements. This is done in a 
high vacuum to prevent contamination and to create long mean free paths for the molecular 
beams. MBE takes advantage of different activation energies for bulk and surface 
diffusion, working in a regime where surface diffusion is possible but bulk diffusion is not. 
Essentially the structure that forms on the surface is buried by subsequent layers and is 
unable to rearrange into a more stable structure because the temperature is too low for bulk 
diffusion to occur. 
 A schematic of a MBE deposition system is shown in Figure I.9. The surface of the 
substrate provides a template for the desired structure, having an epitaxial or near epitaxial 
relationship with the structure being grown. In the energy landscape picture of this 
synthesis method, the structural relationship between the surface and the target phase 
reduces or eliminates the activation energy required to nucleate the targeted compound. 
The temperature of the substrate needs to be high enough that atoms can explore the surface 
to find optimal locations but needs to be low enough to maintain a critical concentration of  
17 
  
 
Figure I.9. A schematic diagram of an MBE growth chamber.  Several deposition sources 
provide fluxes of different elements aimed towards a heated substrate. In-situ analysis tools 
(reflection high-energy electron diffraction and deposition rate monitors) are used to 
control the process. 
 
the most volatile element. The substrate temperature also must be low enough that the 
atoms remain trapped long enough in optimal bonding sites for other atoms being deposited 
to bind to the edges of the growing next layer. The mobility of atoms is significantly 
reduced once additional atoms attach to the edge of the growing layer, and their mobility 
is reduced further as subsequent layers bury them.32 The required reaction conditions to 
nucleate and grow a targeted compound are often very challenging to find.33 A schematic 
of the MBE growth process on a surface is shown in Figure I.10. 
 There are a number of different MBE film growth modes depending on the relative 
flux rates, surface mobility and activation energy required to nucleate the next layer. The 
three major growth modes are island formation (Volmer–Weber34), layer-by-layer growth 
(Frank–van der Merwe35) and simultaneous layer growth and island formation (Stranski– 
18 
  
 
Figure I.10. Schematic of MBE growth, showing arriving atoms, evaporating atoms, a 
growing epitaxial island and atoms moving on the growth surface.  
 
Krastanov36). The rate limiting steps are different in each of these growth modes. In the 
Volmer-Weber growth mode, the interaction between the atoms being deposited is stronger 
than their interaction with the surface, which results in nucleation and vertical growth of 
islands to limit the amount of interface. This results in a rough surface topography of the 
growing film. In the Frank- van der Merwe growth mode, the interaction of the depositing 
atoms with the surface is larger than the interaction with the surface. Hence any island that 
nucleates preferentially grows until the layer is completed. This results in the layer-by- 
layer growth of atomically smooth films. In the Stranski–Krastanov growth mode, the 
interaction energy between the depositing atoms is comparable to the interaction of the 
atoms with the substrate. Hence layer formation competes with nuclei formation. The 
growth mode may change with film thickness, with notable differences between the initial 
layer and subsequent layers.  For example, island growth may dominate the initial 
deposition of A on B, but once B is covered by A there may be a switch to a layer by layer 
growth mode. 
 The energy landscape provides an interesting frame of reference to compare MBE 
experiments with solution synthesis methods used by molecular chemists.  An MBE 
experiment can be tuned to many different locations on the energy landscape by varying 
19 
  
substrates, substrate temperature and atomic fluxes of the different sources. When one is 
in a stable growth mode for a particular compound on a particular substrate, the growth of 
the compound is kinetically favored. The temperature needs to be high enough to permit 
surface diffusion but low enough to prevent bulk diffusion. The interdiffusion of the 
growing film with previously deposited layers, would be a saddle point in the free energy 
landscape at higher temperature, since bulk diffusion has a higher activation energy than 
surface diffusion. Bulk diffusion requires point defects, the existence of dislocations, 
and/or grain boundaries to occur at reasonable rates at lower temperatures. The quality of 
the growing film therefore impacts the upper temperature limit before mixing via bulk 
diffusion occurs. Changing the substrate temperature changes the diffusion rates of atoms 
across the surface and also changes the surface composition as different species have 
different residency times on the surface due to the different temperature dependencies of 
sublimation into the gas phase. A change in surface concentration potentially reduces the 
energy for nucleating a different phase – crossing a different saddle point in the free energy 
diagram. Changes in the ratio of reactant fluxes may be used to maintain growth of the 
target phase. The change in surface temperature and reactant fluxes, however, may result 
in a different growth mechanism as surface diffusion and sublimation rates change.  
 The ability to change the identity of the flux of atoms impinging the surface 
provides a means to jump from one spot on the free energy surface to another. The ability 
to stop the fluxes required to form A and start the fluxes required to form B enables 
researchers to prepare metastable superlattice structures with arbitrary, but controlled 
nanoarchitecture. The ability to toggle sources many times in complex sequences while 
maintaining growth modes is a unique ability of the MBE approach to synthesize complex 
20 
  
nanoarchitectures. Preparing superlattice structures using MBE is challenging and the 
number of systems where it is possible is limited, however, because the proper conditions 
need to be found to achieve the desired growth mode with a common substrate temperature. 
The need for a common, or at least similar substrate growth temperature for the different 
constituents often prevents layer-by-layer growth of both A on B and B on A. The different 
constituents also need to be lattice matched for epitaxy to occur. The ability to toggle 
sources and manipulate growth conditions enables MBE growers to synthesize designed 
structures - the holy grail of solid-state chemistry. 
 The ability of MBE to jump from one spot on the free energy surface to another by 
toggling sources is analogous to adding an additional reactant to a solution reaction to 
transform an intermediate into a desired product. The ability to abruptly remove a reactant 
is analogous to separations (via solubility differences, growth of crystals, etc.)  used in 
multistep solution phase synthesis of molecules to purify an intermediate product. Similar 
addition or subtraction of reagents is key to the topotactic approaches to metastable 
compounds, discussed next, where the product from one reaction is removed from one 
solution and immersed in another.  
 
I.3.4. Synthesis via Topotactic Reactions. 
 Another approach to synthesizing metastable compounds is topotactic (also called 
topochemical) reactions.37 The term “topotactic” refers to reactions in which specific 
motifs within the structure of the reacting solid phase are maintained in the product. These 
reactions are often reversible. Well known example of topotactic reactions include 
intercalation and deintercalation reactions that form the basis of lithium battery 
21 
  
technology.38 The first step of this synthesis approach is the preparation of a precursor (host 
lattice) - typically a thermodynamically stable compound. The precursor usually has a 
strong, covalent, spatially directed bonding network between the elements of the structure 
that are preserved in the topochemical reaction. The structure of the precursor also needs 
an empty system of interconnected lattice sites sharing polyhedral faces, and the lattice 
sites must be large enough for the transport of cations - either into or out of the host lattice 
- at temperatures low enough that the host structure is preserved. For high ionic mobility 
of the species moving into or out of the precursor structure at low temperature, the lattice 
sites along the diffusion path should be of similar energies and the increase in energy of 
the saddle points between the lattice sites along the diffusion path relative to the lattice 
sites should be small. The precursor needs to be able to be oxidized or reduced, and have 
an energetically suitable conduction band for the reversible transport of electrons to the 
redox active element(s). Given this set of constraints, this synthesis approach is obviously 
limited to a small fraction of known compounds that would be suitable precursors.  
 The constraints on a precursor to survive the chemical or electrochemical 
conditions required for a topochemical reaction define a topology for the surrounding 
energy landscape. The cations must have high enough diffusion rates for reasonable 
reaction rates at temperatures low enough to maintain the structural integrity of the 
precursor. The energy landscape therefore has a "basin" containing the precursor and all of 
the possible topochemical products where the structural moiety is preserved. The system 
stays within this "basin" with the addition of reagents or applying the potentials required 
to intercalate or deintercalate the host lattice.  
22 
  
 Intercalation is accomplished by exposing the precursor to high enough 
concentrations of reactive cations - via a reactive organometallic compound, 
electrochemically by applying a potential, or by the direct reaction with an element at low 
temperatures. Deintercalation is typically done electrochemically, by exposing the 
precursor to a solution containing a species that reacts with the cation (an anion such as 
iodide, a cyclic mutidentate ligand such as  crown ether or a polycyclic multidentate ligands 
such as a cryptand), or by gas transport reactions where a product formed with the cation 
can be condensed at the cold end of the reaction vessel (such as a metal iodide). A 
schematic of a system undergoing intercalation/deintercalation  reactions is shown in 
Figure I.11.  
 
 
Figure I.11. Schematic of idealized model of intercalation-deintercalation topochemical 
reactions where the layered moiety is preserved. 
 
 Topotactic reactions can be sequentially used to prepare targeted compounds that 
cannot be prepared in a single step, much in the manner that organic reactions can be 
23 
  
sequentially performed to prepare targeted molecules.39 When reactants are added to the 
precursor, the free energy of the resulting system can be higher than that of the precursor 
alone.  The resulting product can therefore be higher in free energy than the original 
precursor. By separating the product of a first topochemical reaction from the resulting by-
products, it is possible to repeat the process, again forming a compound that is higher in 
free energy than the intermediate product. This is shown schematically in Figure I.12. The 
key to these transformations is that a large fraction of the original structure remains intact 
during the reactions. 
 
Figure I.12. Schematic of a series of sequential topochemical reactions where the addition 
of reactants results in the formation of products that are higher in energy than the precursor. 
 
I.3.5. Synthesis via Amorphous Intermediates. 
 As mentioned earlier in section I.2.1, the reaction of ultra-thin elemental layers - a 
special case of a bulk reaction where diffusion distances are short enough that the system 
interdiffuses before nucleation occurs - can result in the formation of metastable 
compounds. It is instructive to examine the changes in the sequence of phase formation as 
thickness is reduced. In a bulk planar diffusion couple, two elements are placed in contact  
with one another and heated for extended times at an elevated temperature. If the binary 
phase diagram contains compounds,  all of the compounds stable at the annealing 
24 
  
temperature will form at the reacting interface as illustrated in Figure I.13.40 Parallel layers 
of single phase compounds in a sequence dictated by the phase diagram will form, 
assuming that only volume diffusion occurs. Wavy interfaces or precipitate structures are 
thermodynamically forbidden by the phase rule. While the phase diagram dictates what 
compounds will exist, the relative amounts of the different compounds depend on the 
diffusion rates of A and B through the compounds.  
 
Figure I.13. Schematic of a binary diffusion couple of A and B after annealing for sufficient 
time at the temperature of the dashed horizontal line. The phase diagram for A and B is 
shown above the diffusion couple. 
 
 When the elemental layers are decreased in thickness, the reaction pathway 
changes. For thin enough layers, a sequential evolution of phases occurs during annealing 
as the formation of crystalline compounds is alternately limited by diffusion and nucleation 
as shown in Figure I.14.41 This sequence of phase growth in this "thin film regime" results 
from the elemental layers first intermixing at the interfaces forming a composition gradient 
spanning all compositions. As this intermixed region becomes thicker, the rate of change 
of local compositions decreases, enabling nucleation to occur. The compound that 
nucleates first is determined by which phase has the lowest nucleation energy. It has been  
25 
  
 
 
Figure I.14. Schematic of thin film diffusion couples of A and B shown as a function of 
annealing time. The top case is where B is the limiting reagent. The bottom case is where 
A is the limiting reagent. The hypothetical phase diagram for A and B is shown in Figure 
I.13. 
 
suggested that the composition gradient between the elemental layers may develop 
composition plateaus, as all amorphous compositions will not have the same stability nor 
the same diffusion rates for the constituent elements. The formation of these composition 
plateaus may determine which compound nucleates first.42 This first compound grows, 
limited by the diffusion rates of the elements through the compound, until one of the 
elemental reactants is totally consumed. A composition gradient then begins to develop 
between the first compound and the remaining element. Composition plateaus may also 
develop in this second interface region, influencing which compound is the second to 
nucleate. A second compound then nucleates in this second interface. The thickness of the 
second compound will grow at the expense of the amount of the first compound and the 
remaining element till one of them is exhausted. The sequence of compounds that forms is 
determined by the nucleation energies, and the sequence can skip compounds on phase 
diagram that have high nucleation energies. 
26 
  
 If the elemental layer thicknesses are made thinner, a point can usually be reached 
where the system interdiffuses completely before any nucleation occurs at the reacting 
interface, resulting in a homogeneous amorphous intermediate.43 The "critical thickness" 
to avoid interfacial nucleation depends on the relative activation energies for interdiffusion, 
nucleation energies and the rate of change of the composition gradient as a function of 
time.44 The composition of the amorphous intermediate is determined by the relative 
thicknesses of the initial elemental layers. The composition of the amorphous intermediate 
controls what compound nucleates first.45 If a metastable compound has the lowest 
nucleation energy, then it will be the first compound to form.46 If the composition of the 
homogenous amorphous phase matches that of a metastable compound, then the nucleation 
and growth of the metastable compound will be a nearly diffusionless process. A schematic 
of the reaction of ultrathin layers, also called nanolaminates, is shown in Figure I.15. This 
approach has been used to prepare a number of new, metastable binary compounds. 
 
 
Figure I.15. Schematic of an ultra thin film diffusion couple. The system progresses 
through a homogenous amorphous intermediate before nucleation occurs. 
 
 Bene connected the formation of an amorphous intermediate at the interface 
between two reacting elements to the formation of the first phase in thin film diffusion 
couples, suggesting in both cases that the first phase that forms is that which leads to a 
maximum decrease of the Gibbs free energy - dG/dt.47 If the thickness of the elemental 
layers are thin enough and the diffusion rate high enough, then the elemental layers can 
27 
  
completely interdiffuse. Bene also suggested that the reaction rate is proportional to 
diffusion rates, so the rate of decrease of the free energy is related to DΔg where D is the 
diffusion rates and Δg is the change in the Gibbs free energy per atom. Since diffusion rates 
tend to be higher in amorphous phases than bulk diffusion in crystalline phases, the higher 
diffusion rates can compensate for the higher Gibbs free energy of the crystalline phases 
relative to the amorphous intermediate(s).  
 The homogenous amorphous intermediates obtained from the interdiffusion of 
nanolaminates are ideal precursors for the synthesis of compounds with targeted structures, 
such as those that might have been predicted by a theoretical investigation of stability. For 
binary systems, there are several experimental parameters available to control what 
compound nucleates. The most important are the bilayer thickness, which needs to be thin 
enough to avoid interfacial nucleation before the homogenous amorphous intermediate is 
formed, and the composition, which is controlled by the relative thicknesses of the 
elemental layers.46 The processing conditions, time and temperature, and the substrate also 
influence what compound nucleates first. If the desired phase does not nucleate from the 
amorphous intermediate, additional experimental parameters to influence what compound 
nucleates would be useful. One concept that needs to be further explored in the future is 
seeding nucleation with isostructural analogs of the desired compound. 
 When three elements are in the repeating sequence of layers, the order of the layers 
provides another experimental parameter to control the reaction path.48 Binary compounds 
can be avoided as reaction intermediates by using sequences of layers to control what layers 
are adjacent to one another.  For example, suppose the compound AB nucleates at a 
reacting interface even when the layer thicknesses are at an atomic scale. In this case, it is 
28 
  
not possible to prepare an amorphous alloy of A and B by inter diffusing A and B layers. 
In a ternary system, as shown in Figure I.16, the layer sequence ACBC places the element  
 
 
Figure I.16. Schematic of the two different reaction pathways taken by precursors with 
layer sequences ABC and ABCB.  
 
C between the A and B layers. This forces A and B to both intermix with C before they can 
begin to interdiffuse. This can prevent AB from forming before the system forms an 
amorphous ternary intermediate.48 It is more challenging to form a binary compound from 
a ternary amorphous intermediate because it requires disproportionation.   
 
 
Figure I.17. Schematic of the free energy reaction pathway taken by a precursor with thick 
elemental layers of A and B.  
 
29 
  
 It is instructive to examine the evolution of an energy landscape picture of the 
reaction between solids as a function of layer thickness and on the layer sequence of the 
precursor. For thick elemental layers, diffusion and nucleation alternate as the rate-limiting 
step as shown in Figure I.17. The initial layers initially interdiffuse to form a thin 
amorphous region between the elements. The change in local concentration slows with 
time as the concentration gradients decrease. Eventually the movement of a region of 
constant composition is slow enough that there is enough time for an embryonic nucleus 
of a binary compound to grow to the critical nucleus size, resulting in the nucleation and 
rapid growth of the binary compound along the constant composition region along the 
diffusion front. Diffusion of the two elements through the compound to the two growth 
surfaces then becomes the rate limiting step.  New composition gradients become 
established at the growth fronts and the process repeats as nuclei of other binary 
compounds begin to form at the interfaces. 
 
 
Figure I.18. Schematic of the free energy reaction pathway taken by a precursor with thin 
elemental layers of A and B.  
 
30 
  
 For precursors containing thin elemental layers, diffusion and nucleation also 
alternate as the rate-limiting step as shown in Figure I.18, but the growth of the first phase 
to nucleate stops when  one of the elemental layers is exhausted. The rate of free energy 
decrease is then determined by the establishment of the composition gradient at the 
interface between the element and the compound, until the equilibrium solubility is 
reached. This decrease is slower than in the thick film case because there is no more of the 
compound being formed. Nucleation of the next compound to form is the only way for the 
system to further decrease its free energy.  Once the second compound nucleates, it will 
grow until either the first compound to form or the elemental layer is exhausted. The 
process can then repeat if there is another compound in the equilibrium phase diagram that 
can form. Compounds can be skipped in this sequential nucleation and growth process, if 
they have higher nucleation energies. 
 
 
Figure I.19. Schematic of the free energy reaction pathway taken by a precursor of ultrathin 
elemental layers of A and B at a 1 to 2 ratio of the elements. An amorphous intermediate 
is formed from which the metastable compound AB2 nucleates first.  This compound 
decomposes at higher temperatures to form the equilibrium mixture of AB and B.  
 
31 
  
 For ultrathin layers which interdiffuse completely without nucleating  a compound, 
diffusion is the initial rate limiting step. The amorphous solid that forms at low enough 
temperatures is kinetically stable and hence is a local free energy minimum in the energy 
landscape. The crystalline solid that is easiest to nucleate will form first from this 
amorphous alloy. The pathways to potential compounds that could nucleate from the 
amorphous allow are saddle points connecting the minimum of the amorphous alloy to 
other minima containing potential crystalline products. The difference in energies between 
the amorphous alloy and the saddle points are directly related to the activation energy for 
nucleation of the different compounds. This is illustrated schematically in Figure I.19. The 
transformation of the amorphous solid to a crystalline compound does not require long 
range diffusion if the composition of the amorphous solid matches that of the compound. 
Only local rearrangements to form nuclei with the structure of the targeted compound are 
required, which explains why composition is a powerful tool to control what forms.49–51 
This constant composition transformation is shown schematically in Figure I.19 as the 
lowest energy saddle point. The transformation of the intermediate to a mixture of two 
compounds with different compositions is not kinetically favored at low temperatures 
because it requires a local disproportionation that is a large enough fluctuation to form 
critical nuclei of at least one of the compounds in the more stable mixture. This 
disproportionation is also unfavorable with respect to the associated decrease in entropy 
from the unmixing of the amorphous alloy. 
 Since amorphous alloys yield only the easiest solid to nucleate at each composition, 
they have been a very useful reaction intermediate to form metastable crystalline solids. 
Unfortunately, there are no methods currently known to control the nucleation event to 
32 
  
form a specific structure. New approaches to control nucleation need to be developed to 
form different polymorphs at the same composition. Pressure or substrate structure are 
experimental parameters that could be used to control what forms, by altering the relative 
nucleation energies of competing compounds. Creating thin regions with a composition 
that nucleate a known structure might seed the growth of adjacent layers with compositions 
that do not nucleate this structure. There is much to be explored. The inability to predict 
what nucleates first results in a familiar serendipity concerning what compounds are 
actually prepared. 
 
 
I.4. Predicting Undiscovered Compounds 
 A challenge for all of the experimental approaches to metastable compounds with 
extended structure is predicting what compounds might be possible local free energy 
minima in a quantitative way. The simple local coordination rules that enable organic 
chemists to predict the structure and composition of plausible compounds does not exist 
for extended inorganic solids. Synthesizing compounds with specific properties is even 
more challenging. In the last decade, the search for new, potentially stable compounds 
using high-throughput machinery has emerged as a rapidly evolving field of materials 
science.3,4 The basic idea of this new field is straight forward - create and then examine a 
database containing calculated and experimental thermodynamic and electronic properties 
of existing and potentially yet to be discovered compounds to find materials with specific 
properties. The most common theoretical approach to predict undiscovered materials is to 
calculate the energy of known compounds, enabling the energy of mixtures to be 
33 
  
calculated. The formation energies of undiscovered compounds are then calculated, usually 
by starting with placing atoms into a known structure type and allowing the system to relax 
to a minimum in the calculated energy. If the energy of the compound is lower or close to 
the energy of a mixture of known compounds with the same composition, then the 
compound is reported as a potentially stable compound. This is shown schematically in 
Figure I.20. A large number of synthetic targets can now be found in these computational 
repositories.4,52–55 For this high throughput machinery to be ultimately useful, however,  
the properties of the existing and proposed materials must be predicted correctly and 
researchers need to be able to synthesize the proposed undiscovered compounds. 
 
 
Figure I.20. Schematic of a free energy diagram in a binary system of elements showing 
the energy of thermodynamically stable compounds, with lines showing the energy of 
physical mixtures of adjacent compounds.  If the free energy of a compound is above this 
line, it is thermodynamically unstable with respect to disproportionation.  If below the line, 
it is thermodynamically stable 
 
 
 The limited number of new compounds made relative to the number of synthetic 
targets predicted, highlights the challenges in choosing the correct functionals to accurately 
calculate stability using density functional theory and the limitations of traditional synthetic 
approaches. A common result of experimentalists trying to prepare unknown compounds 
predicted to be thermodynamically stable are reaction products that consist of mixtures of 
34 
  
known compounds as expected from existing phase diagrams.5 While some of the reason 
undoubtedly lies on assumptions implicit in the predictions, a significant factor is the 
inability to control reaction pathways to avoid known thermodynamically stable 
compounds. If the predicted compounds are metastable, the traditional high temperature 
reaction of the elements will result in a mixture of binary compounds as they form first in 
the reaction. 
 An alternative approach to theoretically predicting compounds that might be stable 
is to use structural homologies to predict compounds that might be local free energy 
minima. The rules in organic chemistry to predict the structure of compounds are simple 
and based on the local coordination of atoms which needs to be maintained as atoms are 
used as building blocks to create molecules. For example, potential synthetic targets need 
to have all carbon atoms making 4 bonds, oxygen two bonds and hydrogen one. In extended 
inorganic systems, the situation is more complicated as even the same element can assume 
different coordination environments in the same compound based on stoichiometry and the 
chemical nature of neighboring elements. To predict potential undiscovered compounds, 
researchers can identify structural building blocks in a compound and then create new 
compounds by either assembling them in different arrangements or extending them in one 
or more dimensions. The compounds created by extending the size or number of structural 
units are called a homologous family of compounds. A simple example of a homologous 
family of compounds is shown in Figure I.21.  The simplest compound in this family is 
[(PbSe)1.14]1(NbSe2)1, referred to as (PbSe)1(NbSe2)1 or simply as the 1:1 compound of this 
family. It contains a bilayer of a distorted rock salt structured PbSe alternating with a NbSe2 
trilayer with an octahedral transition metal dichalcogenide structure. In addition to the 1:1  
35 
  
 
Figure I.21. Schematic of a free energy diagram in a binary system of compounds showing 
the energy of thermodynamically stable compounds, with lines showing the energy of 
physical mixtures of adjacent compounds.  If the free energy of a compound is above this 
line, it is thermodynamically unstable with respect to disproportionation.  If below the line, 
it is thermodynamically stable.  
 
compound, the 1:2 and 1:3 compounds, containing one, two and three NbSe2 layers 
alternating with a PbSe bilayer are thermodynamically stable ternary compounds and have 
been prepared by directly reacting the elements. The remaining members of this family are 
metastable, and cannot be prepared using traditional approaches. Quite a few members of 
this family of compounds have been prepared using modulated elemental reactants as 
described later in this review. More complicated homologous series are known as described 
in an excellent article by Kanatzidis.2 
 
 
36 
  
I.5. Modulated Elemental Reactants – An Approach to Control Reaction Pathway using 
Designed Precursors. 
 For the remainder of this chapter we focus on synthesis using solid amorphous or 
mostly amorphous mixtures containing just the elements required for the structure that 
forms as reaction intermediates, as they are perhaps the simplest and most general reaction 
system of the four approaches discussed previously. In these neat systems, there is no 
solvent or flux that remains after an extended structure nucleates and grows from the 
amorphous solid. Indeed, if the homogenous amorphous solid has a composition that 
matches the stoichiometry of the nucleating compound, there can be 100% conversion of 
the precursor into the final crystalline product via a near diffusionless process.56  In the 
self-assembly process only short range diffusion is necessary, making nucleation the rate 
limiting step in the formation of a crystalline product. 
 Amorphous solids can be formed with most of the periodic table over a wide variety 
of compositions using a variety of approaches. In the early 1980's, W. Johnson's group 
discovered a way to form amorphous alloys at low temperatures from crystalline foils. 
They showed that amorphous metals are formed by the spontaneous mixing of crystalline 
metal foils driven by a large ΔH of mixing.43 Annealing the amorphous alloys formed by 
the mixing at higher temperatures nucleated crystalline compounds. Novet and coworkers 
extended this work, showing that this approach for forming amorphous alloys at low 
temperatures works in a wide variety of systems if the thickness of the reacting layers is 
below a critical thickness. They also showed that the composition of the amorphous 
intermediate can control which compound nucleates first. Another key result of Novet's 
work was demonstrating the nucleation of a compound from an amorphous intermediate 
37 
  
under conditions where it is thermodynamically metastable.45 They showed that the 
activation energy to nucleate a metastable phase from an amorphous intermediate with a 
composition corresponding to the stoichiometry of the compound can be lower than that 
required to disproportionate and nucleate a thermodynamically more stable mixture of two 
compounds. Figure I.22 shows a schematic energy landscape picture of the reaction 
pathway of a precursor designed to form Fe5Si3 at temperatures where it is metastable. 
 
 
Figure I.22. Schematic of the free energy reaction pathway taken by a precursor designed 
to form Fe3Si5. 
 
 Several research groups followed up on these initial studies, demonstrating the 
utility in using homogeneous amorphous solids as versatile intermediates in synthesis. D. 
Johnson's group prepared a number of metastable binary and ternary antimonide 
compounds with the skutterudite structure by controlling the composition of amorphous 
intermediates.46 Subsequent studies showed that the nucleation energies of compounds 
depended on the composition, and it was necessary to find the range of compositions in 
which the desired compound had the lowest nucleation energy with respect to competing 
compounds.50  Adding a third element to a binary amorphous solid resulted in an increase 
38 
  
in the nucleation energy of the binary compounds.51,57 Jansen's group directly prepared 
amorphous intermediates by co-evaporation onto a cooled substrate. They showed that 
metastable halides could be kinetically trapped as the temperature of the intermediates was 
increased. These studies showed the importance of controlling substrate temperature 
during the evaporation, especially when one of the elements being deposited has a high 
vapor pressure or high surface mobility during the deposition.57 Bensch's group used 
amorphous intemediates to prepare a number of new binary compounds and showed via 
temperature dependent operando diffraction experiments that this is a consequence of 
avoiding more stable compounds.58 Bensch's group also attacked the significant challenge 
of determining the structure of new compounds formed as films using a variety of 
diffraction techniques. A key recent advance in this area is the use of electron microscopy 
techniques to create models for subsequent refinement of x-ray diffraction data.59 
 With several groups demonstrating the ability to prepare new binary compounds 
and metastable polymorphs of known compounds, the fundamental basis of controlling the 
composition of an amorphous intermediate to prepare new compounds seems established. 
The time and activation energy required to nucleate a compound of similar composition 
via a diffusionless transformation is less than the time and activation energy required to 
disproportionate the precursor and nucleate a more stable compound. While the main 
experimental parameter explored in these initial studies to control which compound 
nucleated was the average composition, other parameters, for example pressure, could 
provide additional experimental tools to control what nucleates first. Pressure would 
change the relative saddle point energies of the different potential nucleation events, 
39 
  
permitting compounds to nucleate that are different than the one that forms at one 
atmosphere of pressure. 
 The energy minimum in the free energy landscape for the amorphous phase has 
been proposed to be a useful guide to determine if predicted compounds can be made.60,61 
Compounds that are higher in free energy than the amorphous intermediate will be unstable 
with respect to forming an amorphous structure at the same composition. Therefore, they 
cannot nucleate from the amorphous phase, as this would increase the free energy of the 
system. Compounds that are lower in free energy than the amorphous phase can potentially 
be formed by manipulating experimental conditions so that the saddle point leading to them 
in the energy landscape is the lowest available to the amorphous phase. Amorphous 
intermediates that have compositions that match the stoichiometry of targeted compounds 
are perhaps the best initial approach to prepare the many compounds predicted to be stable 
via theory. An example of this is the free energy diagram in Figure I.23 for the Fe-Sb  
 
 
Figure I.23. The Fe-Sb phase diagram with the metastable compound FeSb3 shown in red. 
FeSb3 decomposes exothermically to a mixture of FeSb2 and Sb.  
 
40 
  
system. The binary compound FeSb3 is thermodynamically less stable than a mixture of 
FeSb2 and Sb. FeSb3 is, however, more stable than an amorphous solid with a one to three 
ratio of Fe to Sb.46 Hence it can be formed by controlling annealing conditions. 
 
I.5.1. More Complex Precursors - Composition Modulation 
 A challenging issue in utilizing designed precursors is finding synthetic targets 
where there are experimental parameters besides the composition of the amorphous 
intermediate that can be used to control the synthetic pathway to compounds with targeted 
structures. Homologous compounds are logical first synthetic targets. A family of 
homologous compounds all contain the same fundamental structural units, or building 
blocks.2,62 The compounds within the family differ from one another by the size and/or 
stacking sequence of the different building blocks. The structural relationship between the 
different building blocks is maintained within the family of homologous compounds.  
 Layered homologous compounds are ideal synthetic targets for the modulated 
elemental reactants (MER) synthesis approach. Consider two building blocks, A and B, 
that both represent the thinnest two-dimensional layer of two different structures that 
maintains the essence of each structure. Conceptually these blocks can be stacked in an 
infinite number of layer sequences where the thickness and/or stacking sequence is varied. 
The thinnest layer sequence would contain two layers, AB.  There are two sequences with 
three layers, AAB and ABB. There are three sequences with four layers ABBB, AABB, 
and AAAB. There are six different sequences with five layers {ABBBB, AABBB, 
ABBAB, AAABB, AABAB, and AAAAB} and eight different sequences with 6 layers 
{ABBBBB, AABBBB, ABABBB, AAABBB, ABAABB, AAAABB, AAABAB, and 
41 
  
AAAAAB}. The number of sequences increases very rapidly above this point, with sixteen 
different sequences with seven layers, twenty four different sequences with eight layers, 
and forty two different sequences with 9 layers. Keeping the total number of layers less 
than 20, there are over 60,000 possible sequences with just two building blocks, and the 
number of possible sequences increases rapidly as the number of constituents increases as 
shown in Figure I.24.63 In a homologous family with three building blocks, there are over  
 
 
Figure I.24. The increase in the number of possible homologous compounds as the number 
of layers in the unit cell is increased. The increase is much greater as the number of distinct 
constituent layers increases. 
 
130 million possible sequences with a total number of layers less than 20. In a homologous 
family with four building blocks, there are over 35 billion possible sequences with a total 
number of layers less than 20. The number of potential new compounds generated by 
homologous relationships is staggering. The challenge is developing synthetic strategies 
that are able to selectively prepare specific sequences of layers. 
 The misfit layer compounds are thermodynamically stable examples of compounds 
that have the desired layered motif.64 The misfit layer compounds contain alternating layers 
42 
  
of a dichalcogenide structured and a rock salt structured constituent. The misfit layer 
compounds are unusual due to an incommensurate relationship between their constituent 
layers, resulting in a non-integer stoichiometry (MX)1+y(TX2)1. The magnitude of y reflects 
the difference in the atom density of the two formula units in their common plane. It takes 
1+y units of MX to cover the same area as 1 unit of TX2 for the respective planes that are 
parallel to the interface between them. Thermodynamically stable misfit layer compounds 
are known with M = Sn, Pb, Bi, Sb and rare earth metals, X = S and Se, and T = Ti, V, Cr, 
Nb and Ta.64 Many more sulfides are known than selenides. Most of the misfit layer 
compounds contain a single layer of both the rock salt constituent and the dichalcogenide. 
There are a few examples of compounds containing a single rock salt layer and two or three 
layer thick dichalcogenide layers that are prepared by changing the composition of the 
initial reactant mixture. The rock salt layer thickness is almost always a single bilayer thick. 
Since these compounds are stable at the high temperature synthesis temperatures, it 
suggests that the interaction between layers must be stronger than the interaction between 
the same structural units in the respective binary compounds. If one tries to make the MX 
layer thicker by changing the composition of the initial reaction mixture, one obtains a 
mixture of (MX)1+y(TX2)1 and MX rather than [(MX)1+y]m(TX2)1 where m is an integer 
greater than one.  
 Layered homologous compounds related to known misfit layer compounds are a 
natural synthetic target using MER. The strong interaction between the rock salt layer and 
dichalcogenide is responsible for the thermodynamic stability of the known misfit layer 
compounds relative to mixtures of the binary compounds. This strong interaction should 
help stabilize homologs of the known (MX)1+y(TX2)1 compounds. One can adjust the 
43 
  
deposition conditions when preparing MER precursors so that there are the correct number 
of atoms in an M|X bilayer to form a single structural unit of MX and, likewise, a T|X 
bilayer can be deposited with the required number of atoms to form a single structural layer 
of TX2. If an initial sequence of layers M|X|T|X is used as the repeating structure of a 
precursor, a layered heterostructure (MX)1+y(TX2)1 can form in a nearly diffusionless 
process. This will make this compound the kinetically favored product if diffusion is 
limited. The known misfit layer compounds will be more stable than two amorphous layers 
as the M-X and T-X bonding will be maximized in forming MX and TX2 layers. The other 
two possibilities are the M|X|T|X repeat can completely interdiffuse to form an amorphous 
M-T-X alloy intermediate or the M|X|T|X precursor can disproportionate into macroscopic 
domains of MX and TX2. In the case of known misfit layer compounds, both of these 
possibilities will be higher in energy than the (MX)1+y(TX2)1 misfit layer compound. A 
precursor with repeating M|X|M|X|T|X elemental layers will be kinetically favored to form 
[(MX)1+y]2(TX2)1, because the M|X|M|X|T|X precursor structure provides very similar 
initial composition profiles to [(MX)1+y]2(TX2)1, enabling a near diffusionless 
transformation. While annealing may result in changing concentration gradients during 
annealing before nucleation occurs due to the thicker M|X region, it is reasonable to expect 
local compositions to control what nucleates. Indeed, this approach works, producing 
heterostructures with amazing fidelity due to the large stability difference between the 
precursor and the targeted heterostructures.65–67 Appropriately designed precursors have 
enabled the synthesis of compounds with specific sequences of layers as shown in Figure 
I.25.68 This approach enables the synthesis of extensive families of homologous 
compounds, because the criteria for formation is to be more stable than the precursor. This  
44 
  
 
Figure I.25. HAADF-STEM images of structural isomers containing four bilayers of PbSe 
and four TiSe2 trilayers. The notation on the bottom of the images provides the number of 
PbSe bilayers in bold and the number of TiSe2 layers in normal font. The sequence of 
numbers matches the sequence of layers in each isomer. 
 
differs from traditional synthetic techniques, where the uncontrolled formation of 
intermediates requires products to be more stable than any mixture of thermodynamically 
stable compounds and the elements.  
 Families of compounds of rock salt structured constituents alternating with 
transition metal dichalcogenide blocks have also been prepared using designed precursors 
where no family members were previously reported via direct reaction of the elements. Of 
the Group 6 metals (Cr, Mo or W), only Cr containing misfits have been reported to form 
as thermodynamically stable misfit compounds and only with trivalent cations.69,70 Lin et 
al reported the synthesis of over a hundred new compounds in the [(PbSe)0.99]m(WSe2)n 
homologous family.71 Heideman et al reported the synthesis of analogous family of 
homologous compounds, [(PbSe)1.00]m(MoSe2)n.72 Beekman et al reported the synthesis 
from designed precursors of a homologous family of [(SnSe)1.04]m(MoSe2)n compounds, 
where  0 < m, n < 32.73 There have been no reports of additional [(MSe)1.23]m[CrSe2]n 
compounds, but to our knowledge the use of designed precursors to prepare them has yet 
45 
  
to be attempted. The first reported telluride misfit layer compounds containing rock salt 
structured PbTe with a layered TiTe2 were also prepared using modulated elemental 
reactants.74 Other examples are expected with different dichalcogenides or rock satl 
structures, as there are many potential rock salt structured compounds that have yet to be 
explored using designed precursors. More complicated sequences have also been created 
with two different dichalcogenides and a rock salt structured layer in ordered 
sequences.63,75 Specific layers within layering sequences have also been alloyed, with the 
nanoarchitecture of the precursor preserved as it self assembles into the desired 
compound.59,76–78 There appears to be an unlimited number of combinations that can be 
prepared. 
 Designed precursors have also enabled synthesis of new layered solids with a wide 
variety of constituents having different structures than the rock salt structure and transition 
metal dichalcogenides found in misfit layer compounds. New families of homologous 
compounds have been prepared by layering two different dichalcogenides, including  
 
 
Figure I.26. The different layered constituents that can be used as building blocks to 
prepare heterostructures via designed precursors.  
 
46 
  
SnSe2.79–84 New families of homologous compounds (shown in Figure I.26) have been 
prepared with transition metal dichalcogenide layers alternating with layers of Bi2Se3 and 
Bi2Te3,85,86 GeSe2,87 and V3Se4.88 These metastable compounds are prepared using 
precursors as described for misfit layer homologs discussed previously. Key to the 
synthesis is preparing the precursors such that each elemental bilayer contains the 
appropriate number of atoms to form a structural unit of the desired constituent. Gently 
heating the precursor caused the individual layers to nucleate the desired structures through 
a near diffusionless reaction which maintains the nanoarchitecture of the precursor. 
 Designed precursors also permit the formation of compounds containing three or 
more different constituents and the different constituents can each have a different 
structure. An example of a heterostructure containing 3 different structures is 
(BiSe)1+δ(Bi2Se3)1+γ(BiSe)1+δ(TiSe2)1,89 while an example of a heterostructure containing 
three different compounds is [(PbSe)1+δ]m(TiSe2)n[(SnSe2)1+γ]m(TiSe2)n.63 As mentioned 
earlier, this greatly expands the number of potential compounds that can be prepared. All 
of the compounds in a family of homologous compounds containing two constituents fall 
on the compositional tie line between the two compounds as shown schematically in the 
phase diagram in Figure I.27. In a family of homologous compounds containing three 
constituents, the compounds fall in an area bounded by the 3 tie lines between the three 
constituents, also represented in the phase diagram in Figure I.28 for a case where two of 
the structures contain the same elements but have different stoichiometries. In a family of 
homologous compounds containing four constituents, the compounds are in a volume 
bounded by the areas of the four combinations of three constituents Figure I.29. 
 
47 
  
 
Figure I.27. The ternary phase diagram of Pb-V-Se. The three elements do not have a 
ternary thermodynamically stable compound. However, using designed precursors, 
metastable heterostructures containing PbSe and VSe2 have been made and are contained 
as red circles in the ternary phase diagrams. For two constituent heterostructures, the 
metastable heterostructures lie on the tie line (black line) connecting the two building 
blocks. 
 
 
 
 
 
Figure I.28. The ternary phase diagram of Bi-Ti-Se. A three-component heterostructure 
containing BiSe, Bi2Se3, and TiSe2 will be contained in an area enclosed by the tie lines 
connecting Bi2Se3 and TiSe2, and BiSe and TiSe2. Shown as a red circile in that area is 
metastable three-component heterostructure (BiSe)1+δ(Bi2Se3)1+γ(BiSe)1+δ(TiSe2)1, first 
synthesized by Lygo et al. via MER.89  
48 
  
 
Figure I.29. The quaternary phase diagram of Pb-Sn-Ti-Se. Each phase in the tetrahedron 
represents a ternary phase diagram containing 3 elements. The three-component 
heterostructure is contained in the area defined by the tie lines connecting the three 
components in three different ternary phase diagram.  
 
 Both the shortfall in the number of ternary compounds and the inability to prepare 
a significant fraction of compounds predicted to be stable result from the inability of 
materials scientists, solid state chemists and physicists to control the reaction pathway to 
obtain specific kinetically stable products. Developing approaches to control reaction 
intermediates is one of the keys to enabling the synthesis of targeted and other yet to be 
prepared solids.  
 
I.5.2 Ideas Concerning the Reaction Mechanism of the Self-Assembly of Precursors into 
Products 
 While many compounds have been prepared via designed precursors, why this 
approach works is not really understood. The simplest mechanism presented to date is 
schematically shown in Figure I.30. Consider a precursor containing a chosen sequence of 
 
49 
  
 
Figure I.30. A schematic representation of the a|x and b|x bilayers interdifusing to form 
amorphous layers of a-x and b-x before nucleation and growth of crystalline A and B layers 
(top). The density of the nucleation sites determines the laterial grain sizes and the random 
orientation of the different nucleation sites results in the turbostratic disorder found in the 
self-assembled product. 
 
elemental a|x and b|x bilayers, each with the number of atoms per unit area required to form 
a single structural unit of the targeted constituents. If the thicknesses of the elemental 
bilayers are lower than the critical thickness for the binary a-x and b-x systems at the 
targeted compositions, the bilayers are expected to interdiffuse on annealing to form an 
amorphous intermediate. At low temperatures and short times, the composition modulation 
of a and b will be maintained if a-x and b-x interdiffuse faster than a into b-x or b into a-x. 
Nucleation of the target compounds AX and BX must occur before the composition 
modulation diffuses away in order for the final product to maintain the nanoarchitecture of 
the precursor.  
 The nucleation rates of A and B along with the order of nucleation play important 
roles as revealed by the microstructure of final products. In all of the compounds prepared 
to date using an elementally modulated precursor, the same common plane is found at all 
the interfaces between two constituents. This suggests that one constituent nucleates first 
50 
  
and grows with a preferred orientation, perhaps partially as a result of the anisotropic, 
layered morphology of the compositionally modulated amorphous a|x|b|x precursor. In 
almost all of the compounds prepared to date, there is extensive rotational disorder between 
the constituent layers.90 This turbostratic disorder, as it is called in the clay literature, may 
be a consequence of multiple nucleation sites in each ax and bx layer, with subsequent 
lateral growth resulting in a random mosaic of different relative orientations of the two 
compounds. The observed disorder suggests that there is not a strong preferred, rotational 
orientation for heterogeneous nucleation of A on B or B on A. The lateral grain size of the 
constituents A and B tend to be less than 100 nm, suggesting that there are many nucleation 
sites. Presumably the extensive nucleation sites result from the high extent of 
supersaturation of the layers in the precursor, leading to a low activation energy for 
nucleation. Finally, the final structures have long coherence lengths perpendicular to the 
substrate, remarkably consistent layers in STEM images with structurally abrupt interfaces, 
and high carrier mobility that suggests a low concentration of defects that scatter the 
carriers.71,91 Since the precursors have larger variations in local composition and layer 
thicknesses than the final products, lateral and/or vertical diffusion must occur during 
growth to average out local variation. 
 The proposed reaction mechanism involves both nucleation and diffusion, both of 
which are challenging to control. Nucleation can be controlled by the absolute composition 
and thickness of the sequences of layers in the elemental precursors. Very thin a|x and b|x 
bilayers results in very large local super saturation in the as deposited precursor if the 
compositions are close to that of a known binary compound. The thin elemental layers 
typically interdiffuse extensively during the deposition process or at low temperatures. The 
51 
  
extent of lateral diffusion across the surface of the precursor during deposition can be 
considerable, even for nominally room temperature substrates with deposition via 
evaporation. The large surface area of the different elemental bilayers in the precursor, 
which have relatively constant composition, results in many potential nucleation sites 
either during the deposition process or during annealing at low temperatures. A key 
question in this simplified mechanism is why the same crystalline surfaces are parallel to 
the interface between constituents. Atkins proposed that an initial nucleation event results 
in subsequent heterogeneous templated nucleation off of the first formed crystalline region 
by adjacent layers.92 He tested this hypothesis by looking at the structure of binary 
dichalcogenides formed from layered a|x precursors, and found that ordered crystals 
formed if the dichalcogenide only existed as a 1T polytype and disordered layers formed 
if the dichalcogenide existed as a multilayer polytype, for example 2H, because of the 
choice of different orientations for the next layer (see Figure I.31). Additional studies on 
MoSe2 were consistent with this proposed mechanism. MoSe2 forms a disordered 
polymorph from Mo|Se precursors and exists as a 2H polymorph in the bulk.56 When there 
are two different constituents that are not structurally related, the orientation of the template 
nucleation of the second phase to crystalize is expected to be random.84  
 A large number of compounds homologous to misfit layer compounds have been 
investigated using HAADF-STEM, providing a considerable library of images to explore 
the proposed mechanism of Atkins. In heterostructures containing only one layer of each 
constituent, turbostratic disorder is observed between all MSe layers and TSe2 layers.93 If 
the rock salt layers contain multiple bilayers, the entire layer within a grain usually has the 
same crystallographic orientation. This suggests that 3 dimensional growth occurs from a  
52 
  
 
Figure I.31. Differences in structure between crystalline and ferecrystalline phases from 
HAADF-STEM. Crystalline VSe2 have the same orientation across several layers. 
Ferecrystalline TaSe2 exhibits multiple zone axes across multiple layers. The 
ferecrystalline heterostructure [(PbSe)1+d]1(VSe2)1 exhibits different zone axes across 
adjacent repeat units.  
 
nucleation site, although the rate of growth might be different along and perpendicular to 
the substrate. If the dichalcogenide layer contains multiple TSe2 layers, it follows the 
Atkins model. Moderately thick TiSe2 and VSe2 layers (2 – 6 layers) typically have the 
same orientation for each TSe2 layer.  For TaSe2, NbSe2, WSe2 and MoSe2, the different 
TSe2 units within a layer have different orientations, even in bilayers.66,90,94 In special 
cases, where there is an accidental epitaxial relationship between the two constituents, 
preferred orientations over multiple unit cells can be observed, consistent with 
heterogeneous nucleation of subsequent layers off of an initially nucleated layer.95 Figure 
I.32 shows different STEM images illustrating the variety of behaviors observed depending 
on the identity of the constituents. Adjacent rock salt bilayers form with the same 
orientation as observed in [(PbSe)1+d]2(WSe2) in Figure I.32a. Dichalcogenides that have 
only one polytype in the bulk, like TiSe2 and VSe2 have a single orientation when multiple 
layers are present in a repeating unit in the heterostructure. Dichalcogenides with multiple 
53 
  
polytypes in the bulk like NbSe2 and MoSe2 can have multiple orientations. These 
observations are consistent with Atkin's suggestion of heterogenous nucleation. 
 
 
Figure I.32. The structural coherence of between planes of atoms in different 
crystallographic layers depends on their crystal structure and the structure of the layers 
adjacent to them. In (a), the adjacent rock salt structured bilayers of PbSe have the same 
crystallographic orientation. In (b) the adjacent layers of VSe2, TISe2 and NbSe2 with the 
same block have the same crystallographic alignment while the alignment of the MoSe2 
layers in the same block are different. 
 
 Controlling the extent and rate of diffusion in the deposition of the precursor and 
during the annealing process is also challenging. Diffusion is driven by the free energy 
decrease associated with the enthalpy and entropy changes during the mixing of the 
elemental layers. The rate of diffusion also depends on the concentration and type of 
defects that are present in the layers. An as deposited precursor is typically amorphous with 
a density that is 5 to 10 % less dense than expected if the layers were crystalline elements. 
As temperature is increased, defects that are mobile enable the elemental layers to mix and 
there is a concomitant increase in the density as the mobile defect is eliminated. When 
temperature is increased, new defects become mobile leading to a jump in the diffusion 
rate.96 If one or more of the other elements in the precursor are not miscible in a binary 
compound that has nucleated, the growth of the binary compound will drive a 
disproportionation as the immiscible elements are excluded. Conversely, the nucleation of 
54 
  
a thermodynamically stable ternary compound can drive interdiffusion and mixing of 
layers in the precursor. 
 Two experimental parameters in the design of a precursor that can be used to 
modify the interdiffusion of layers in a precursor are the thickness of the elemental layers 
and the sequence of elemental layers. The rate of mixing of elemental layers depends on 
the thickness of the elemental layers in the precursor, with thicker layers taking longer to 
interdiffuse as concentration gradients are more gradual and the distance between the 
elemental layers increase as the interdiffused region becomes thicker.81 For example, if one 
compares the relative rates of mixing of the elemental layers two precursors, a|x|a|x|a|x|b|x 
versus 3a|3x|b|x, the a-x layer with a single bilayer that is three times thicker, [3a|3x], will 
mix 9 times slower relative to the layer with three layers that are 1/3 of the thickness if 
Fick's laws for diffusion hold.97 This difference in thickness can be used to control which 
layer nucleates and grows first. The layer sequence in a precursor can also have dramatic 
effects on the sequence of compounds that form, particularly if there are large differences 
in the interdiffusion rates of the elements through similar matrices. For example, Cu 
diffuses very quickly through Se at low temperatures while Cr and In diffuse much slower 
at similar temperatures.  Hence, Cu|M|Se layer sequences, where M = Cr and In, will evolve 
on annealing to form CuSe|M structures, leading to the formation of binary copper 
selenides. Creating precursors with M|Cu|M|Se layer sequences eliminates the interfaces 
between Cu and Se, resulting in the initial mixing of M and Se. This leads to the formation 
of an amorphous M-Cu-Se alloy, which directly nucleate ternary compounds (CuInSe2 or 
CuCr2Se4), avoiding the formation of intermediate CuSex as an intermediate  binary 
compound  (Figure I.33) 
55 
  
 
Figure I.33. Synthesis of CuCr2Se4 can be accomplished without the formation of CuSe as 
a reaction intermediate by controlling the sequence of Cu, Cr, and Se layers.  
 
 Mixing of elements in the precursor and the subsequent formation of alloys is an 
aspect of MER synthesis that needs to be carefully controlled since it impacts the properties 
of the heterostructures. Significant mixing and alloying can take place in heterostructures 
that consists of constituents that have the same coordination and/or similar in-plane lattice 
parameters. For example, in (TiSe2)6(NbSe2)6 the extent of metal cross-substitution is more 
than 35% at the NbSe2-TiSe2 interface.79 Different strategies have been employed in 
attempts to control the extent of alloying. The individual building blocks for 
heterostructures can be strategically chosen to have vastly different crystal structures. 
Transition metal dichalcogenides and rock salt bilayers are an obvious example of this 
strategy, as the differences in their basal plane shape (hexagonal vs square) and 
coordination favors the post transition metal cations being in the rock salt structured 
constituent. To form heterostructures that consists solely of a single structure, for example 
hexagonal transition metal dichalcogenides, the building blocks must have drastically 
different 2D crystal structures or large difference in their lattice parameters. Compositional 
56 
  
and structural analysis via HAADF-STEM and EDS have demonstrated the formation of 
distinct layers of GeS2-structured GeSe2 and CdI2-structured VSe2 as a heterostructure with 
no mixing of metals across layers.87 Similarly structured dichalcogenides have been made 
as heterostructures, such as (SnSe2)1(MoSe2)1.32 with minimal intermixing of the cations 
due to the large misfit between their respective in-plane lattice parameters.84 In the case of 
(SnSe2)1(MoSe2)1.32, islands of SnSe2 within a MoSe2 layer can occur, however, if the 
initial precursor does not contain the correct number of atoms of each constituent. An 
intervening constituent can act as diffusion barriers to prevent metals in different layers 
from mixing. A MoSe2-NbSe2 heterostructure exhibits alloying of up to 20% at the 
interfaces, but this interdiffusion can be reduced to near zero when 4 bilayers of SnSe are 
present between the two different dichalcogenides.98 Alloying can be deliberately done to 
achieve modulation doping between rock salt or transition metal dichalcogenide layers. 
This is accomplished by depositing a trilayer of a|b|x where b is the dopant and the total 
number of atoms of a and b is that required to completely occupy the crystallographic site 
in the building block., The rock salt alloyed heterostructure  (BixSn1-xSe)1+y]1(TiSe2)199 and 
transition metal dichalcogenide  alloyed heterostructure  [(SnSe)1+y]1(TaxV1-xSe2)1100 have 
been synthesized using this synthetic strategy. These compounds obey Vegard’s law and 
the amount of the dopant atom can be very large because of the closely similar basal plane 
sizes of  (SnSe and BiSe) and (TaSe2 and VSe2). 
 While traditional inorganic chemists usually rely on controlling the composition of 
the initial reactant mixture to drive what products form, the MER route depends on 
composition, the exact number of atoms in the precursor and where the atoms are located 
in the precursor. Having the correct number of atoms in each repeating period results in the 
57 
  
low temperature self- assembly of targeted compounds via an essentially diffusionless 
process.56,84  Key to discovering this effect was the ability to determine the number of 
atoms of each element in a film using x- fluorescence,101 which greatly simplified the 
calibration of the deposition process. A significant amount of the self-assembly can occur 
during the deposition process. When there is a slight deviation from the targeted area 
density of the elements, partial layers, extra layers, or incomplete repeat units need to be 
fixed during the self-assembly, a process that requires longer range diffusion. If the 
measured amount of each element deviates enough from the target, a mixture of the 
thermodynamic products can form as the extent of long-range diffusion eliminates the 
kinetic advantages of the nanoarchitecture of the precursor. The ability to conveniently 
measure the area density of elements in designed precursor,102 has expedited the discovery 
of new heterostructures. Which structure forms when there are competing compounds in a 
phase diagram is dictated by the area density of the precursor. For example, the two 
compounds present in the Sn-Se phase diagram, SnSe and SnSe2, can each be made as 
heterostructure building blocks by depositing Sn|Se with the correct area density for either 
the basal plane of tetragonal SnSe or hexagonal SnSe2. 
 
 
I.6. Next Steps in Materials Synthesis 
 The ability to prepare new solids with designed structure and properties has 
historically been limited by the lack of analytical techniques to follow the course of 
reactions on the atomic scale. How experimental variables impact the reaction pathways 
during many of the synthesis approaches used to make extended solids, described earlier 
58 
  
in the review, is not known. The heterogeneous intermediate states in typical solid state 
reactions enhances the difficulty of obtaining information about key reaction events and 
what experimental parameters control them. When the system being investigated is near 
equilibrium, phase diagrams greatly assist the logical development of processing 
conditions towards particular compounds or microstructures. A great example of this is the 
precipitation hardening of metal alloys. When a system is far from equilibrium or when the 
system is very complex, we have much to learn. In the next sections we briefly discuss 
currently developing analytical techniques that may provide insight into the reaction 
mechanisms of several of the synthesis approaches discussed in this review.  
 
I.6.1 Pair Distribution Function Analysis 
 Pair distribution function analysis (PDF) of total scattering data provides structural 
information from disordered materials by analyzing both the Bragg scattering and the 
underlying diffuse scattering. The long range order of the atoms is determined from the 
position and intensities of the Bragg reflections. The local atomic structure is deduced from 
the less well- defined features of the diffuse scattering. This local structure is described 
quantitatively by the atomic pair distribution function. The pair distribution function 
analysis of X-ray total scattering measurements of amorphous materials has yielded 
important information about local structure and the spatial extent of long range order which 
has been correlated with physical properties.103 Similar information about the reaction 
intermediates would be a valuable asset in the development of systematic methods to 
prepare targeted solid-state compounds from the techniques discussed in this review. The 
challenge is to remove the scattering background from those parts of the sample that are 
59 
  
not of interest. As an example, the diffuse scattering from the solvent in a reaction 
occurring in a liquid media dominates because it makes up most of the sample. This 
scattering needs to be subtracted to leave the diffuse scattering from the reacting molecules. 
If possible, such total scattering studies as a function of temperature and time provide 
information about the species in solution. These types of investigations are just appearing 
in the literature.  For example, Iversen’s group has published a number of in situ 
synchrotron small-angle X-ray scattering/wide-angle X-ray scattering/pair distribution 
function studies of the formation and growth of compounds in solution and in supercritical 
fluid conditions.18,104,105  While similar studies of the direction reaction of solids would be 
difficult, studying the structure of amorphous thin films as a function of composition and/or 
nanoarchitecture may enable correlations between the structure and composition of the 
amorphous phase and the structures that nucleate. Several approaches to obtaining and 
analyzing total scattering data from thin films on a substrate have been developed, which 
has enabled studies addressing the evolution of structure in amorphous films as a function 
of annealing temperatures and time.106,107 The grazing incidence geometry requires 
complicated data analysis procedures and assumptions about the sample volume and 
geometry, but the signal of the sample relative to the background from the substrate is 
high.103,108 The normal incidence thin film PDF approach simplifies the data processing 
and allows for quantitative analysis of the total scattering data, however subtracting the 
large background signal to obtain the scattering from the thin film is challenging. Total 
scattering pair distribution analysis has have been used to follow the chemical 
transformation and structural evolution of sol gel films and during processing and the 
crystallization of the metastable compound, FeSb3 from an amorphous intermediate.109,110 
60 
  
PDF and difference PDF were also used to examine other solid state reactions.111–113 While 
these experiments show the promise of using total scattering investigations to follow solid 
state reactions, there remain significant experimental challenges. The most significant are 
the subtraction of background scattering and the lack of a method to analyze total scattering 
from samples that are textured.  
 
I.6.2 In-situ studies 
 Time and temperature dependent in situ studies of reactions by NMR, thermal 
analysis, diffraction techniques, EXAFS and different spectroscopies have played an 
important role in unravelling reaction pathways in both molecular and solid synthesis, often 
discovering new compounds formed as intermediates during the transformation of 
reactants into the final products.30,114–116 Advances in detectors, enhanced intensity and 
energy resolution of synchrotron facilities and advances in analysis software packages 
provide new opportunities to rapidly obtain and analyze data obtained during reactions. 
Simultaneously using multiple probes during in-situ and operando investigations is 
becoming  increasingly common, as the additional constraints imposed by the different 
techniques eliminate possible interpretations of the data.30 It is important to recognize that 
different techniques may be looking at different parts of the sample, for example x-ray 
techniques may probe the entire sample volume while spectroscopies based on lower 
energy radiation may probe mainly the surface of the sample. Continued development of 
experimental configurations that permit simultaneous measurements via multiple 
techniques will provide insights to the key transformations that lead to the formation of 
targeted compounds.  
61 
  
 
Figure I.34.  Local minima within the energy landscape of an Sn|Se|V|Se precursor can be 
determined by constraining Sn and Se atoms between layers of VSe2. Calculations 
demonstrate that the formation of CdI2-structured SnSe2 is favored while MoSi2-structured 
SnSe2 is not.  
 
 In parallel with these experimental probes, theoretical efforts are beginning to probe 
aspects of the energy landscape to provide guidance to synthetic efforts. The pioneering 
work of Schon and Jensen, combining experimental investigations of amorphous 
precursors with theoretical modeling of the evolution of atoms placed in unit cells with 
arbitrary configurations, illustrates the challenges and the promise of pairing theory and 
experiment.9 More recently Rudin has proposed a model to mimic the evolution of 
modulated elemental layer precursors, exploring the stability of islands constrained 
between crystalline layers.117 This method determines what atomic configurations are local 
minima in the energy landscape (Figure I.34). New models for nucleation and growth via 
agglomeration are providing insights to solution phase growth. As more in-situ data is 
published additional ideas will be created.  
 
 
 
62 
  
I.6.3 EDX and other STEM techniques 
 The continued development of electron microscopy techniques with enhanced 
capabilities combined with the advances in the ability to prepare cross sectioned samples 
from chosen locations via focused ion beam approaches is providing unprecedented 
information about structure and composition on a sub Ångstrom scale. Resolution of better 
than 0.5Å can be reached on modern aberration correction scanning transmission electron 
microscopes.118 Increased energy resolution in electron energy loss spectroscopy enable 
measurements of small energy differences caused by local structure and even 
measurements of phonon spectra.119 Coincident electron, ion and optical beams in plasma 
assisted dual beam focused ion beam instruments provide unprecedented ability to prepare 
cross sections from bulk samples quickly and efficiently with minimum damage from the 
focused beams.120 Clever liquid flow and electrochemical cells enable in situ investigations 
of chemical reactions such as the nucleation and growth of precipitates or electrochemical 
intercalation/deintercalation.121,122 Enhanced detectors enable the determination of local 
composition using energy dispersed fluorescence measurements of atoms excited by the 
electron beam with increased sensitivity.123 These advances create opportunities to 
reexamine systems studied in the 1970’s and 80’s, probing the evolution of structure and 
composition at reacting interfaces. This will provide new insights on the development of 
composition gradients and nucleation of compounds at reacting interfaces. The information 
about local structure and composition will be very useful to develop models for 
complementary experiments that probe larger sample volumes, such as x-ray diffraction 
experiments.   
 
63 
  
I.7 Conclusions 
 The next decade promises to yield a much greater understanding of the energy 
landscape involved in the synthesis of compounds due to advances in experimental 
techniques and theory. The need to integrate new materials into devices will further 
increase the push to understand how processing conditions impact reaction mechanisms 
and rates. We anticipate a new era of solid state synthesis, inspired in part by physical 
preparation of precisely layered solids via the “scotch tape approach”, the continued 
expansion of new operando approaches to following solid state reactions, and new 
analytical techniques to probe reacting condensed phase systems. This will have a dramatic 
impact on the rate of discovery of new materials, and increase the importance of theoretical 
approaches to discover synthesizable materials with properties of technological or practical 
importance.  
 
I.8 Dissertation Overview 
 The introduction highlights a widely underappreciated aspect of solid state 
synthesis: the reaction mechanism. This dissertation focuses on developing tools and 
concepts designed to understand how modulated elemental reactants self-assemble to form 
ferecrystalline structures with the goal of rational synthesis in mind. More specifically, it 
emphasizes the role of the precursor in defining the energy landscape of a potential 
compound. Chapter II discusses important structural, compositional, and physical 
characterization techniques utilized throughout this dissertation. A large section of this 
chapter is dedicated to a new method of XRF metrology the group has developed that is a 
groundbreaking innovation in thin film synthesis. This is based on published work that is 
64 
  
done in collaboration with Danielle M. Hamman, Dylan Bardgett, Liese A. Maynard, Dr. 
Erik C. Hadland, Alexander C. Lygo, Dr. Suzannah R. Wood, Dr. Marco Esters, and Dr. 
David C. Johnson. Experimental work on dropcast calibration was done in collaboration 
with Sarah Chu, Dylan Galutera, and Jack Congel. Chapter III talks about the strong 
interaction between PbSe and VSe2 and the development of a test for the feasibility of two 
constituents as misfit layer compounds. This work was published in collaboration with 
Shannon S. Fender, Taryn M. Kam, Yu Hsin Tsai, and Dr. David C. Johnson.  
 Chapter IV expands on Chapter III and describes the synthesis and characterization 
of [(PbSe)1+d]m(VSe2)1 compounds with charge density waves published in collaboration 
with Shannon S. Fender, Taryn M. Kam, Robert Fischer, Johann Seyd, Dr. Manfred 
Albrecht, and Dr. David C. Johnson. Chapter V expands on Chapters III and IV by 
demonstrating the limit of the strength of the interaction between PbSe and VSe2. The work 
describes the instability of monolayer thick PbSe on VSe2 using [(PbSe)1+d]q(VSe2)1 
heterostructures where q is the number of PbSe monolayers and equal to 1 to 11. This 
chapter was written in collaboration with Mina Buchanan, Taryn M. Kam, Shannon S. 
Fender, Renae F. Gannon, Robert Fischer, Dr. Benjamin Hanken, Dr. Mark Asta, and Dr. 
David C. Johnson. Finally, Chapter VI demonstrates the use of a reaction monitoring based 
on XRR and XRD to track lateral and perpendicular film growth in order to study reeaction 
mechanisms. It also highlights how precise control over precursor composition and 
nanoarchitecture can direct the formation of [(SnSe2)1+d]1(VSe2)1 over a 
thermodynamically stable compound, [(SnSe)1+d]1(VSe2)1 and the uncovering a reaction 
pathway towards a new alloy, SnxV1-xSe2. This chapter was written in collaboration with 
Taryn M. Kam, Renae F. Gannon, Robert Fischer, and Dr. David C. Johnson. 
65 
  
 Overall this dissertation attempts to address a long-standing problem in solid state 
chemistry: the reliance on serendipity to control a solid state reaction. Here, we provide a 
systematic approach on how to drive a MER reaction towards a specific pathway in its 
energy landscape by precisely controlling the number of atoms and the nanoarchitecture in 
the multilayer precursor. The ability to control these two parameters also allow mechanistic 
aspects of the synthesis method to be unmasked. 
   
66 
  
CHAPTER II 
 
STRUCTURCAL, COMPOSITIONAL, AND ELECTRICAL CHARACTERIZATION 
TECHNIQUES 
 
Authorship Statement 
 Parts of Section 2 were based a paper published in Chemistry of Materials, volume 
30, issue 18, pp. 6209-6216. This work was done in collaboration with Danielle Hamann 
(as first author), Dylan Bardgett, Liese Maynard, Dr. Erik C. Hadland, Alexander C. Lygo, 
Dr. Suzannah R. Wood, and Dr. Marco Esters. Dropcast calibration section of Section 2 is 
based on unpublished data from experimental work done in collaboration with Sarah Chu, 
Dylan Galutera, and Jack Congel. Dr. David C. Johnson is my advisor and was consulted 
in the preparation of this chapter. 
 
II.1 Structural Characterization via X-ray Diffraction 
 In solid state synthesis, structure determination plays a crucial role in developing 
new materials with novel functionalities. The products of solid state chemistry are 
distinctly different from molecular chemistry - they contain different structural features 
that are essential in structure determination. In molecular/organic chemistry, molecules are 
an assembly of atoms linked together in a specific manner via bonds. The way they are 
connected to each other defines the structure. Molecular chemists rely on methods like 
mass spectrometry (MS), infrared spectroscopy (IR), and nuclear magnetic resonance 
(NMR) techniques to determine the identity and number of elements, the type of bonds, 
and the connectivity of the bonds. Each piece of information from the various methods 
mentioned serves as a puzzle piece to the overall structure. The way the structure of solids 
are elucidated also fits this puzzle analogy. The extended structure of solids can be 
67 
  
conceptualized as an assembly or collection of coherent atomic planes with various 
orientations. How these atomic planes orient with each other dictates what the overall 
structure is. Solid state structure of powders and thin films is typically elucidated by 
studying how a material interacts, or more specifically, diffracts incident x-rays. This 
section is dedicated to discussing the various x-ray diffraction (XRD) techniques applied 
to the structure elucidation of thin films. 
 
 
Figure II.1. Schematic of an atomic lattice describing the conditions required for Bragg's 
law. 
 
 Bragg's law is a mathematical equation that relates interplanar spacings with the 
relative directions of incident and scattered radiation.1  It is the quantitative basis of 
structural characterization via x-ray diffraction. Consider a set of parallel planes that 
consists of arrays of atoms shown in Figure II1. Each plane is separated by a perpendicular 
distance of d and the system is irradiated by x-rays at a glancing angle, q. When atoms are 
irradiated with x-rays, the electron cloud oscillates such that electromagnetic waves with 
the same frequency as the incident radiation is re-emitted (elastic scattering). Scattered 
68 
  
radiation is emitted in all directions and can interact with each other to produce interference 
phenomena. 
 Figure II.1 illustrates the conditions required for constructive interference. When 
atoms from two adjacent planes scatter simultaneously, two x-ray beams with the same 
wavelength are produced. The x-ray radiation can either interfere constructively or 
destructively depending on the path difference between the two. If the path difference, 
shown as the segment FGH, is equal to nl, where n is an integer and called the diffraction 
order, the waves will interfere constructively. Mathematically, the segment FGH is can be 
expressed in terms of the incident angle, q, and the interplanar spacing, d. 
FGH = 2d sin q 
nl = 2d sin q    "Bragg's Law"                         Equation II.1 
d = interplanar spacing 
q = angle of Bragg peak 
n = diffraction order 
l = wavelength of incident radiation 
When Bragg's law is satisfied, there is constructive interference and high intensity is 
observed at the incident angle. If Bragg's law is not satisfied, there is destructive 
interference and no intensity observed at the incident angle. X-ray diffraction experiments 
are performed by irradiating a sample with x-rays at different incident angles and collecting 
intensity information from the angular scans. 
69 
  
 
Figure II.2. (a) A simulated x-ray diffraction pattern of powder PbSe. (b) Atomic planes 
and their Miller indices represented in the simulated x-ray diffraction pattern. 
 
 A simple x-ray diffraction experiment can be performed on powdered samples. A 
simulated diffraction pattern of powdered PbSe is shown in Figure II.2a. Reflections 
(peaks) can be observed at specific angles where Bragg's Law is satisfied and each peak 
can be correlated to atomic planes that can be observed in the PbSe crystal structure (inset 
of Figure II2a). These atomic planes can be defined by their Miller indices (hkl). For every 
crystal structure, there are a specific set of atomic planes that lead to constructive 
interference of the incident beam. A crystal structure can be elucidated by analyzing the 
observed peaks, correlating them to the Miller indices of the atomic planes, and 
constructing the crystal structure from that information. For PbSe, the only allowed 
reflections by the structure are those with Miller indices where h, k, and l are either all even 
or all odd. Models for some of the atomic planes elucidated from powdered PbSe are shown 
in Figure II.2b. Other rules apply to different structures. One can refer to any standard solid 
70 
  
state chemistry text for more information on Miller indices and allowed reflections of 
different crystal structures. 
 Thin films synthesized via modulated elemental reactants (MER) require more 
specialized x-ray diffraction experiments to account for the preferred alignment. MER thin 
films exhibit crystallographic alignment parallel to the substrate and turbostratic disorder.2 
The turbostratic disorder does not permit any atomic planes with an x, y, and z component 
to be present, so hkl reflections cannot be observed. Because of this orientation constraint, 
there is order in the x-y plane that is independent of the order in the z-axis. To account for 
this, two x-ray diffraction geometries are used to probe independent crystallinity in the x-
y plane and the z-axis. To probe order in the z-axis, specular geometry is used. To probe 
order in the x-y plane, grazing incidence in-plane geometry is utilized. The combination of 
these two methods permits the structural characterization of MER thin films. 
 Specular x-ray diffraction and x-ray reflectivity are executed using the same 
configuration and are used to probe crystallinity in the z-axis direction of MER thin films. 
For specular x-ray diffraction and x-ray reflectivity experiments, a locked coupled q-2q 
scan is collected. In this experiment, the sample moves simultaneously with the detector 
such that the detector angle, 2q, is always twice the incident angle, q. With this 
configuration, only planes that are parallel to the substrate are probed. The magnitude of 
the order that can be probed can be controlled by modifying the angular range used in this 
experiment. X-ray reflectivity data is collected over a small angular range (0-15° 2q) and 
provides information on the overall structure of the entirety of the film. Specular x-ray 
diffraction data is collected over a large angular range (5-70° 2q) and provides more well-
resolved information on the atomic positions in the z-direction. 
71 
  
II.1.1 X-ray Reflectivity 
 
Figure II.3. Schematic of the geometry for x-ray reflectivity. 
  
 An x-ray reflectivity experiment follows Bragg's law, however, the reflected x-rays 
come from the top and bottom of the entirety of the film (Figure II.3). To maximize the 
information that can be gathered from x-ray reflectivity data, a film with reasonable 
smoothness is required. The constructive and destructive interference of the reflected x-
rays from the film causes oscillations in the x-ray reflectivity patterns called Kiessig 
fringes.3 These oscillations can be used to determine the period or the thickness of the film 
by using a modified form of Bragg's law that includes critical angle of the film. Bragg’s 
law needs to be modified at low angles to account for the difference between the index of 
refraction occurring at the interface due to Snell’s law.4 
ml = 2t [sin2(qi) - sin2(qf)]1/2                            Equation II.2 
Modified Bragg's Law 
t = film thickness 
qi = angle of Kiessig fringe 
qf = critical angle 
m = Kiessig fringe index 
l = wavelength of radiation 
72 
  
Kiessig fringes provide valuable information on the thickness uniformity or the 
"smoothness" of a film. Generally, the higher the angle the Keissig fringes extend to, the 
smoother the film. Quantitatively, the thickness uniformity (Dt) or smoothness of a thin 
film is described by Parrat's equation.5 
Dt = l/[4(qn - qc)]1/2                                   Equation II.3 
Parrat's Equation 
l = wavelength of incident radiation 
qn = angle of last Kiessig fringe 
qc = critical angle 
 
Figure II.4. X-ray reflectivity patterns of V|Se precursors annealed in different conditions 
demonstrating changes in film structures during self-assembly. 
 
 XRR patterns of VSe2 films annealed in different conditions are shown in Figure 
II.4. There are clear changes in the thickness and smoothness of the film as the precursor 
is annealed. Annealing increases the smoothness of the film, apparent from the appearance 
of Kiessig fringes close to 15°. The increase in the period of the Kiessig fringe suggests 
that the film also decreases in thickness as it is annealed. This demonstrates how XRR can 
be used both qualitatively and quantitatively to describe MER thin films. 
73 
  
II.1.2 Specular X-ray Diffraction 
 
Figure II.5. Schematic of the geometry for specular x-ray diffraction. 
  
 A specular/out-of-plane x-ray diffraction experiment follows Bragg's law, but only 
planes that are parallel to the substrate are examined (Figure II.5). This configuration is 
especially suitable for MER films that have preferred alignment to the 001 plane.6 In a 
specular x-ray diffraction pattern of MER films, only Bragg peaks of type 00l can be 
observed. Atomic planes that have an x or y component will not be parallel to the surface. 
The c-lattice parameter can be calculated from the interplanar spacing, calculated via 
Bragg's law. Since this experiment treats the film as a one-dimensional system, the c-lattice 
parameter and interplanar spacing are related through the following expression. 
1/d2 = l2/c2                                           Equation II.4 
d = interplanar spacing 
l = z-axis Miller index 
c = c-lattice parameter 
 An example of a specular pattern of VSe2 is shown in Figure II.6. Some of the 
reflections that are normally allowed in randomly oriented (powder) VSe2 is not observed 
in the specular pattern. This is a result of a specular scan selectively enhancing the 00l 
reflections because of the experiment geometry. 
 
74 
  
 
Figure II.6. X-ray diffraction patterns of VSe2 with various orientations. (red) powder 
simulation, (blue) specular MER film, (red) in-plane MER film. 
 
II.1.3 Grazing Incidence In-plane X-ray Diffraction 
 
 
Figure II.7. Schematic of the geometry for grazing incidence in-plane x-ray diffraction. 
  
 Similar to specular diffraction experiments, in-plane x-ray diffraction is performed 
with a geometry that constrains what structural features can be probed. In this configuration 
the detector is positioned in the plane of the thin film sample, while the incident x-ray is 
set at a low angle (Figure II.7). Only planes that are perpendicular to the surface are probed, 
so only hk0 Bragg peaks can be observed.7 This type of analysis is particularly useful for 
MER films since it can determine the different 2D constituents of a heterostructure that 
75 
  
diffract independently.6 An example of an in-plane x-ray diffraction pattern of VSe2 is also 
shown in Figure II.6. Bragg's law can be used to show that the VSe2 film consists of a 
hexagonal basal plane based on the reflections present. This experiment is particularly 
powerful in the analysis of MER heterostructures, where it has been demonstrated to 
resolve up to 3 different xy lattices.8 
 
II.2 X-ray Fluorescence 
 Controlling composition plays a vital part in conventional solid state synthesis. 
Starting materials are carefully weighed out and combined to match the composition of the 
desired product. In MER synthesis, however, the actual number of atoms deposited is a 
more important factor and more useful metric compared to the composition of the 
precursor. X-ray fluorescence (XRF) is used to determine the number of atoms per unit 
area in a thin film. In a typical XRF setup (Figure II.8), the sample is initially irradiated 
with high energy x-rays to knock off electrons in its inner shell, generating a hole. An 
electron from a higher energy level, relaxes and occupies the generated hole. During this 
transition, energy is released in the form of x-ray radiation. The energy of these fluorescent  
 
Figure II.8. Schematic of x-ray fluorescence analysis. 
 
76 
  
x-rays is related to the atomic number of the elements in the sample. Fluorescent x-rays are 
resolved using analyzer crystals with fixed d-spacings to yield an x-ray diffraction pattern. 
The peak angle and the d-spacing of the analyzer crystal is used to determine the 
wavelength and energy of the fluorescent x-rays. This is the mechanism by which elements 
can be identified using XRF.9 
 
II.2.1 X-ray Fluorescence Analysis of Thin Films 
 The intensities of the fluorescent x-rays are related to the number of atoms of each 
element in the sample (Figure II.9). This correlation is difficult to apply to bulk samples 
because the large volumes involved make it prone to re-absorption, hence, not all 
fluorescent x-rays from the sample may reach the detector. However, it has been 
determined that there is a linear relationship between the amount of material present and 
intensity for thin film samples by assuming there is no re-absorption. Mathematically, the 
XRF intensity is dependent on several factors. 
Iij = {Kj(ls)Ci/µT(lij)}{1-exp[-µT(lij)rd]}                Equation II.5 
Iij = XRF intensity from specific line, j, or element, i 
Ci = mass fraction of element i in film 
lij = wavelength 
r = average film density 
d = film thickness 
µT(lij) = total mass absorption coefficient at lij 
Kj(ls) = product of constants related to experiment 
 
77 
  
 
Figure II.9. The linear relationship of amount of material deposited and intensity for 
different elements deposited on Si substrate. All linear fits pass through zero. 
 
For very thin films, the term µT(lij)rd becomes small and the expression can be simplified 
to, 
Iij = Kj(ls)Cird                                       Equation II.6 
at low thickness regimes. In this more simple form, the XRF intensity is only directly 
proportional to Cird, which is the number of atoms of element i per unit area of the film 
that is probed. This equation typically applies to films that are less than 100 nm in 
thickness.10 
Net intensity
Background
intensity
2θ / º  
Figure II.10. Background correction (dashed line) using pre-installed software. 
 
78 
  
 The XRF measurement of thin films deals with intensities that are very low in 
magnitude, making the analysis extremely sensitive to background effects. Programmed 
background correction pre-installed in XRF instruments are not completely adequate for 
very thin films because it assumes a functional background form. For example, one method 
defines the background by connecting a two points at the shoulder of an XRF peak and 
measures the net intensity for analysis (Figure II.10). 
 
Background
intensity Net intensity
2θ / º  
Figure II.11. Manual background correction using the data from a blank substrate. 
  
 In reality, XRF backgrounds are more complicated, schematically shown in Figure 
II11. To account for the true background, a blank substrate must be analyzed alongside the 
actual sample.  To increase the magnitude of the signal, the integrated area under the curves 
are measured instead of intensity at one specific point. Subtracting the measured integrated 
intensity of the background from the sample provides a more representative measurement. 
This type of XRF analysis and background correction has proven useful for investigating 
elements that yield low magnitude signals.10 
 
 
 
79 
  
II.2.2 X-ray Fluorescence Calibration Methods 
 Two methods have been developed to construct calibration curves for XRF analysis 
of elements. Each method relies on depositing a known amount of material within the 
analytical area of a substrate. The first method requires the synthesis of thin films of 
heterostructures or dichalcogenides that are well-characterized with XRR, specular XRD, 
and in-plane XRD. The calibration samples must have a known phase (with known 
stoichiometry), known number of layers and basal plane area. Information from x-ray 
diffraction data is used to calculate the number of atoms per unit area of each element in a 
calibration sample. The total number of atoms per unit area (area density, AD) of an 
element, i, can be calculated via the equation, 
ADi = r * (Z/Aip)                                Equation II.7 
r = number of layers/repeating units in the film 
Z = number of atoms of each element in unit cell 
Aip  = basal plane area 
 
 
Figure II.12. The linear relationship between the total number of Sn atoms per square 
Angstrom and background corrected integrated intensity.  
 
80 
  
There will be a linear relationship between the area density of the films and intensity 
(Figure II.12) as long as the films do not pass the thickness threshold and the analytical 
area remains constant.10  
 A second, more convenient method was developed if well-characterized thin films 
are not available. Dropcast film samples were used to construct the calibration curve. These 
samples were made by drop casting a very small volume of a salt solution with known 
concentration containing the element of interest on the analytical area of the substrate. The 
number atoms per unit area can be calculated from the moles of salt deposited and the 
analytical area. 
 A representative calibration curve for Pb is shown in Figure II.13. There is only a 
10% difference in the slope derived from dropcast samples and thin film samples (Figure 
II13). Replicate calibration points from dropcast samples have a large spread presumably 
due to the non-uniformity of the films. Table II.1 shows the proportionality constants 
obtained from different elements. 
 
 
Figure II.13. Calibration curve for Pb obtained using thin film and dropcast samples. The 
linear fits for both methods agree with each other with 10% error. 
  
81 
  
Table II.1. Comparison of the proportionality constants of different elements 
Slope (kcps/atom) Slope (kcps/atom per square 
Element Angstrom) 
Dropcast Uniform thin film Dropcast Uniform thin film 
Pb 5.8(3) ´ 10-17 6.45(4) ´ 10-17 0.454 0.507(3) 
Cu 1.23(2) ´ 10-17  0.0966  
Cr 3.6(1) ´ 10-18  0.0283  
 
 X-ray fluorescence is a versatile and valuable tool in MER synthesis as a way to 
determine if precursors have the correct number of atoms. Additionally, it can also be used 
to optimized deposition conditions. Routine analysis of thickness-normalized XRF 
intensities informs one about the behavior of the deposition and make appropriate 
adjustments as necessary. XRF monitoring serves as a guide to establishing more 
reproducible depositions, which is the key to concise synthesis. 
 
II.3 Electrical Transport Measurements 
 Thin films have found a place in modern technology as a means to enhance the 
properties of solid interfaces.11 Electronic devices contain thin films with different 
properties that enable control over current flow through a system. Two important properties 
of thin films that dictates their use in electronics are resistivity and carrier density. 
Resistivity is related to how well a material permits a current flow and the carrier density 
is the number of charge carriers normalized to the volume.12 
 
 
 
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II.3.1 Van der Pauw Method for Measuring Resistivity 
 A simple method of obtaining resistivity is by running a current across a bar of 
material through two contacts and measuring the resulting voltage. However, a two-point 
probe measurement can have large contribution from contact resistance.13 A four-point 
probe measurement like the van der Pauw method permits the resistivity to be collected 
from a lamella of arbitrary shape without significant influence from contact resistance.14 
Thin film materials can be analyzed using the van der Paw method if the following 
conditions are met: 
1. The thin film is uniform in thickness and free of holes. 
2. The contacts are small. 
3. The contacts are at the edges of the sample. 
For the MER samples discussed in this work, the thin films were deposited to form a highly 
symmetric cross-shaped lamella and indium contacts were pressed onto the four vertices 
(FigureII.14). 
 
Figure II.14. Thin film sample shape, and current and voltage contact configuration for a 
van der Pauw resistivity measurement. 
 
 To measure resistivity, a current is sourced through two adjacent contacts (e.g. 1 to 
83 
  
2, I12) while the generated voltage is measured across the other two adjacent contacts (e.g. 
3 to 4, R34,12). The resistivity is related to the current and voltage through the equation, 
r = (pt/ln2)R34,12.                                                      Equation II.8 
t = film thickness 
R = measured voltage 
There are four different ways to connect the contacts and 8 different combinations to source 
a current and measure a resistance. Because the shape of the lamella is symmetric, the 
calculated resistivity should not change when the connections are changed. For example, 
the horizontal line of symmetry indicates that R34,12 = R21,43. If the ratio R34,12 /R21,43 is not 
unity because of asymmetry in contact placement, a geometry factor, f, must be considered.  
ρ = πt R34,12+R21,43 f                                     Equation II.9 
ln(2) 2
The geometry factor is a function of R34,12 /R21,43. 
 
II.3.2 Van der Pauw Method for Measuring Carrier Density 
 The carrier density, n, is an important thin film property that can be calculated from 
the Hall coefficient (RH), which can also be obtained using a van der Pauw experiment.14 
The sign of the Hall coefficient is dependent on the type of carrier present, negative for 
electrons and positive for holes. Carrier densities can be calculated from the Hall 
coefficient using the equation, 
RH = - 1/qn (electrons)                              Equation II.10 
RH = 1/qp (holes)                                  Equation II.11 
n = carrier (electron) density OR p = carrier (hole) density 
q = charge. 
84 
  
 
 
Figure II.15. Thin film sample shape, and current and voltage contact configuration for a 
van der Pauw carrier density measurement. 
 
 To measure the Hall coefficient (Figure II.15), a magnetic field normal to the 
sample is applied, then, a current is sourced across two opposite contacts (e.g. 2 to 4, I24) 
and the voltage is measured across the other two opposite contacts (e.g. R1,3). The measured 
voltage, called the Hall voltage, is a result of the deflection of electrons from a Lorenz 
force. The Hall voltage (VH) is shown mathematically as, 
VH = R
I
HB                                         Equation II.12 t
B = applied magnetic field 
t = thickness 
In this work, a constant current was sourced across a sample and the voltage was measured 
while the magnetic field is varied. The slope of the best fit line of the VH vs BI/t data gives 
the calculated Hall coefficient.  
85 
  
CHAPTER III 
 
STRONG NON-EPITAXIAL INTERACTION: CRYSTALLOGRAPHICALLY 
ALIGNED PbSe ON VSe2 
 
Authorship Statement 
 This chapter was published in Physica Status Solidi A: Applications and Materials 
Science, volume 2019, page 1800896. I am the primary author of this work. Taryn Kam, 
Shannon Fender, and Yu Hsin Tsai assisted with analysis of x-ray diffraction and x-ray 
fluorescence data. Dr. David C. Johnson is my advisor and group leader, consulted in 
preparation of the manuscript. 
 
III.1 Introduction 
 The number of known ternary and multinary compounds is much less than 
expected.1 There are many ternary systems that do not contain any known ternary 
compounds. Traditional solid-state synthesis techniques that directly react elements or 
mixes of elements and binary compounds evolve through complex mixtures of elements, 
binary compounds and/or ternary compounds as diffusion occurs. The search for new 
compounds is often difficult, because only trace amounts of a new compound are formed 
using the initial reaction conditions. Potential new compounds are found by identifying 
reflections in diffraction patterns of mixtures that cannot be explained by known phases. 
Reaction conditions are then modified to increase the amount of the new compound. For a 
new ternary or multinary compound to be the primary product in this reaction after long 
times at high temperatures, they need to be more stable than any of the intermediate 
mixtures. Other approaches have been developed that use a fluid phase to increase diffusion 
86 
  
rates and make nucleation the rate-limiting step in the synthesis (flux-based growth 
techniques, vapor phase transport, molecular beam epitaxy, etc.). While there has been 
recent progress in understanding the speciation in fluids that control product formation, 
serendipity controls what forms.2 The reacting systems are more complicated and there is 
little fundamental understanding of how to adjust the composition of the system to change 
speciation and impact which compound nucleates.  
 In an attempt to increase the rate of discovery of new materials, a variety of high 
throughput methods have been developed in projects such as the Materials Genome 
Initiative.3–5 Typically these methods combine information in databases and computational 
approaches to predict the stability and properties of materials that have yet to be 
synthesized in the lab. Unfortunately, attempted syntheses of many of the new compounds 
that have been predicted to be stable have failed. For example, a recent paper predicted 24 
likely new compounds in phase diagrams that did not contain any known ternary 
compounds.6 The authors tried to prepare these predicted compounds, containing a cation, 
a transition metal and a chalcogen, using several synthesis approaches. The products of the 
reactions were mixes of known binary compounds and the elements. While the predicted 
compounds are potential local free energy minima in the energy landscape based on the 
calculations, the synthetic protocols used could not prevent the formation of binary 
compounds as reaction intermediates. In three systems, a compound forms with a 
stoichiometry close to that of a predicted compound, but the structure that forms is a misfit 
layer compound rather than the predicted structure. Calculating the formation energy of 
misfit layer compounds is challenging due to the incommensurate interface between the 
constituents. The surprising thermodynamic stability of misfit layer structures has long 
87 
  
puzzled researchers.7 Misfit layer structures consist of two interwoven lattices that are 
commensurately stacked along the crystallographic c axis. A common pairing of structures 
is a transition metal dichalcogenide such as NbSe2 with a rock salt structured layer such as 
PbSe.8 In the a-b plane, there is a size mismatch between the constituents and often a 
symmetry difference that results in an incommensurate relationship between the 
constituent layers. The atoms at the interface in each layer are displaced from their average 
position due to the interaction with the atoms of the other layer. This results in a structurally 
incoherent interface between the two layers. Given the varying and irregular local 
coordination environment between the atoms at the interface that results from the structural 
incoherence, one would expect that a mix of the binary compounds (for example NbSe2 + 
PbSe) to be more stable than the misfit layered compound (PbSe)1.14NbSe2, which contains 
alternating planes of the dichalcogenide trilayer (Se-Nb-Se) with bilayers of PbSe.  The 
misfit compound (PbSe)1.14NbSe2, however, is the product that is formed on heating a 
stoichiometric mix of the elements at 1000°C for an extended time.9 This indicates that the 
interaction between the PbSe and NbSe2 at the interface must be stronger than the sum of 
the interactions between NbSe2 layers in NbSe2 and between (001) planes of PbSe. 
 There have been several explanations presented in the literature for the surprising 
stability of misfit layer compounds.  While van der Waals forces certainly exist between 
the two structures, the interaction between the layers needs to be much stronger. For misfit 
layer compounds containing trivalent cations such as rare earth metals in the rock salt layer, 
there is abundant evidence that there is electron transfer from the rock salt layer to the 
dichalcogenide. Such charge transfer would result in a strong enough ionic interaction 
between the layers  (LnX)1+dδ+(TX2) δ- to stabilize the misfit layer structure.8,10 There is 
88 
  
significant controversy in the literature, however, about whether charge transfer occurs in 
misfit layer compounds containing a semiconducting divalent rock salt structure (such as 
SnX or PbX where X = S or Se) paired with a transition metal dichalcogenide. Ohno 
performed x-ray photoemission, x-ray absorption and reflection electron energy loss 
spectroscopy on misfit layer compounds containing alternating layers of PbS and TiS2 and 
SnS and NbS2. He concluded that a small amount of charge transfer occurs from the rock 
salt layer to the dichalcogenide.11 A subsequent photoelectron spectroscopy study of the 
misfit compounds (MS)1+d(TS2) where M = Sn and Pb and T = Ti, Nb and Ta indicated 
that there was no, or only a very small amount of charge transfer and that the Pb and Sn 
were divalent.12 Band structure calculations also suggest that there is no charge transfer.13 
If only a very small amount of charge transfer occurs, then the amount of ionic stabilization 
will be small. A subsequent study of several misfit layer compounds indicated that there 
was a systematic excess of the transition metal dichalcogenide cation (T) and a systematic 
shortfall in the rock salt cation (M).  The authors suggested that T cations were substituting 
for M cations in the rock salt structure, resulting in layers that have high enough charges 
to stabilize the misfit layer structure via an ionic interaction between the constituents.14 
They also suggested that these deviations from stoichiometry are necessary to stabilize the 
misfit layer structure. The cross substitution of M and T cations was supported by a 
subsequent photoelectron spectroscopy investigation.7 
 In this work we probe the interaction between a rock salt compound, PbSe, and the 
surface of a dichalcogenide (VSe2). We examine the formation and structure of PbSe, VSe2, 
(PbSe)1.11VSe2 and PbSe on a layer of VSe2 from precursors prepared by depositing 
sequences of ultrathin layers of the respective elements to form films of varying 
89 
  
thicknesses. The ultrathin layer thicknesses eliminate diffusion as a rate limiting step, while 
constraining the extent of long range diffusion because low reaction temperatures can be 
used. In all of the precursors, the respective crystalline compounds nucleated and grew 
during the deposition process. Post deposition annealing increased both crystallite size and 
the amount of material crystalized in all films. The PbSe precursors deposited on a SiO2 
surface formed rough films with randomly oriented PbSe crystals. The VSe2 precursors 
deposited on a SiO2 surface formed a crystallographically aligned films, with the basal 
plane of VSe2 parallel to the substrate. In plane diffraction scans indicated a random 
rotational orientation of the VSe2 crystallites. The precursor to the metastable misfit layer 
compound [(PbSe)1.11]1(VSe2)1 deposited on SiO2 formed a crystallographically aligned 
film, with the basal plane of VSe2 parallel to the substrate. In plane diffraction scans 
indicated a random rotational in plane orientation of both the PbSe and VSe2. The PbSe 
precursor deposited on thin film of VSe2 was also crystallographically aligned, with the 
(001) surface of the PbSe crystallites parallel with the basal plane of the VSe2 substrate. 
This is an indication of a strong interaction between PbSe and VSe2 at the interface. At the 
low reaction temperatures, it is unlikely that there is sufficient energy to exchange Pb with 
V cations from the VSe2 substrate. This suggests a simple test to see if it is likely that a 
misfit layer compound can be formed between a new constituent and a dichalcogenide. If 
there is not crystallographic alignment of a proposed new constituent on a dichalcogenide, 
a new misfit layer compound is unlikely. If there is crystallographic alignment of a 
proposed new constituent on the dichalcogenide, it is much more likely that a new misfit 
layer compound can be formed. 
 
90 
  
III.2 Experimental 
 Thin film precursors consisting of elemental Pb (99.8%, Alfa Aesar), V (99.995%, 
Alfa Aesar), and Se (99.99%, Alfa Aesar) were deposited on silicon substrates with a native 
oxide layer using a low pressure (< 3 x 10-7 torr) physical deposition chamber. The 
elements were evaporated by using Thermionics 6 kW electron beam guns or custom-built 
Knudsen effusion cells producing a plume of atoms that deposit on the substrate. The 
thickness of each element deposited is controlled by opening and closing a pneumatic 
shutter that blocks the plume for a specific time. The deposition time is determined by the 
measured Angstrom thickness by a quartz crystal microbalance and custom-made LabView 
software. Crystallization of the films was accomplished by annealing the precursor in an 
inert N2 atmosphere (O2 < 0.8 ppm). 
 Out-of-plane specular diffraction and x-ray reflectivity were collected using a 
Bruker D8 Discover diffractometer to determine the lattice parameters and degree of 
crystallographic alignment of the film constituents. Grazing incidence in-plane diffraction 
was collected on a Rigaku Smartlab diffractometer to assess the crystallized constituents 
in the film. X-ray fluorescence measurements were taken using a Rigaku Primus II ZSX 
spectrometer to determine the elemental composition of the films. 
 
III.3 Results and Discussion 
 The precursors designed to self-assemble the PbSe, VSe2, (PbSe)1.11VSe2, and PbSe 
on a few layers of VSe2 films were made by sequentially depositing alternating layers of 
either Pb and Se or V and Se. The number of M|Se pairs deposited was varied to obtain the 
desired total film thickness. The thickness of the Pb and Se layers in each Pb|Se pair 
91 
  
contained the number of atoms required to form a single rock salt structured PbSe bilayer. 
The thickness of the V and Se layers in each V|Se pair contained the appropriate number 
of atoms to form a single trilayer of VSe2. The number of atoms of each element was 
calculated from the lattice parameters of PbSe15 and VSe2.16 For example, the number of 
Pb atoms per unit area in a PbSe bilayer is given by the product of the number of Pb atoms 
per unit cell divided by the basal plane area of the unit cell [4 Pb atoms / 6.112 Å2  = 0.107 
Pb atoms Å-2]. X-ray fluorescence analysis was used to determine the number of atoms per 
square Angstrom in the total film thickness.17 Dividing the number of atoms per square 
Angstrom in the total film thickness by the number of layers deposited yields the average 
number of atoms deposited in each bilayer. We investigated what structure is formed as 
the precursors are deposited and how the structure evolves as the film is annealed using x-
ray diffraction.  
 Figure III.1 contains specular x-ray diffraction data of as deposited and annealed 
PbSe films of various thicknesses (16, 32, and 82 layers) deposited on SiO2. The measured 
number of Pb and Se atoms per bilayer in each film are given in Table III.1. In the high 
angle specular diffraction scans of the as deposited precursors (Figure III.1a), Bragg 
reflections consistent with the known rock salt structure of PbSe are observed in all of the 
films. This indicates that the Pb and Se atoms self-assemble during the deposition process 
forming PbSe. The a-axis lattice parameters are given in Table III.2. The degree of 
crystallographic alignment in the as deposited films is similar, based on the ratios of the 
intensities of the (111), (200) and (220) reflections. Crystallographic alignment increases 
as the films are annealed, with significant growth of the intensity of the (002) and (004) 
reflections in all of the films. In the 16 layer film the only non-00l reflection visible after  
92 
  
 
 
Figure III.1. (a) Specular x-ray diffraction and (b) x-ray reflectivity patterns of various 
thicknesses of PbSe films on SiO2 as deposited (black) and annealed at 300°C for 30 
minutes (red). The presence of non-00l reflections in the specular diffraction patterns 
indicate that PbSe is randomly oriented. Kiessig fringes that extend only up to ~2° suggest 
that the film is rough. *substrate 
 
annealing is a weak (220) reflection. In the 82 layer film, the intensity of the (002) 
reflection increases 5 fold after annealing, but other non-00l reflections remain prominent. 
The x-ray reflectivity patterns of these films (Figure III.1b) suggest that the roughness 
increases as the film thickness increases, as the angle where Kiessig fringes are no longer 
resolvable decreases with increasing film thickness.18 Table III.2 summarizes the measured 
lattice parameters of the three PbSe films both before and after annealing.  
 
 
 
93 
  
Table III.1. The number of Pb and Se atoms in the different PbSe precursors determined 
by x-ray fluorescence. The target composition to obtain a bilayer of PbSe is: Pb and Se: 
0.107 atoms per Å2 
 
2
# layers Pb atoms per Å  Se atoms per Å
2 Composition 
Pb|Se total per layer total per layer ratio (Se/Pb) 
16 1.62 0.101 1.63 0.102 1.01 
32 3.15 0.098 3.10 0.097 0.98 
82 8.44 0.103 8.14 0.099 0.96 
 
Table III.2. Lattice parameters calculated from specular x-ray diffraction patterns of PbSe 
on SiO2. AD = as deposited, AN = annealed 
 
# layers a-lattice 
Pb|Se parameter [Å] 
16 AD 6.08(1) 
 AN 6.10(1) 
32 AD 6.11(1) 
 AN 6.11(1) 
82 AD 6.08(1) 
 AN 6.10(1) 
 
Table III.3. The number of V and Se atoms in the different VSe2 precursors determined 
by x-ray fluorescence. The target composition to obtain a trilayer of VSe2 is: V = 0.103 
atoms per Å2 and Se = 0.205 atoms per Å2 
 
2
# layers V atoms per Å  Se atoms per Å
2 Composition 
Pb|Se total per layer total per layer ratio (Se/Pb) 
49 5.08 0.104 11.0 0.224 2.17 
82 9.18 0.112 17.6 0.215 1.92 
  
94 
  
 
Figure III.2. Specular x-ray diffraction of representative V|Se precursors after annealing at 
each of the indicated temperatures for 30 minutes. The prominent 00l reflections appearing 
in the as deposited sample indicates that crystallographically aligned VSe2 forms upon 
deposition and becomes more ordered as the film is annealed.  
  
 An annealing study was carried out on several V|Se precursors to investigate how 
the structure evolves as the temperature is increased. Table III.3 summarizes the amount 
of each element in each of the as deposited films. The slight excess of Se in one as deposited 
film is lost through evaporation as the sample is annealed. The specular x-ray patterns of a 
representative sample collected after annealing at several temperatures is shown in Figure 
III.2. The diffraction pattern of the as deposited precursor contains four 00l reflections 
indicating that VSe2 self assembles during the deposition, crystallographically-aligned to 
the SiO2 substrate. The (001) reflection at around 15º, however, has a shoulder at low 
angles from the artificial layering of the precursor. This suggests that only part of the film 
has formed VSe2. As the annealing temperature increases, the intensity of this low angle 
shoulder decreases while the 00l reflections become more intense and have narrower line 
widths. The increased intensity suggests that more of the film becomes VSe2 and/or the 
VSe2 is becoming more crystallographically-aligned to the substrate. The decreasing line 
widths indicate that the structural coherence of the VSe2 perpendicular to the substrate is 
95 
  
increasing. At 300°C Laue fringes were observed on either side of the (001) reflection of 
the thinner sample due to the finite number of unit cells, suggesting a uniform thickness 
exists over a significant portion of the film. In plane diffraction patterns, done on a subset 
of samples, contained only hk0 reflections, which gives further support that the VSe2 film 
is crystallographically aligned to the substrate. Table III.4 contains a summary of the 
structural parameters derived from the diffraction studies of the VSe2 films. 
 
Table III.4. Structural parameters (c and a lattice constants) calculated from specular and 
in-plane x-ray diffraction patterns of VSe2 on SiO2. AD = as deposited, AN = annealed 
350°C for 30 minutes 
 
# layers V|Se c-lattice parameter a-lattice parameter [Å] [Å] 
49 AD 6.20(1) - 
 AN 6.07(1) 3.37(1) 
82 AD 6.10(1) - 
 AN 6.03(1) - 
 
Table III.5. The total number of Pb, V, and Se atoms in the different  Pb|Se|V|Se precursors 
determined by x-ray fluorescence.  
 
Pb atoms per Å2 Se atoms per Å2 2# layers  V atoms per Å  
Pb|Se|V|Se total per layer total per layer total per layer 
41* 4.39 0.107 12.6 0.308 4.67 0.114 
24 2.66 0.111 8.21 0.342 2.09 0.087 
*(sample used in annealing study) 
 
 A similar annealing study was carried out on Pb|Se|V|Se precursors to compare the 
formation of (PbSe)1.11(VSe2)1 relative to that of the individual constituents. Table III.5  
 
96 
  
  
 
Figure III.3. (a) Specular x-ray diffraction of [(PbSe)1.11]1(VSe2)1, (b) in-plane diffraction 
of [(PbSe)1.11]1(VSe2)1, and (c) x-ray reflectivity patterns of of [(PbSe)1.11]1(VSe2)1 after 
annealing at the indicated temperatures for 30 minutes. Since the film is 
crystallographically aligned to the substrate, only 00l reflections are observed in the 
specular scans. The higher order 00l reflections observed in the as deposited film suggest 
crystallization of the superlattice taking place upon deposition. Reflections for independent 
lattices of PbSe and VSe2 are observed in the in-plane diffraction pattern show that both 
constituents are present starting at the as deposited state. Kiessig fringes are retained in the 
x-ray reflectivity pattern even after multiple steps of annealing suggest that the film 
remains smooth throughout the self-assembly process. 
 
summarizes the amount of each element in each of the as deposited films. Figure III.3 
contains the diffraction patterns collected in the annealing study of a representative film. 
The appearance of higher order 00l reflections in the specular diffraction pattern, (Figure 
III.3a), indicates that a superstructure forms during the deposition. Since only 00l 
reflections are observed, it is crystallographically-aligned to the substrate. The c-axis lattice 
parameter determined from the 00l reflections (12.28(1) Å) is close to the previously 
reported value for [(PbSe)1.11]1(VSe2)1,12.25(1) Å.19 The in-plane diffraction pattern of the 
as deposited sample (Figure III.3b) contains broad reflections of both PbSe and VSe2, 
further indicating that [(PbSe)1.11]1(VSe2)1 forms during the deposition. Only hk0 
reflections are observed for PbSe and VSe2 in the in plane diffraction pattern, indicating 
strong crystallographic alignment of each constituent with respect to the substrate. X-ray  
97 
  
Table III.6. Structural parameters (superlattice d-spacing and a-lattice consants) calculated 
from specular and in-plane x-ray diffraction patterns of Pb|Se|V|Se precursor annealed at 
various temperatures. AD = as deposited 
 
PbSe a- VSe2 a-
Temperature d-spacing lattice lattice 
[°C] [Å] parameter parameter 
[Å] [Å] 
AD 12.28(1) - - 
100 12.38(1) - - 
200 12.38(1) - - 
250 12.36(1) - - 
300 12.31(1) 6.03(1) 3.43(1) 
350 12.25(1) - - 
400 12.17(1) - - 
 
reflectivity of the as deposited sample indicates that the Pb|Se|V|Se precursor is much 
smoother than the films of PbSe or VSe2. The as deposited Pb|Se|V|Se precursor contains 
significantly more order than the corresponding films of the individual constituents. As the 
annealing temperature is increased, the 00l and hk0 reflections become more intense and 
narrow as atoms diffuse forming a more coherent structure perpendicular to the substrate 
and larger domains of PbSe and VSe2 in the plane of the substrate. While the misfit layer 
compound [(PbSe)1.11]1(VSe2)1 has not been reported in the literature, the 
[(PbSe)1.11]1(VSe2)1 formed from the ordered precursor is at least kinetically stable at 
400°C. Table III.6 contains a summary of the structural parameters derived from the 
diffraction studies of Pb|Se|V|Se precursors. Precursors that have around the targeted 
layering thickness and composition also form [(PbSe)1.11]1(VSe2)1, although a variety of 
defects (extra PbSe or VSe2 layers between [(PbSe)1.11]1(VSe2)1 crystals, partial 
98 
  
replacement of a PbSe (or VSe2) layer with VSe2 (or PbSe), extra PbSe or VSe2 on the 
surface) are present. This suggests that [(PbSe)1.11]1(VSe2)1 is at least a significant local 
free energy minimum in the free energy landscape. The large difference in the degree of 
order observed in Pb|Se|V|Se versus either Pb|Se or V|Se precursors in both as deposited 
and annealed states indicates a strong interaction must be present between bilayers of PbSe 
and trilayers of VSe2. 
 We prepared precursor films with different thicknesses of PbSe on a thin layer of 
VSe2 to determine if the PbSe layer was different than that found when PbSe was deposited 
on SiO2 coated silicon described earlier. Table III.7 summarizes the amounts of each 
element in the as deposited films. Figure III.4 contains diffraction data collected on two 
samples. For both films, PbSe forms during the deposition process. For the 20 layer PbSe 
sample on 4 layers of VSe2, only 00l reflections of PbSe are present, indicating that the 
PbSe is crystallographically aligned. After annealing, there is a relatively small change in 
the intensity (about 1.5x) of the 002 reflection suggesting that the as deposited film was 
already mostly crystalline and/or that the extent of crystallographic alignment increases. 
Kiessig fringes extending up to 5º, suggesting that the film is smooth, with calculated 
roughness of ~10Å. In the as deposited 82-layer PbSe on 8 layer VSe2 film, weak non-00l 
reflections of PbSe are observed indicating that some grains are randomly oriented. 
However, since the intensity ratio of these reflections are low compared to the expected 
values of a randomly oriented powder, the majority of the film is crystallographically 
aligned. After annealing, the non-00l reflections disappear completely and the intensity of 
the 00l reflections increase. The amount of the intensity increase is significantly less than 
was observed in a similar thickness film of PbSe on SiO2, suggesting that the as deposited  
99 
  
Table III.7. The total number of Pb, V, and Se atoms in the different PbSe precursors on 
VSe2 determined by x-ray fluorescence. Exact composition ratio of Pb/Se cannot be 
determine because of the presence of Se in both constituents 
 
2 2 2
# layers Pb atoms per Å  Se atoms per Å  V atoms per Å  
PbSe:VSe2 total per layer total per layer total per layer 
20:4 2.66 0.133 3.05 - 0.450 0.113 
82:8 8.76 0.107 8.40 - 0.953 0.119 
 
 
Figure III.4. (a) Specular x-ray diffraction and (b) x-ray reflectivity patterns of 20 layers of 
PbSe on 4 layers of VSe2 (20:4) and 82 layers of PbSe on 8 layers of VSe2 (82:8) films as 
deposited (black) and annealed at 300°C for 30 minutes (red). The thicker (82:8) film has 
weak non-00l reflections implying that there is a small fraction of randomly oriented 
grains. Annealed film samples have very strong 00l reflections indicating crystallographic 
alignment to the substrate due to the presence of the intervening layers of smooth VSe2. 
The films are exceptionally smooth compared to PbSe on SiO2 because the Kiessig fringes 
extending to higher angles. 
 
film on VSe2 is mostly crystalline and aligned as deposited. The (001) reflection of VSe2 
also appears after annealing. The thicker film on VSe2 is significantly smoother than the 
film on SiO2. The x-ray reflectivity scan of the thicker PbSe film on VSe2 contains high  
100 
  
Table III.8. Lattice constants calculated from specular x-ray diffraction PbSe on VSe2.  
AD = as deposited, AN = annealed 
 
# layers  a-lattice 
Pb|Se:V|Se parameter [Å] 
20:4 AD 6.13(1) 
 AN 6.12(1) 
82:8 AD 6.12(1) 
 AN 6.11(1) 
 
frequency fringes coming from the thick PbSe layer and broader low frequency fringes due 
to the VSe2 layers beneath the PbSe. Table III.8 contains a summary of the structural 
parameters derived from the diffraction studies of Pb|Se precursors deposited on thin VSe2 
layers. The difference between the diffraction data of films of PbSe deposited on VSe2 and 
on SiO2 reflects the presence of a strong interaction between the PbSe and VSe2.  
 
III.4 Conclusions 
 There are a large number of potential misfit layer compounds, especially because 
there is not a requirement for lattice matching at the interface between different 
constituents. The incoherent interfaces and the lack of an understanding why the 
interactions between constituents at the interfaces is strong make it difficult to theoretically 
predict which misfit layer compounds might be thermodynamically stable or at least local  
free energy minima in the free energy landscape. Figure III.5 compares grazing incidence 
in-plane diffraction patterns of PbSe on SiO2, PbSe on VSe2, and (PbSe)1.11VSe2 annealed  
101 
  
 
Figure III.5. Grazing incidence in-plane diffraction patterns of 82 layers of PbSe on SiO2, 
20 layers of PbSe on 4 layers of VSe2, and [(PbSe)1.11]1(VSe2)1. The PbSe films have 
reflections that can be indexed to rock salt PbSe. All possible hkl reflections are observed 
in PbSe in SiO2 film, indicating that the grains are randomly oriented. The absence of hkl 
reflections in the 20:4 film indicates that grains are parallel to the substrate.  
 
at 300ºC for 30 min. The difference in the degree of crystallographic alignment reflects the 
strong interaction between the PbSe and VSe2 layers. This suggests that comparing the 
degree of crystallographic alignment of films of A and B on SiO2 or another convenient 
substrate with films of A on B (and/or B on A) may provide a way to quickly determine 
whether a misfit layer compound will form from a designed precursor with repeating layers 
of A and B. Since there are many possible potential combinations of constituents, such a 
fast screening test would save a significant amount of time.  
 
III.5 Bridge 
 The crystallographic alignment of PbSe on VSe2 suggests that there is a strong non-
epitaxial relationship between PbSe and VSe2 that is likely responsible for the stability of 
misfit layered compounds or ferecrystals containing the two constituents. The results 
102 
  
presented here promotes the idea that the compatibility of two constituents as misfit layered 
compound combination can be tested by checking for crystallographic alignment. The 
strong interaction between PbSe and VSe2 shows that other misfit layered compounds 
between containing the two constituents can be synthesized. The next chapter focuses on 
the synthesis of [(PbSe)1+d]m(VSe2)1, where m = 1-4, heterostructures, a new family of 
PbSe and VSe2 heterostructures with charge density wave (CDW) properties 
.  
103 
  
CHAPTER IV 
 
DESIGNED SYNTHESIS AND STRUCTURE-PROPERTY RELATIONSHIPS OF 
KINETICALLY STABLE [(PbSe)1+d]m(VSe2)1 (m = 1, 2, 3, 4) HETEROSTRUCTURES 
 
 
Authorship Statement 
 This work was published in Chemistry of Materials, volume 31, issue 20, pages 
8473-8483. I am the primary author of this work. Shannon Fender and Taryn Kam collected 
and analyzed x-ray diffraction and x-ray fluorescence data, and in the preparation of the 
manuscript. Johann Seyd and Dr. Manfred Albrecht assisted in the collection of electrical 
transport measurements. Robert Fischer and Dr. Ping Lu collected HAADF-STEM data. 
Dr. David C. Johnson is my advisor and consulted in preparation of this manuscript. 
 
IV.1 Introduction 
 The discovery of emergent properties in single layer and very thin layers of quasi-
two-dimensional systems has resulted in many reports of new systems and 
heterostructures.1 Initially the majority of the systems being investigated were 
semiconducting because large changes in properties were discovered in semiconducting 
systems and because single sheets of metallic systems were found to be unstable in air.2 
More recently, a number of interesting properties of metallic system have been explored as 
a function of thickness including superconductivity and charge density waves (CDW).3–5 
The trends with layer thickness and/or layer separation depend on the specific property and 
compounds being investigated. The onset temperature of superconductivity is lowered 
when the thickness of NbSe2 layers is reduced6 or the separation between NbSe2 layers in 
a heterostructure is increased.7 Varying the layer thickness of different dichalcogenides 
104 
  
produced opposite effects on the onset temperature of charge density wave transitions. 
Studies on mechanically-exfoliated TiSe2 have shown that as thickness of the exfoliated 
TiSe2 is decreased, the onset temperature of the CDW increased.8 The opposite has been 
found for TaSe2, with the onset temperature of the CDW decreasing as the thickness of the 
mechanically-exfoliated film is decreased.9 Unraveling the relationships between physical 
properties and the interaction between constituents at interfaces, the structure of the 
constituents, and/or the electronic or magnetic properties of the constituents is a focus of 
continued interest. 
 The electrical and magnetic properties of vanadium dichalcogenides have been 
extensively investigated both computationally and experimentally, with a variety of 
contradictory results presented as the number of layers of VSe2 are reduced. Bulk VSe2 has 
vanadium in octahedral coordination in a 1T structure and is metallic. It also has a small 
Pauli paramagnetism due to the conduction electrons and exhibits a CDW transition. 
Density functional theory calculations predict the ground state of undistorted VSe2 layers 
to be the ferromagnetic 2H-polytype with a metal to semimetal/semiconductor transition 
when going from the bilayer to the monolayer.10–12 There are contradictory reports on how 
the CDW changes as the number of VSe2 layers are reduced in this n-type metal and how 
magnetic behavior changes as the sample is thinned to a monolayer. The onset of the CDW 
in bulk single crystals of VSe2 is 100 K13 and it has been reported that this increases to 135 
K as thickness is reduced to 4-8 trilayers of VSe2 prepared via liquid exfoliation.14 An 
opposite trend was reported for micromechanically-exfoliated nanoflakes, where the onset 
temperature decreases to 81 K at the lowest thickness measured, 11.6 nm.5 The thin 
nanoflakes are n-type conductors, as is bulk VSe2, but the carrier concentration increases 
105 
  
as the nanoflake thickness is decreased. Both solvent-aided and mechanical exfoliation 
techniques were not able to precisely control the thickness of the VSe2 flakes or reach the 
monolayer limit.14,15  
 Monolayer VSe2 has been reported to have a charge density wave with a different 
distortion than found in the bulk.16–18 The transition temperature is higher in the monolayer, 
and the transition temperature depends on both the material below it and the relative 
orientation of the adjacent layer. Monolayers of VSe2 have also been reported to be 
ferromagnetic.19 Other reports present data showing that their VSe2 monolayers are non-
magnetic and suggest that the ferromagnetism results from oxide impurities.20 Studies of 
[(SnSe)1+δ]m(VSe2)1 and [(PbSe)1+δ]1(VSe2)1 prepared by annealing designed precursors 
show that they are p-type metals with a CDW that depends on the thickness of the rock salt 
constituent.21,22 The changes in electrical resistivity and charge carrier concentration at the 
CDW transition temperature are much larger than that observed in bulk VSe2. Compounds 
with thicker VSe2 layers, [(SnSe)1+δ]1(VSe2)n and [(PbSe)1+δ]1(VSe2)n where n is larger than 
two, are n-type metals and CDW transition and transition temperature are similar to that 
found in bulk VSe2.22,23  
 In this paper we probe the effect of changing the PbSe layer thickness on the CDW 
found in [(PbSe)1+δ]1(VSe2)1. The synthesis, structure and electrical properties of a family 
of new, metastable compounds, [(PbSe)1+δ]m(VSe2)1 are discussed. 22 The synthesis of 
[(PbSe)1+δ]m(VSe2)1 with m = 2, 3, and 4 was more challenging than the synthesis of the m 
= 1 compound because the higher m compounds have smaller barriers towards 
disproportionation into PbSe and VSe2. Deviations in the composition of the precursor 
from the stoichiometry of the desired products result in disproportionation of the precursor 
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during low temperature annealing. The structure of the PbSe layers in [(PbSe)1+δ]m(VSe2)1 
compounds is significantly less distorted than found in the analogous semiconducting 
[(PbSe)0.99]m(WSe2)n24 and [(PbSe)1.00]m(MoSe2)n25 compounds. The electrical resistivity 
data of all of the [(PbSe)1+δ]m(VSe2)1 compounds contain a CDW transition at ~100 K that 
is distinctly different than that found in bulk VSe2. The electrical resistivity can be 
successfully modeled using a parallel resistor circuit when m is three or greater, indicating 
composite behavior. These findings are very different from that previously reported for the 
isoelectronic [(SnSe)1+δ]m(VSe2)1 compounds, where the CDW transition temperature 
changes systematically with m.21 This suggests that the interaction between the constituent 
layers is more important than the separation of VSe2 layers in determining the CDW 
transition temperature. The differences between these two sets of isoelectronic compounds 
demonstrate the sensitivity of emergent properties in heterostructures to the identity of the 
constituent layers.   
 
IV.2 Experimental 
 Precursors designed to form the compounds [(PbSe)1+δ]m(VSe2)1 where 1 ≤ m ≤ 4, 
were synthesized using the modulated elemental reactants (MER) technique. Pb (99.8% 
Alfa Aesar), V (99.995% Alfa Aesar), and Se (99.99% Alfa Aesar) were deposited using 
6 kW electron beam guns (Pb and V) and a custom-made Knudsen effusion cell (Se) under 
high vacuum (< 3 x 10-7 torr). The precursors were prepared by sequentially evaporating 
elemental sources in the sequence [Pb|Se]mV|Se onto Si wafers or quartz substrates. The 
mass of each element deposited was monitored using quartz crystal monitors. A LabView-
based program opened and closed pneumatic shutters that control the amount of material 
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deposited using either the integrated thickness or the product of the deposition rate and 
time. A more detailed explanation of the chamber and the deposition procedure is described 
by Fister, et al..26 The amount of each element deposited in each sample was measured 
using X-ray Fluorescence (XRF) on a Rigaku Primus II ZSX spectrometer. The 
proportionality factor between the measured fluorescence intensity and the number of 
atoms per unit area of each element in the film was determined as described by Hamann, 
et al..27 The deposition conditions were iteratively adjusted to obtain precursors with the 
desired amounts of each element.  
 The layered precursors were crystalized by annealing in an inert N2 atmosphere 
with an O2 concentration less than 1 ppm. Out-of-plane specular x-ray diffraction (XRD), 
x-ray reflectivity (XRR), and x-ray rocking curve data were performed on a Bruker D8 
Discover diffractometer with Cu Ka radiation (l = 0.15418 nm). Grazing incidence in-
plane x-ray diffraction scans (GIXRD) were performed on a Rigaku Smartlab 
diffractometer. Le Bail fitting of the diffraction patterns was used to determine the in-plane 
lattice parameters using FullProf  and GSAS software.28,29 Rietveld refinement of the 
specular x-ray diffraction patterns was done to determine the position of the atomic planes 
along the c-axis also using GSAS software.29,30 High-angle annular dark-field scanning 
transmission electron microscopy (HAADF-STEM) images were collected by a FEI 
TitanTM G2 80-200 STEM with a Cs probe corrector, operated at 200 kV, using an annular 
detector with a collection range of 60-160 mrad. STEM samples were prepared by focused 
ion beam technique.   
 Resistivity and Hall coefficients were measured as a function of temperature on a 
film deposited on a quartz substrate using the van der Pauw technique. Data was collected 
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at a temperature range between 25 K and 295 K. Seebeck coefficients were measured using 
a custom measurement system in which Cu and constantan thermocouples were used to 
measure temperature and the voltage created by a small temperature difference in a film. 
 
IV.3 Results and Discussion 
 The MER precursors were designed to have the correct composition and 
nanoarchitecture necessary to crystallize the target compounds. The number of atoms per 
square Angstrom necessary to form the individual building blocks (PbSe and VSe2) was 
calculated from the in-plane lattice parameters of the bulk structures of PbSe31 and VSe232 
by dividing the number of atoms per unit cell by the basal plan area. The solid lines in 
Figure 1 give the calculated number of atoms of each element per unit area per repeating 
unit of the precursor for each targeted compound. The target number of V atoms per unit 
area per repeating sequence is constant since there is one VSe2 trilayer in each repeat unit, 
while the number of atoms per unit area of Pb and Se increase linearly as the number of 
PbSe bilayer units (m) are increased. To prepare each of the compounds, m Pb|Se layers 
and a single V|Se layer were sequentially deposited. For example, the precursor for 
[(PbSe)1+δ]2(VSe2)1 was made by repeatedly depositing the following sequence of 
elemental layers: V|Se|Pb|Se|Pb|Se. The amount or each element in the Pb|Se and V|Se 
bilayers was iteratively adjusted to obtain the desired number of atoms per unit area make 
a single unit cell thick layer of PbSe and VSe2, respectively. The number of atoms/Å2 per 
repeating unit for each element in the precursors were measured using XRF.27 There is 
good agreement between the experimental and targeted number of atoms/Å2 of each 
element in each precursor (Figure IV.1).  
109 
  
 
 
Figure IV.1. The calculated number of atoms per square Angstrom for V, Pb, and Se based 
on bulk lattice parameters are shown as solid lines. The measured amounts of each element 
in the precursors are shown as filled circles.  The deviations from the calculated number 
reflect the experimental challenges of controlling the deposition process to fractions of a 
monolayer. AD: as-deposited precursor. 
  
 The nanoarchitecture of the precursors was measured using XRR and the data is 
presented in Figure IV.2. The XRR scans of each of the precursors contain Bragg 
reflections from the artificial layering of the elements and weaker subsidiary maxima from 
the finite thickness of the film. The first order Bragg reflections shift to lower angles as the 
number of Pb|Se building blocks increases due to the increased thickness of the repeating 
structure. Precursor modulation lengths (λ) calculated from the first order reflection 
linearly increase with the number of Pb|Se building blocks in the precursor (Figure IV.2 
inset) and the measured thicknesses are all reasonable for the targeted heterostructures. The 
presence of the subsidiary maxima (Keissig fringes33) to greater than 5° 2θ indicates that 
the films are smooth, with roughness calculated using the formula derived by Parratt of 
less than 6-8 Å across the analytical area.34 The combination of the XRF and XRR data 
110 
  
indicate that each precursor has close to the targeted amount of each element per unit area 
and the desired nanoarchitecture to form the targeted [(PbSe)1+δ]m(VSe2)1 heterostructures.  
 
 
Figure IV.2. The x-ray reflectivity patterns of the precursors designed to form the targeted 
[(PbSe)1+δ]m(VSe2)1 compounds. The modulation length of the (Pb|Se)mV|Se layer 
sequence determined from the position of the first order Bragg reflection is graphed versus 
the number of Pb|Se layers (m) in the repeating layer sequence in the inset.  
  
 The optimum annealing conditions to self-assemble the target heterostructures from 
the precursors were determined by an annealing study of the precursor with a 4(Pb|Se) + 
(V|Se) repeating sequence. The sample was annealed at a sequence of increasing 
temperatures for 1 hour in an inert atmosphere and changes in structure was followed by 
collecting specular and in-plane x-ray diffraction scans after each annealing temperature. 
Specular x-ray diffraction scans (Figure IV.3) were used to track changes in long range 
order in the c-axis direction in the film. The as-deposited diffraction pattern contains low 
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angle reflections from the artificial modulation of the deposited elemental layers and broad 
high order reflections (20-40° 2θ) indicating the film has begun to self-assemble with a 
period consistent with the targeted heterostructure. The reflections from both phenomena  
 
 
Figure IV.3. X-ray reflectivity and specular x-ray diffraction patterns collected as a 
function of increasing temperature after annealing a 4(Pb|Se)(V|Se) precursor at the 
indicated temperatures for 1 hour.  
 
can be indexed as 00l reflections. The period of the low angle reflections (30.21(1) Å) is 
reasonably close to that expected from the repeating structure deposited. The c-axis lattice 
parameter of the developing heterostructure is slightly larger, 30.67(3) Å. The higher angle 
reflections become narrower and more intense after the sample is annealed at 200°C, 
indicating the start of crystal growth of one or both constituent layers at this temperature, 
resulting in a more coherent structure. After the 250, 300 and 350°C annealing periods, the 
intensity of the reflections increase, indicating continued crystal growth. There are only 
small changes in the peak locations, however, indicating a near constant c-axis lattice 
parameter. The low angle reflections become broader and shift to higher angle as annealing 
temperature is increased, becoming consistent in line width and c-axis lattice parameter 
112 
  
with the higher angle reflections of the heterostructures after the 300°C anneal. The Laue 
reflections from the finite number of unit cells in the film also increase in intensity, 
indicating that a coherent structure is forming with a uniform number of unit cells across 
the analytical area. After the 400°C annealing, the superlattice reflections are almost 
completely absent, suggesting that the heterostructure has decomposed. The two intense 
reflections remaining can be indexed as 002 and 004 reflections of PbSe. The broad 
reflection at ~14° 2θ is consistent with the 001 reflection of small VSe2 crystallites. This 
suggests that at 400°C there is enough energy to disproportionate the heterostructures into 
a mixture of the binary constituents. The targeted heterostructures with thicker PbSe layers 
are less thermally stable than [(PbSe)1+δ]1(VSe2)1 which was reported to be stable at 
400°C.35 
 
Figure IV.4. In-plane X-ray diffraction patterns collected as a function of increasing 
temperature after annealing a (V|Se) + 4(Pb|Se) precursor at the indicated temperatures for 
1 hour. 
  
 In-plane diffraction patterns were collected during the annealing study to follow the 
evolution of the in-plane structure of the films and are shown in Figure IV.4. In the as-
deposited precursor, broad reflections are present that can be indexed as hk0 reflections of 
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a hexagonal and a square lattice. The reflections shift to slightly higher angles after the 
sample is annealed at 100°C. The lattice parameters of the hexagonal (a = 3.393(4) Å) and 
square lattices (a = 6.0891(2) Å) above 100°C are close to the lattice parameters of bulk 
VSe232 and PbSe.31 There is a significant increase in the intensity of the 110 VSe2 peak 
after annealing at 200°C, suggesting that significant crystal growth of VSe2 occurs at this 
temperature. Intensities of both the VSe2 and PbSe reflections continue to increase as the 
annealing temperature is increased up to 350°C. Weak reflections are present with odd 
indices for the square constituent. The reflections are consistent with the condition that h 
+ k = 2n, indicating that the PbSe bilayer is distorted from the bulk face centered cubic 
structure. Both constituents are still present at 400°C, although the intensity of all 
reflections are lower and the reflections with odd indices in the square lattice are no longer 
detectable. This suggests that the loss of the heterostructure reflections in the specular 
diffraction data after annealing at 400°C results from disproportionation of the 
heterostructure into PbSe and VSe2 regions. The broad 001 reflections for VSe2 in the 
specular scan indicate that large crystallographically-aligned domains of VSe2 do not form. 
The specular and in-plane diffraction data collected as a function of annealing temperature 
suggest that optimal processing conditions to convert the 4(Pb|Se)-(V|Se) precursor into 
[(PbSe)1+δ]4(VSe2)1  is 300°C for 1 hour. 
 The absolute amounts of each element in each layer were found to be very 
important in controlling whether the targeted compounds self-assembled. The low 
temperature of the substrate during the deposition limits surface diffusion rates, so atoms 
cannot move far before being buried by the incoming flux of atoms. The diffraction data  
 
114 
  
 
Figure IV.5. Proposed reaction pathway for the formation of products from a 3(Pb|Se) + 
1(V|Se) precursor. The pathway depends on the absolute number of atoms per repeat unit 
of the precursor. The thermodynamic product is a disproportionation of the precursor into 
isolated regions of PbSe and VSe2. 
 
in the annealing study indicate that both PbSe and VSe2 nucleate and grow during the 
deposition. If the amount of each bilayer (Pb|Se or V|Se) deposited corresponds to a 
complete single structural unit and nucleation occurs during the deposition, then the 
precursor layers develop significant long range order during the deposition (Figure IV.5, 
Scheme II). If the amount of a deposited element deviates from the targeted value, then the 
115 
  
extra (or missing) atoms result in partial layers. This increases the roughness in the layers 
and causes nucleation of the binary structures at different heights relative to the substrate. 
Annealing the sample at elevated temperatures activates diffusion, enabling atoms to move 
around to lower the free energy by eliminating defects and optimizing local coordination 
geometries Off-composition samples have partial layers in addition to interstitials and/or 
vacancies in the heterostructures (Figure IV.5, Scheme III). If the number of atoms in each 
layer deviates significantly from that required for an integer number of layers, then 
disproportionation occurs during annealing (Figure IV.5, Scheme I). The ability to 
determine the number of atoms of each element per repeating layer in the precursor using 
XRF is a critical advance, as it speeds up optimization of the deposition process and also 
enables us to predict which precursors are likely to form the targeted compounds.  
 Our assumption in this study is that precursors with the correct composition and 
nanoarchitecture, when annealed in the right conditions, should assemble to the target 
structure. We annealed the four precursors whose data is contained in Figures IV.1 and 
IV.2 using the optimized processing parameters and the specular diffraction patterns of the 
resulting compounds are shown in Figure IV.6. All the peaks in the diffraction patterns can 
be indexed as 00l reflections, consistent with heterostructures forming with their c axis 
perpendicular to the substrate. The c-axis lattice parameters of the annealed sample have a 
linear relationship with the number of PbSe bilayers in each repeat unit, which is consistent 
with the modulation length of the as precursors being preserved as they crystallize. The 
average change in c-axis lattice parameter per PbSe bilayer added (6.12(1) Å) is within 
error of the c-lattice parameter of bulk rock salt PbSe (6.1213(8) Å)31 and equivalent PbSe  
 
116 
  
 
Figure IV.6. Specular x-ray diffraction patterns of [(PbSe)1+δ]m(VSe2)1 (m = 1, 2, 3, 4) 
heterostructures. 
 
bilayer thicknesses found in other heterostructures ([(PbSe)1+δ]m(NbSe2)1) (6.12) and 
([(PbSe)1+δ]1(TiSe2)n)), (6.13(6) Å).36,37 PbSe bilayer thicknesses in [(PbSe)1+δ]1 (NbSe2)n 
and [(PbSe)1+δ]m(MoSe2)n are slightly greater than found in this work.7,38 Since there is 
only one VSe2 in each repeat unit, the y-intercept of a graph of the c-axis lattice parameter 
versus the number of PbSe bilayers (Figure IV.SI1) is greater than observed in bulk VSe2, 
as the intercept is the sum of the average thickness of each VSe2 trilayer and the thickness 
of the van der Waals gap. The PbSe and VSe2 thicknesses obtained from this graph are 
close to their respective bulk equivalents and previous work on PbSe- and VSe2-containing 
heterostructures. The c-axis lattice parameters of the PbSe-containing heterostructures are 
very close to those reported previously for analogous SnSe containing heterostructures 
(Figure A.1), and the change in inter-VSe2 distances as m increases are similar. 
 The low angle x-ray reflectivity patterns (Figure IV.7) contain Kiessig fringes / 
Laue reflections between Bragg reflections extending to high angles, indicating that the  
 
117 
  
 
Figure IV.7. Low angle x-ray reflectivity patterns of [(PbSe)1+δ]m(VSe2)1 (m = 1, 2, 3, 4) 
heterostructures. 
 
films consist of a consistent number of unit cells over the analytical volume. The films 
become smoother after annealing, with roughness decreasing to 4-6 Å, as evidenced by the 
increase in the number of observed Kiessig fringes. Indexing the low angle Kiessig fringes 
and using a modified version of Bragg's law corrected for refraction enabled us to calculate 
the total film thicknesses. Each film has a total thickness of approximately 50 nm, 
consistent with the targeted thicknesses. Dividing the total film thickness by the calculated 
c-axis lattice parameter of the heterostructures yields the integral number of unit cells in 
the films. The number of repeat units formed calculated from the number of Kiessig fringes 
between Bragg peaks (Table IV.1) and the number of repeat units deposited are equal to 
one another, except in the m = 1 sample, where the number of unit cells formed is two less 
than the number of deposited layers. XRF data show that there is an increase in oxygen in 
this film after annealing; suggesting that the two layers might have been lost to oxidation 
at the top of the film. The specular diffraction data indicate that each Pb|Se and V|Se bilayer 
118 
  
in the deposited precursors crystallizes a PbSe bilayer or VSe2 layer in the targeted 
structures. 
 
Table IV.1: Structural parameters calculated from the x-ray reflectivity and specular x-ray 
diffraction patterns. 
 
m,n c-axis lattice Total film targeted # of parameter (Å) thickness (Å) # of layers layers 
1,1 12.273(4) 481.3(3) 39 41 
2,1 18.343(8) 492.5(2) 27 27 
3,1 24.486(9) 491.8(3) 20 20 
4,1 30.617(9) 493.3(4) 16 16 
 
 The in-plane diffraction patterns of the [(PbSe)1+δ]m(VSe2)1 (m = 1, 2, 3, 4) 
heterostructures are shown in Figure IV.8. All of the reflections can be indexed as hk0 
reflections of a hexagonal and a square in-plane unit cell, consistent with the formation of 
VSe2 and PbSe layers in the heterostructures. This indicates that the film has a preferred 
alignment with the c-axis perpendicular to the substrate, consistent with the specular 
diffraction data. The hexagonal basal plane unit cell with a lattice parameter of 3.40-3.43 
Å is consistent with that reported for VSe2.32 The square basal plane unit cell is smaller for 
the m = 1 compound (6.03 Å)) than for the m = 2 - 4 compounds (6.11-6.13 Å), but all are 
close to that reported for PbSe.31 However, the hk0 Bragg reflections where h and k are 
both odd, forbidden in an undistorted rock salt structure, are observed. The presence of 110 
and 130 reflections indicates that Pb and Se are not located at (0,0) and (½,½) respectively 
in the intergrowth. A possible distortion that may give rise to these forbidden reflections is  
119 
  
 
Figure IV.8. Grazing incidence in-plane diffraction of self-assembled [(PbSe)1+δ]m(VSe2)1 
(m = 1, 2, 3, 4) heterostructures. 
 
 
Table IV.2: In-plane lattice parameters derived from the diffraction patterns via LeBail 
fitting. Misfit lattice parameters were calculated using the lattice parameters and the 
stoichiometric coefficients of each constituent.  
 
m,n a-axis lattice a-axis lattice parameter, VSe2 (Å) parameter, PbSe (Å) Misfit parameter, δ 
1,1 3.425(1) 6.030(1) 1.12 
2,1 3.447(1) 6.116(1) 1.10 
3,1 3.404(1) 6.106(5) 1.08 
4,1 3.408(1) 6.130(1) 1.07 
 
a lateral translation of one of the PbSe layers relative to one another. The intensities of the 
forbidden reflections decrease as the thickness of the PbSe constituent is increased, 
indicating that the magnitude of the distortion decreases. Forbidden reflections have also 
been observed in the in-plane diffraction patterns of [(PbSe)1.14]1(NbSe2)n 
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heterostructures,39 suggesting that a distortion is a common feature of PbSe bilayers flanked 
by dichalcogenides in ferecrystals.  
 HAADF-STEM was collected to show the bonding arrangement of the atoms in the 
film and the relationship between the PbSe and VSe2 layers in the heterostructures. This 
information is not present in the specular and in-plane diffraction patterns due to the 
preferred alignment in the films. The HAADF-STEM image of a representative portion of 
the [(PbSe)1+δ]3(VSe2)1 sample is shown in Figure IV.9a. Both constituents are clearly 
distinguishable from each other because the PbSe layers are significantly brighter than the 
VSe2 layers. The microscopy data confirms that the film consists of alternating layers of 
PbSe (6 planes or three bilayers) and one VSe2 trilayer. Defects are clearly present, 
presumably due to different nucleation sites that grow together during the self-assembly 
process. The atoms in the VSe2 layers, when viewed down the <110> zone axis, appear 
along a diagonal line, indicating that the V atoms are octahedrally coordinated, similar to 
the bulk binary compound.40 The PbSe layers, observed down <100> and off-axis zones, 
both show that it has a structure similar to the rock salt structure found in the analogous 
[(PbSe)1+δ]m(WSe2)n heterostructure.41 The integrated intensity profile across the slice of 
the image provides the positions of the atomic planes along the c-axis as shown in Figure 
IV.9b. The average atomic plane distances between Pb/Se planes, shown in the right of 
Figure IV.9b, are all within error of each other. This is different from what was observed 
in the analogous compound [(PbSe)1+δ]3(MoSe2)1, where the PbSe planes had alternating 
short and long distances indicating discrete bilayers.42 The lack of this distortion in 
[(PbSe)1+δ]3(VSe2)1 perhaps results from a change in the interaction between the PbSe and  
 
121 
  
 
Figure IV.9. (a) HAADF-STEM image of the [(PbSe)1+δ]3(VSe2)1 heterostructure showing 
the film consists of PbSe (bright rows) and VSe2. 
 
dichalcogenide layers due to the change in electronic properties of the dichalcogenide 
(trigonal prismatic MoSe2 is semiconducting43 while octahedral VSe2 is metallic44). The 
availability of available states in metallic VSe2 will result in virtual states between PbSe 
and VSe2 as found at metal-semiconductor interfaces.45 The reduced distortion in the PbSe 
layer in [(PbSe)1+δ]3(VSe2)1 relative to [(PbSe)1+δ]3(MoSe2)1 indicates a weaker interaction, 
consistent with the reduced kinetic stability of [(PbSe)1+δ]3(VSe2)1 relative to 
[(PbSe)1+δ]3(MoSe2)1.42 The distance between the metal plane in the dichalcogenide to the 
average position of Pb/Se distance in the V-compound is 10% smaller (4.5(1) Å) than in 
the Mo-compound (5.0 Å), reflecting both the different coordination in the dichalcogenide 
and the different interaction between PbSe and the different dichalcogenides. In Figure 9a, 
122 
  
multiple zone axes for the PbSe layers are observed, indicating rotational disorder between 
the constituents.  
 
Figure IV.10. Results of a Rietveld refinement of the corresponding specular x-ray 
diffraction of the heterostructure and a comparison of the structural model refined to the 
HAADF-STEM-derived atomic positions. 
 
 Fractional z-axis coordinates obtained from the HAADF-STEM analysis of the 
[(PbSe)1+δ]3(VSe2)1 heterostructure were used as an initial model for a Rietveld refinement 
of the specular diffraction data. The diffraction data, calculated diffraction intensities from 
the refined structural model and the difference between them are shown in Figure IV.10, 
along with the refined structural model. The consistency between the structure derived 
from the HAADF-STEM and Rietveld refinement of the x-ray diffraction suggests that the 
majority of the film consists of the heterostructure. The Pb and Se planes are not coincident 
and there is an alternation of short and long distances between Pb (or Se) planes consistent 
with the formation of PbSe bilayers. This distortion is smaller than that observed in 
[(PbSe)1+δ]3(MoSe2).42  
  
123 
  
 
Figure IV.11. Room temperature Seebeck coefficients and resistivity graphed as a function 
of the number of PbSe bilayers in the respective compounds. 
 
 Resistivity, Hall coefficients and Seebeck coefficients were measured to investigate 
the impact of the increased PbSe thickness and associated structural changes on electrical 
transport properties. Since PbSe is semiconducting46 and VSe2 is metallic44, conduction in 
the compounds studied here is expected to take place primarily in the VSe2 layers as 
previously reported for [(PbSe)1+δ]m(NbSe2)1 and [(PbSe)1+δ]1(VSe2)n ferecrystals and 
misfit layer compounds containing metallic dichalcogenides.22,36 The room temperature 
resistivity of [(PbSe)1+δ]1(VSe2)1 is consistent with previously published values,22 and the 
resistivity values systematically increase as m increases (Figure IV.11). The differences in 
the resistivity between samples with adjacent m values decrease as m increases. The 
increase in resistivity as m increases was expected since a larger fraction of the film consists 
of semiconducting PbSe as m increases. The room temperature resistivity values for the 
[(PbSe)1+δ]m(VSe2)1 compounds, however, are approximately twice as large as those 
reported for the analogous [(SnSe)1+δ]m(VSe2)1 compounds.21 We speculate that this is a 
consequence of the differences in the band gaps of SnSe and PbSe and a difference in the 
alignment of the VSe2 bands with those of SnSe and PbSe. The room temperature Seebeck 
124 
  
coefficients are positive and the magnitude is typical for metallic behavior. The Seebeck 
coefficients, however, do not systematically increase as m is increased, which would be 
expected from the decrease in carrier concentration. The larger than expected Seebeck 
coefficient for the [(PbSe)1+δ]1(VSe2)1 compound suggests that transport in this compound 
is more complicated, perhaps because only a 0.6 nm bilayer of PbSe separates the VSe2 
layers.  The wave function tails of VSe2 within the PbSe layer overlap more in 
[(PbSe)1+δ]1(VSe2)1 than in the compounds with thicker PbSe layers. 
 The resistivity and carrier concentrations calculated from Hall coefficients 
assuming a single band are graphed in Figure IV.12 as a function of temperature. The room 
temperature Hall coefficients are all positive and change systematically as m is increased, 
indicating that holes are the majority carrier and that a decrease in carrier concentration 
causes the increase in resistivity as m increases. The carrier concentrations calculated 
assuming a single band model are in the range expected for a metal, consistent with the 
data presented in Figure IV.11. The sign of the Hall coefficient is opposite to that reported 
for bulk VSe2. The temperature dependence of the resistivity of the different 
[(PbSe)1+δ]m(VSe2)1 compounds are all very similar. Between 150 and 300 K, the resistivity 
slowly decreases with decreasing temperature as expected for a metal. The rate of the 
decrease is 2-3 times smaller than that found in bulk VSe2, suggesting a reduced electron-
phonon scattering. Between 90 and 105 K, depending on the value of m, the resistivity 
rapidly increases to a value at about 20 K that is 2-3 times larger than the room temperature 
value. This substantial increase in the resistivity is different from what is found in bulk 
VSe2 and similar to the reported for the analogous [(SnSe)1+δ]m(VSe2)1 compounds, which  
 
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Figure IV.12. (a) Temperature dependence of resistivity and (b) carrier concentrations 
calculated from Hall coefficients assuming a single band model for [(PbSe)1+δ]m(VSe2)1 (m 
= 1, 2, 3, 4) heterostructures. Inset of top plot shows a comparison of the CDW transition 
temperatures for [(PbSe)1+δ]m(VSe2)1 and [(SnSe) 1+δ]m(VSe2)1 compounds. 
 
was shown to be caused by a charge density wave transition.21 The transition in 
[(PbSe)1+δ]1(VSe2)1 is sharper than in the compounds with thicker PbSe layers and occurs 
at approximately 90 K. For the other three compounds, the transition is broader and the 
transition temperature occurs at slightly higher temperature. The addition of PbSe bilayers 
to the [(PbSe)1+δ]1(VSe2)1 does not systematically increase the charge density wave 
transition temperature (Figure IV.12a inset), as was observed in [(SnSe)1+δ]m(VSe2)1 
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compounds.21 The ~10 K increase in the CDW onset temperature as m is increased is also 
significantly smaller than the increase observed for [(SnSe)1+δ]m(VSe2)1 compounds.21 
 The temperature dependence of the carrier concentrations provides additional 
information, although we unfortunately were not able to measure the Hall coefficient for 
the higher m compounds below the CDW onset temperature. For the m = 1 compound, the 
carrier concentration has a strong temperature dependence, increasing as temperature is 
decreased from room temperature and then decreasing abruptly at the CDW onset. The 
temperature dependence suggests that a simple single band, free electron model is probably 
not appropriate for this compound. A similar temperature dependence was observed for 
[(SnSe)1+δ]1(VSe2)1. The carrier concentrations of the samples with thicker PbSe layers 
increase slightly as temperature decreases. The carrier concentration decreases as m is 
increased as the semiconducting PbSe dilutes the carriers from the metallic VSe2 layer. 
 A simple model for the electrical properties of the [(PbSe)1+δ]m(VSe2)1 compounds 
is to consider the sample to be a composite consisting of non-interacting parallel 
conductors. If we assume that the resistivity of the PbSe layer is much higher than the 
resistivity of the VSe2 layer, then it can be shown that   
ρVSe2 = ρexp [n/(m + n)]        Equation IV.1 
where ρexp is the measured resistivity, n is the number of VSe2 layers in the repeating unit 
(one for this set of samples), and m is the number of PbSe bilayers.36 If Equation IV.1 is 
valid, then the resistivity obtained for a monolayer of VSe2 from each compound will be  
 
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Figure IV.13. Calculated (a) resistivity and (b) carrier concentrations for a monolayer of 
VSe2 using Equation 1 and the data in Figure IV.11. If Equation1 is valid, the resistivity 
and carrier concentration calculated from each of the compounds should be the same. 
 
the same. Equation IV.1 also describes the expected change in carrier concentration 
assuming composite behavior. Figure IV.13 graphs the temperature dependence of the 
resistivity and carrier concentration of a VSe2 monolayer obtained from each compound 
using this equation. The calculated resistivity of the VSe2 monolayer increases as m 
increases, with the m = 3 and 4 samples having very similar resistivity values. The 
calculated carrier concentration for a monolayer of VSe2 from [(PbSe)1+δ]1(VSe2)1 data is 
higher than those calculated from the higher m compounds. The carrier concentrations are 
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very similar for the higher m compounds between 200 and 300 K. There is an increase in 
the carrier concentrations as the CDW transition temperature is approached. This suggests 
that the electrical properties can be described as that of a composite of a metallic VSe2 
monolayer separated by a non-conducting PbSe layer when m is 3 or greater. Though 
composite behavior is observed higher values of m, the electrical transport properties of 
[(PbSe)1+δ]m(VSe2)1 is still distinctly different from its bulk constituents. The CDW wave 
of the heterostructures is also distinctly different from bulk VSe2, with holes being the 
majority carrier and markedly different temperature dependences of resistivity and Hall 
coefficients, suggesting a distinctly different CDW in the VSe2 monolayers.  
 Since the wave function of the metallic VSe2 monolayer will extend into the 
semiconducting PbSe, which acts as a dielectric,45 this composite behavior suggests that 
when m is 3 the distance between adjacent VSe2 monolayers is large enough that the 
wavefunction tails in adjacent layers do not significantly overlap. The lower resistivity 
observed for the VSe2 monolayer in [(PbSe)1+δ]1(VSe2)1 would then result from the overlap 
of the wave function tails of adjacent VSe2 monolayers, as the bilayer of PbSe that separates 
them is only 0.6 nm thick.  
 It is interesting to compare the electrical properties of the [(PbSe)1+δ]m(VSe2)1 
compounds presented here with those reported previously for [(SnSe)1+δ]m(VSe2)1 
compounds21 and members of both families with thicker VSe2 layers. In both sets of 
compounds, the electrical data indicate that VSe2 monolayers are metallic and have a 
distinctly different charge density wave than that found in thicker VSe2 layers. Both 
compounds with m = n = 1 have similar changes in the carrier concentration calculated 
from the Hall coefficient assuming a single band model, increasing significantly as 
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temperature is decreased and then dropping precipitously at the CDW onset temperature. 
[(PbSe)1+δ]m(VSe2)1  compounds with m = 3 and 4 have composite behavior, however, 
while the analogous [(SnSe)1+δ]m(VSe2)1 compounds21 do not. This is perhaps related to 
the structural changes in the MSe layers as a function of thickness. In both PbSe and SnSe, 
there are two distortions that occur from a rock salt structure; a puckering distortion of the 
layers where the metal atoms are above and the Se atoms below the average plane, and an 
alternating long and short interlayer distance between MSe bilayers. Both of these 
distortions change systematically as m is increased. In the [(SnSe)1+δ]m(VSe2)1 
compounds21 the puckering distortion increases as m increases as the SnSe. In 
[(PbSe)1+δ]m(VSe2)1  compounds, however, both the puckering distortion and the difference 
between the inter- and intra- bilayers decrease as m increases. This difference in behavior 
is related to the different structures of SnSe and PbSe. SnSe has an orthorhombic structure 
at room temperature that becomes cubic as temperature is raised.47 A single bilayer of SnSe 
has a structure close to the cubic high temperature structure, and the structure approaches 
the bulk low temperature structure as layer thickness is increased.48 As many as 30 bilayers 
of SnSe are required to obtain lattice parameters that are consistent with the bulk struture.49 
PbSe, however, has a simple rock salt structure. A single bilayer of PbSe distorts from the 
rock salt structure and the distortion decreases as m increases and approaches the bulk 
structure when m is typically around 5 or 6.42 In the [(PbSe)1+δ]m(VSe2)1 series, however, 
the structure seems to be approaching the bulk quicker. The transition from a new material, 
with properties distinct from the constituent layers, to a composite of VSe2 monolayers 
separated by a PbSe nonconducting layer occurs at 3 to 4 PbSe bilayers based on electrical 
properties. 
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IV.4 Conclusions 
 In this work we showed that the compounds [(PbSe)1+ δ]m(VSe2)1 with m from 1 to 
4 could be prepared from designed precursors. The correct local number of atoms per unit 
area per repeating unit and the correct nanoarchitecture was necessary for the precursor to 
self-assemble into the targeted metastable products during low temperature annealing. The 
compounds with larger m values are less kinetically stable than [(PbSe)1+δ]1(VSe2)1 and the 
precursors need to be closer to the targeted number of atoms per unit area. Diffraction data 
and HAADF-STEM images indicate that PbSe in the heterostructures has a lower 
symmetry structure than face centered cubic, presumably due to the interface and interlayer 
interactions. All of the [(PbSe)1+δ]m(VSe2)1 compounds have an abrupt increase in 
resistivity as temperature is decreased, which is consistent with a charge density wave. The 
onset temperature of the CDW transition does not change significantly as m is increased. 
The transport behavior for the m = 3 and 4 compounds can be described using a composite 
model consisting of a conducting monolayer of VSe2 and a non-conducting PbSe layer that 
do not interact. The difference in the rock salt layer thickness dependence of the CDW 
transition temperature between members of [(PbSe)1+δ]m(VSe2)1  and [(SnSe)1+ δ]m(VSe2)1 
which have approximately the same VSe2 inter-layer distance, suggests that the identity of 
the intervening constituent and its interaction with the VSe2 monolayer determines the 
CDW onset temperature. 
 
IV.5 Bridge 
 The charge density wave properties of VSe2-containing heterostructures is not 
strongly dependent on the inter-VSe2 separation. Rather, it is strongly dependent on the 
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identity and chemistry of the intervening material separating VSe2 monolayers. We 
highlight the importance of controlling nanoarchitecture and the number of atoms per 
square Angstrom in the successful targeting of [(PbSe)1+δ]m(VSe2)1 compounds. This work 
opens up opportunities for targeting other PbSe- and VSe2- containing heterostructures. 
The next chapter discusses our work on the synthesis and stability of [(PbSe)1+δ]q(VSe2)1 
compounds, where q is 1 to 11 and the number of PbSe monolayers, which is made possible 
by the ability to measure sub-monolayer quantities by XRF and precise control over 
precursor nanoarchitecture. 
  
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CHAPTER V 
 
THE INSTABILITY OF MONOLAYER THICK PbSe ON VSe2 
 
 
Authorship Statement 
 At the time of writing this manuscript is unpublished. A paper is to be submitted 
with me as the primary author, Mina Buchanan, Taryn M. Kam, Shannon S. Fender, Renae 
F. Gannon, Robert Fischer, Dr. Ping Lu, Dr. Benjamin Hanken, and Dr. Mark Asta, and 
Dr. David C. Johnson. Mina Buchanan performed annealing studies for the precursors. 
Taryn M. Kam and Shannon S. Fender assisted in the analysis of x-ray diffraction data. 
Renae N. Gannon, Robert Fischer, and Dr. Ping Lu collected HAADF-STEM data. Dr. 
Benjamin Hanken and Dr. Mark Asta provided the computational data. Dr. David C. 
Johnson is my advisor and consulted in preparation of the manuscript. 
 
V.1 Introduction 
 The discovery of 2-dimensional materials with so called emergent properties, those 
not observed in the constituent bulk compounds, has resulted in a boom in research on 
monolayers, heterostructures and ultrathin materials.1 The expansion of this field is fueled 
by predictions of unusual quantum states and properties that might be observable in 2D 
materials, including unusual quantum spin Hall states,2,3 Weyl Fermions,4 indirect to direct 
band gap transitions,5 and topological states.6 The surfaces and interfaces in 2D materials 
are responsible for many of the observed emergent properties. In monolayers, the lack of 
adjacent layers removes bonding and antibonding interactions between layers, which can 
result in property changes such as the transition from an indirect to a direct band gap in 
MoS2.5 Interlayer coupling at the non-epitaxial interface between constituents in 
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heterostructures can produce new properties, for example charge transfer can cause 
modulation doping in heterostructures.7,8 The interaction between layers can also prompt 
structural changes, such as the formation of octahedrally coordinated MoSe2 when layered 
with BiSe.9 The rapid development of this field experimentally was initially driven by the 
ability to obtain monolayers of naturally layered compounds via mechanical cleaving10,11 
and the ability to detect thicknesses rapidly using optical techniques.12 The large interest 
in 2D materials as potentially important components of new technologies has resulted in 
the development of additional approaches to synthesizing films with precise control of 
thickness and heterostructures with controlled nanoarchitecture.11,13 
 While initially focused on materials with layered structures with obvious cleavage 
planes, recent theoretical papers have predicted unusual properties associated with 2D 
layers of materials with three dimensional structures.14–19 Preparing 2D layers of materials 
with 3D structures, however, is synthetically more challenging than for structurally 2D or 
layered compounds. As a material becomes more 3D, cleaving thin layers in desired 
directions becomes increasingly more difficult. During vapor phase growth, the strength of 
the interaction between the growing layer and the substrate is very important. If the 
interaction between the layer and the substrate is too strong, it will modify the electronic 
structure that is being targeted synthetically. If the interaction between the layer and the 
substrate is too weak during, there will be a tendency to form islands rather than continuous 
thin films of uniform thickness. Recent calculations have predicted that a free-standing 
monolayer PbSe could be a 2D topological crystalline insulator, with Dirac-cone-like edge 
states.20 PbSe ultra thin films have been grown on SrTiO3 substrates by co-depositing Se 
and Pb atoms, forming crystalline PbSe islands after post-annealing.21 A large compressive 
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strain exists in the epitaxial few-layers PbSe islands, with the lattice parameters changing 
from 5.85 Å  for a 3 monolayer thick island to 6.1 Å  for a 9 monolayer thick island 
compared to 6.14 Å for bulk PbSe. The large change in lattice parameters indicates a strong 
interaction between the substrate and the PbSe. The data presented suggest that the PbSe 
islands have Dirac-cone-like edge states. The distortion of the lattice with thickness also 
impacts properties, in addition to layer thicknesses. 
 Here we report our investigation of the growth of monolayer and controlled 
thickness PbSe layers between transition metal dichalcogenide layers, prompted by the 
thermodynamic stability of misfit layered compounds containing well defined bilayers of 
PbSe alternating with dichalcogenides.22,23 Precursors were deposited to mimic the 
nanoarchitecture of [(PbSe)1+y]q(VSe2)1 heterostructures where q is an integer number of 
PbSe monolayers. The precursors with even layer and with q ³ 7 thicknesses had the 
expected as deposited nanoarchitecture and evolved into the desired heterostructures. 
Surface diffusion during the deposition process of the q = 1, 3 and 5 precursors, however, 
resulted in more complex initial nanoarchitectures, which impacted the resulting self-
assembly of products. Consistent with the as deposited nanorarchtecture, the q = 5 sample 
formed the [(PbSe)1+d]4(VSe2)1[(PbSe)1+d]6(VSe2)1, heterostructure, the q = 3 sample 
formed [(PbSe)1+d]2(VSe2)1[(PbSe)1+d]4(VSe2)1 and the q = 1 sample disproportionated into 
regions of [(PbSe)1+d]2(VSe2)1 and VSe2. DFT calculation of PbSe rock salt blocks of 
various thickness separated by vacuum yielded structural distortions that matched the 
experimental data and an odd-even alternation in energy as a function of layer thickness.  
The computational and experimental reveal that for small values of odd q, the formation of 
the PbSe rock salt block on a dichalcogenide is not kinetically stable and has a higher 
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energy compared to disproportionation its adjacent (q+1 and q-1) even counterparts.  The 
preparation of monolayer thick PbSe will require finding a substrate that has a stronger 
film-substrate interaction. 
 
V.2 Experimental 
 Precursors were deposited on <100> Si wafers with the native oxide using a 
custom-built physical deposition chamber described by Fister et al.31 Elemental V 
(99.995% Alfa Aesar), and Pb (99.8% Alfa Aesar) were deposited using 6 keV electron 
beam guns while elemental Se (99.99% Alfa Aesar) was deposited using a Knudsen 
effusion cell. Elemental layers were deposited by exposing the substrate to a plum of atoms 
from the heated sources. The time the substrate is exposed is controlled by pneumatic 
shutters that close after the desired thickness has been deposited. The desired thickness was 
measured using a quartz crystal microbalance and the sequence and thickness of elemental 
layers can be controlled by custom LabView software. The number of atoms of each 
element deposited is optimized by measuring the x-ray fluorescence (XRF) of the films ex-
situ using a Rigaku Primus II ZSX spectrometer. The measured XRF intensities are 
converted into the number of atoms per unit area for each constituent as described by 
Hamman et al.24 The period of the deposited sequence of layers was measured using X-ray 
reflectivitiy (XRR). 
 Ex-situ annealing was performed on a hot plate in an inert N2 atmosphere (O2 < 0.8 
ppm). The changes as a function of annealing temperature and time were followed using 
x-ray diffraction. Specular x-ray diffraction (XRD) and X-ray reflectivity (XRR) were 
collected on a Bruker D8 Diffractometer with Cu-Ka radiation (l = 0.15418 nm). Grazing 
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incidence in-plane x-ray diffraction (GIPXRD) was collected on a Rigaku Smartlab 
Diffractometer, also with Cu-Ka radiation (l = 0.15418 nm). LeBail fitting of the GIPXRD 
data was performed on the FullProf Suite.32 
 An FEI TitanTM G2 80-200 STEM with a Cs probe corrector and ChemiSTEMTM 
technology (X-FEGTM and SuperXTM EDS with four windowless silicon drift detectors) 
operated at 200 kV was used in this study.  HAADF images were recorded with an electron 
probe of size (FWHM) of about 0.13 nm, convergence angle of 18.1 mrad and current of 
~75 pA, and an annular dark-field detector with a collection range of 60-160 mrad.    
 
V.3 Results and Discussion 
 A sequence of precursors was designed that mimics the targeted structures that 
contain the correct number of atoms of each element in a repeating sequence of elemental 
layers. We calculated the number of atoms needed to form a monolayer of rock salt 
structured PbSe in a <001> plane and a VSe2 trilayer from the in-plane lattice parameters 
of each constituent in [(PbSe)1+d]1(VSe2)1, which contains a bilayer of PbSe alternating 
with VSe2.23 Figure V.1 shows the number of atoms of each element required to form 
[(PbSe)1+d]q(VSe2)1 compounds plotted as a function of q, where q is the number of PbSe 
monolayers. To prepare the compounds where q is even, we deposited a repeating unit 
(RU) of the sequence of elemental layers [V|Se + q/2(Pb|Se)] r times, where each V|Se 
bilayer is targeted to have the number of atoms required to form a VSe2 layer and each 
Pb|Se layer is targeted to have the number of atoms required to form a PbSe bilayer. To 
prepare the compounds where q is 1, 3, 5, 7 or 9 monolayers (1.5, 2.5, 3.5 and 4.5 bilayers), 
we deposited a similar sequence of elemental layers, where each Pb|Se layer contained the 
137 
  
either the number of atoms required to form a monolayer or a bilayer of PbSe such that the 
total number of layers atoms deposited equaled the value needed for q monolayers. For 
example, to prepare a 7-1 precursor, we deposited the RU sequence [V|Se + 3(Pb|Se)bilayer+ 
1(Pb|Se)monolayer]. 
 
 
Figure V.1. The targeted number of atoms per square Angstrom for each element per repeat 
unit for each of the designed precursors are shown as lines. The circles are the amounts 
determined using XRF data. 
 
 The compositions and structures of the deposited precursors were determined using 
XRF, XRR and XRD. The total number of atoms of each element deposited in each 
precursor was measured using XRF and the average number of atoms per repeating unit 
was obtained by dividing the total by the number of repeating units deposited.24 The 
measured number of atoms per unit area deposited for each precursor are shown as circles 
in Figure V.1. The number of V and Pb atoms per unit area of all of the odd number 
precursors are within 5% of the calculated values. The deviations from the calculated lines 
are a consequence of the challenges of depositing targeted numbers of atoms per unit area 
that are on the order of a monolayer of each element. Excess Se is observed in some 
precursors, but the excess was anticipated to evaporate during the annealing process. The 
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precursors all contain close to the number of atoms of each element in the repeating 
sequence of layers to form the targeted compounds. 
 
 
Figure V.2. X-ray reflectivity patterns show that all precursors are smooth and the 
modulation is retained upon deposition.  
 
 The XRR patterns of the precursors contain intensity oscillations (Kiessig fringes) 
due to the finite thickness of the entire film and Bragg maxima due to the repeating 
sequence of elemental layers in the precursor (Figure V.2). The position of the first order 
Bragg reflection due to the layering of the precursor systematically shifts to lower angle as 
the thickness of the PbSe layer (q) is increased. For the q = 1 sample, the Bragg maxima is 
139 
  
much broader than for the other samples and shifted to lower angle than expected, 
indicating that the repeating period is thicker than the targeted value. The precursor 
modulation length, calculated from the total thickness divided by the divided by the number 
of repeating units deposited, is as expected from the deposition process (Figure V.4). This 
discrepancy suggests that there must have been long range surface diffusion during the 
deposition that resulted in the precursor consisting of domains with different structures. 
 
 
Figure V.3. X-ray diffraction patterns of all precursors show two different groups based 
on the relationship of the high angle peaks with the precursor modulation length. 
 
 The high angle diffraction patterns (Figure V.3) of the as deposited samples have 
high angle reflections that indicate that the samples have already begun to self-assemble 
140 
  
during the depositions. The positions of these weak reflections divide the precursors into 
two groups. The weak reflections for the precursors with even order q and odd q ≥ 7 
monolayers thick are at positions consistent with their being indexed as 00l reflections 
yielding a c-axis unit cell size consistent with the precursor modulation length and the 
targeted nanoarchitecture. The precursors with q = 1, 3 and 5 all have weak reflections in 
the high angle scans that cannot be indexed as 00l reflections from the precursor 
modulation length. For q = 3 and 5, the positions of the weak reflections indicate that the 
precursor modulation length is double that expected from the deposition sequence. For the 
q = 1 sample, the weak reflections are not related at all to the precursor modulation length, 
consistent with disproportionation during the deposition process.  
 
 
Figure V.4. The dependence of the precursor modulation length on the number targeted 
number of PbSe monolayers per RU.  
 
 The XRF, XRR and XRD data indicate that the precursors with q of 2, 4 and six or 
larger all have the correct the number of atoms of each element and the targeted 
nanoarchitecture. The precursor with q = 1 has the required number of atoms, however the 
XRR and XRD data indicates that nanoarchitecture is more complicated that the desired 
141 
  
sequence of a Pb|Se monolayer and a V|Se bilayer. The XRD data for the precursors with 
q = 3 and 5 indicates that these precursors have a modulation length that is twice that 
expected from the deposited sequence of layers. The precursor modulation length (l) 
calculated from indexing the 00l reflections for samples with q greater than 1 and plotted 
versus q, the number of PbSe monolayer per repeat unit are shown in Figure V.4. For the 
q = 3 and 5 samples, ½ of modulation length calculated falls where expected based on the 
deposition parameters, our XRF measurements and the thicknesses of the even layer 
thickness samples q = 2, 4 and 6. For the q = 1 sample, the modulation length calculated 
from the total thickness divided by the number of repetitions of the elemental layer 
sequence deposited is close to the extrapolated value from the even PbSe layer thickness 
samples. The linear relationship between the precursor modulation length and target 
number of PbSe monolayers has a slope of (3.01(6) Å), which is the thickness of an 
elemental Pb|Se layer with the number of Pb and Se atoms calculated to yield a monolayer 
of PbSe. The intercept (6.3(4) Å) is the thickness of the elemental V|Se bilayer with the 
number of atoms calculated to yield a VSe2 unit. The intercept is slightly thicker than the 
thickness of a crystalline VSe2 trilayer because the precursors do not fully crystallize during 
deposition and are less dense than fully crystallized layers. The linear relationship in 
Figures 1 and 4 reflects the reproducibility of the precursor preparation.  
 X-ray reflectivity (XRR) and specular x-ray diffraction (XRD) scans were collected 
after annealing the precursors at different temperatures to obtain information on how the 
structure of the precursors evolve. Three different behaviors were observed that depend on 
the number of target PbSe monolayers per repeating unit of the precursor.  
  
142 
  
 
Figure V.5. X-ray reflectivity data collected after annealing the q = 7 precursor at the 
designated temperatures. The blue dashed lines (---) are the expected peak positions for a 
[(PbSe)1+d]7(VSe2)1 heterostructure.  
 
 Precursors with even order q and odd q ≥ 7 monolayers thick evolved to form the 
targeted heterostructures.  The x-ray reflectivity scans collected on the q = 7 precursor 
(Figure 5) collected as a function of temperature illustrates this behavior. The 001 and 002 
reflections change in intensity and shift to lower angles as the annealing temperature is 
increased. The 003 reflection increases in intensity when the precursor is annealed between 
150 and 350 °C. The 004 reflection first appears after the 150ºC annealing and grows in 
intensity up to and including the 350°C annealing temperature. These changes all indicate 
that the nanoarchitecture is preserved and long range order increases as the sample self-
assembles into the targeted heterostructure. The Kiessig fringes due to the reflection of x-
rays from the top and bottom of the films and the Laue interference pattern due to the finite 
number of unit cells in the films are present at each step, suggesting that the films remain 
smooth throughout the annealing process. The film thickness decreases a small amount 
(<5%) as long range order develops. The number of diffraction orders decreases when the 
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precursors are annealed above 350°C as the sample, indicating that the initial 
nanoarchitecture is being lost. 
 
 
Figure V.6. Specular x-ray diffraction data collected after annealing the q = 7 precursor at 
the designated temperatures. The blue dashed lines (---) are the expected peak positions for  
[(PbSe)1+d]7(VSe2)1.  
 
 The specular diffraction patterns collected at higher angles as a function of 
annealing temperature support the conclusions drawn from the XRR data. Figure V.6 
contains the data collected on the q = 7 precursor. Broad high order 00l reflections (>15º) 
are observed in the as deposited precursor, indicating that the sample forms domains with 
significant long range order during the deposition. The higher angle reflections have the 
same periodicity (27.62(8) Å) as the low order (<15º) 00l reflections (27.6(3) Å), 
suggesting that the nucleated structure has the same layering of the precursor. As the 
temperature is increased to 350ºC, the low and high order 00l reflections increase in 
intensity and converge to have similar peak widths and to positions that give a c-lattice 
parameter of 27.52(6) Å. At 400ºC, the 00l reflections start to diminish and we see the 
growth of a broad VSe2 reflection at ~13°. At 450 ºC, the high angle scan contains only the 
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001 VSe2, and 002 and 004 PbSe reflections, while the XRR scan shows a very reduced 
intensity of the 001 reflection from the heterostructure. This suggests that the superlattice 
is decomposing to its thermodynamic products. 
 
 
Figure V.7. In-plane x-ray diffraction pattern of a q = 7 precursor annealed at 300ºC.  
 
 
 
Figure V.8. The c-lattice parameters of even and odd samples with q ≥ 7 monolayers as a 
function of q.  
 
 
 Further evidence for the formation of the targeted heterostructures at moderate 
annealing temperatures comes from grazing incidence in-plane x-ray diffraction 
(GIPXRD) of the precursors after annealing to 300°C and the systematic change in c-axis 
lattice parameters of the products as q is varied. The in-plane diffraction of the q = 7 
precursor after annealed at 300ºC, shown in Figure V.7, is representative of the samples 
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with even order q and odd q ≥ 7. All the observed reflections can be indexed as hk0 
reflections from either a hexagonal or a square unit cell. The in plane lattice parameter of 
the hexagonal unit cell (3.40(1) Å) is close to those reported for bulk VSe2 (3.359 Å). The 
lattice parameter of the square unit cell (6.12(1) Å) is close to that reported for bulk PbSe 
(6.122 Å). Since only 00l and hk0 reflections are observed in the specular and in-plane x-
ray diffraction respectively, the heterostructure is crystallographically-aligned to the 
substrate with the PbSe <100> and VSe2 <100>  planes parallel to substrate. The c-lattice 
parameters of the annealed q = even and q ³ 7 precursors are plotted against q and shown 
in Figure 8.  The linear relationship between the c-lattice parameters and q suggests that 
heterostructures in this category can be predictably synthesized with the correct precursor. 
The slope (3.07(1) Å) is close to the value of half of a PbSe unit cell (6.117 Å).25 The y-
intercept (6.06(9) Å) is close to the c-lattice parameters of bulk VSe2 (5.96-6.11 Å).26  
 HAADF-STEM images were collected on annealed precursors to provide 
additional structural information on the products formed. Figure V.9 contains 
representative images from the q = 7 sample. The whole film image (Figure V.9a) shows 
that there is a consistent layered structure over the entire sample. The higher magnification 
(Figure V.9b) shows that most of the sample consists of a repeating unit cell containing 1 
VSe2 and 7 PbSe monolayers. There are local regions, however, where a repeating 
sequence of  6 PbSe monolayers - VSe2 - 8 PbSe monolayers - VSe2 (Figure V.9b, white 
box) replaces two 7 PbSe monolayers -VSe2 sequences. This replacement is random and 
does not occur very often. The local information obtained from the HAADF-STEM data is 
consistent with the diffraction data discussed previously. The q = 7 sample forms mostly 
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[(PbSe)1+d]7(VSe2)1 with local regions consisting of 
[(PbSe)1+d]6(VSe2)1[(PbSe)1+d]8(VSe2)1. 
 
 
Figure V.9. Representative HAADF-STEM image of an annealed q = 7 precursor. 
 
 A different behavior as a function of annealing was observed for the q = 3 and 5 
precursors, where the as deposited precursors have reflections that suggest a doubling of 
the modulation length. XRR scans for the q = 3 precursor collected as a function of 
annealing temperature are shown in Figure V.10. Superimposed on the diffraction scan are 
blue vertical lines locating angles where reflections are expected from the targeted q = 3 
product and red lines vertical lines showing where additional reflections are expected for a  
147 
  
 
Figure 10. X-ray reflectivity data collected after annealing the q = 3 precursor at the 
designated temperatures. The blue dashed lines (---) are the expected peak positions for a 
[(PbSe)1+d]3(VSe2)1 heterostructure and the red solid lines are the expected positions for 
twice the unit cell size of the aforementioned.  
 
precursor with a doubled modulation length.  The 001 reflection of the precursor persists 
up to 400°C, but the expected second order reflection from the precursor does not appear 
(at the blue vertical dashed line at ~5.5 degrees). Reflections do grow in, however, at the 
approximate locations expected for the third and fifth order reflections from a doubled 
modulation length. The diffraction intensities decrease when annealed at 400°C and only 
Kiessig fringes from the interference between the front and back of the film remain after 
the 450°C anneal. Specular diffraction data collected on the q = 3 sample, shown in Figure 
V.11, provides additional information about the structural changes that occur during 
annealing. The diffraction pattern of the as deposited sample contains several higher angle 
reflections indicating long range ordering occurs during the deposition process to form a 
modulation length twice that which was expected. The high angle 00l reflections intensify 
for annealing temperatures between 150°C and 400°C and all of the observed reflections  
 
148 
  
 
Figure 11. Specular x-ray diffraction data collected after annealing the q = 3 precursor at 
the designated temperatures. The blue dashed lines (---) are the expected peak positions for 
a [(PbSe)1+d]3(VSe2)1 heterostructure and the red solid lines are the expected positions for 
twice the unit cell size of the aforementioned. 
 
can be indexed as 00l reflections of a unit cell with twice the repeating period expected 
from the deposited elemental layers. The positions of several reflections deviate from that 
calculated from the average c-axis lattice parameter (30.5(1) Å at 350°C), which is 
probably a consequence of stacking faults apparent in the HAADF-STEM data discussed 
in a later paragraph. Only 001 VSe2 and 002 and 004 PbSe reflections are observed in the 
specular scan after annealing at 450°C, indicating that the sample has disproportionated. 
In-plane x-ray diffraction data collected on a q = 3 precursor annealed at 300°C contains 
maxima that can be indexed as hk0 reflections from a hexagonal base (a = 3.42(1) Å) and 
square base (a = 6.12(1) Å) (See Figure B.1). These lattice parameters are consistent with 
the formation of VSe2 and PbSe respectively. The XRR, specular and in-plane diffraction 
data indicate that the q = 3 and 5 precursors self-assemble to form superlattices with twice 
the expected c-axis lattice parameter. The unit cell consists of twice the number of 
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crystallographically-aligned VSe2 and PbSe layers per repeating unit expected from the 
deposition sequence used to form the precursor. 
 
 
Figure V.12. Representative HAADF-STEM image of an annealed q = 3 precursor. 
 
 HAADF-STEM images were collected to corroborate on the structure of the self-
assembled q = 3 precursor. The sample (Figure V.12a) contains a surface region containing 
light and dark regions without regular order above a layered film that contains light layers 
(PbSe) of various thicknesses separate by dark layers (VSe2). Large Pb-rich and V-rich 
areas are observed at the top of the film indicating that some of the film has already 
disproportionated. Within the layered part of the film, there are small domains that contain 
a regular local stacking pattern. The higher magnification image (Figure V.12b) shows that 
the light layers are rock salt PbSe and the dark layers are CdI2-structured VSe2. Small 
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regions with different stacking sequences appear adjacent to one another. For example 
[(PbSe)1+d]2(VSe2)1[(PbSe)1+d]4(VSe2)1 regions labelled as '2141' and 
[(PbSe)1+d]4(VSe2)1[(PbSe)1+d]2(VSe2)1 regions labelled as '4121' are adjacent to one 
another. These observed "isomer" regions in the film cannot be distinguished using  
diffraction alone. Presence of these regions suggests that there is lateral diffusion during 
the deposition process. The HAADF-STEM image is consistent with the diffraction data. 
  
 
Figure V.13. (a) Specular x-ray diffraction and x-ray reflectivity patterns of the as-
deposited (gray) and annealed (black) ‘2141’ precursor (b) HAADF-STEM image of the 
annealed precursor film. 
 
 We prepared a precursor for one of the q = 3 products, ’2141’ to demonstrate the 
importance of designing a precursor such that only short range diffusion are required to 
form the targeted. Specular diffraction and x-ray reflectivity pattern of the as-deposited and 
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annealed precursors are shown in Figure V.13a. The as deposited precursor has 
significantly more long range order that the q = 3 precursor discussed previously. The self-
assembled heterostructure forms at lower temperatures and the diffraction maxima are 
significantly more intense and narrower than those shown in Figure V.10 and V.11, 
reflecting a more coherent structure. The cross section HAADF-STEM image of the entire 
film thickness shown in Figure V.13b contains very distinct PbSe and VSe2 layers and a 
regular stacking pattern across the entirety of the film. This image is similar to those 
obtained on films with even order q and odd q ≥ 7 monolayers, where also only short range 
diffusion in the precursor was required during self-assembly.  
 
 
Figure V.14. X-ray reflectivity data collected after annealing the q = 1 precursor at the 
designated temperatures. The blue dashed lines (---) are the expected peak positions for the 
calculated modulation length and the red solid lines are the expected positions for a 
[(PbSe)1+d]2(VSe2)1 heterostructure.  
 
 The precursor with q = 1 evolves differently than all of the other samples. The XRR 
data as a function of annealing temperature is shown in Figure V.14. Vertical blue lines 
indicate the reflections expected from a period calculated from the total thickness divided 
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by the total number of layers deposited. Vertical red lines indicate the reflections expected 
for [(PbSe)1+d]2(VSe2)1. The angle of the first reflection observed is significantly smaller 
than expected in the as deposited sample and shifts further to lower angles as the precursor 
is annealed at increasing temperatures. A second reflection appears after annealing at 
150°C and its intensity increases after annealing at higher temperatures. At 300°C, both of 
these reflections can be indexed as 00l reflections of a heterostructures with a 12.24(3) Å 
c-axis lattice parameter (red lines), which matches that expected for [(PbSe)1+d]2(VSe2)1.  
 
 
Figure 15. Specular x-ray diffraction data collected after annealing the q = 1 precursor at 
the designated temperatures. The blue dashed lines (---) are the expected peak positions for 
the calculated modulation length and the red solid lines are the expected positions for a 
[(PbSe)1+d]2(VSe2)1 heterostructure. 
 
 The specular diffraction data, Figure V.15, contains additional maxima that 
increase in intensity as annealing temperatures are increased. All of the reflections can be 
indexed as 00l reflections from [(PbSe)1+d]2(VSe2)1 after annealing at 250°C. The even 
order reflections appear to have a narrower peak width than the other reflections and higher 
intensities compared to what is expected from [(PbSe)1+d]2(VSe2)1, suggesting that a 
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second phase, VSe2, is likely present. This is consistent with the XRF-determined 
composition of the film. After annealing at 500°C, the XRR pattern contains only Kiessig 
fringes and the diffraction pattern contains maxima that can be indexed as the 001 reflection 
from VSe2 and the 002 and 004 reflections from PbSe. 
 
 
Figure V.16. Representative HAADF-STEM image of an annealed q = 1 precursor.  
 
 The structure of the self-assembled q = 1 precursor was further probed by collecting 
HAADF-STEM data. The whole film cross section (Figure V.16a) clearly demonstrates a 
different behavior as the others as the sample contains dark regions laterally separated from 
bright regions. This indicates segregation of large grains of VSe2 from PbSe. Figure 16b 
shows that the brighter regions consist of alternate layers of VSe2 and PbSe bilayers while 
the darker regions are VSe2. A closer look at the bright region (white box in Figure V.16b) 
154 
  
suggests that the local structure of the film consists of a mixture of [(PbSe)1+d]2(VSe2)1 and 
VSe2.The segregation into these two distinct regions suggests that there is lateral diffusion 
taking place during deposition. A consistent theme from the HAADF-STEM data is that 
the formation of an even number of monolayers of PbSe appears to be favored over odd 
layers, especially for small odd q. The as-deposited XRR and XRD suggests that the 
formation of even number of monolayers stems from the initial structure of the precursor. 
Based on the data presented above, all the precursors deposited only had PbSe bilayers. 
 The underlying assumption of the MER synthesis approach is that preparing a 
precursor with the nanoarchitecture of a specific target compound enables its synthesis 
because atoms do not need to move large distances to form this product relative to more 
stable alternatives. The nanoarchitecture of the precursor is experimentally controlled by 
the sequence of elements and the amount of each element deposited. In the system 
investigated here, the deposition sequence produced precursors with close to the desired 
structure for q = even and q ³ 7, but the nanoarchitecture of the precursors with q = 1, 3, 
and 5 were different than expected from the deposition process. The data presented above 
suggest that the atoms in the Pb|Se layer in the q = 1, 3, and 5 samples underwent significant 
lateral diffusion during the deposition process to form PbSe layers containing an even 
number of PbSe monolayers. For the q = 1 sample, lateral diffusion of atoms in the V|Se 
layer is also required to explain the uniform thickness and the observed modulation length 
of the precursor. The precursors preferred to form a defect-rich film with bilayers rather 
than a fully ordered film with a PbSe layer containing an odd number of monolayers. 
 DFT calculations shed light on the underlying reason for this behavior. Different 
thickness layers (q = 2-6) of PbSe with ideal rock salt atomic positions and 001 surfaces 
155 
  
separated by a nanometer of vacuum were allowed to relax to minimize the energy. Figure 
17 contains the minimum energies obtained as a function of q, the number of monolayers 
of PbSe in the block. Energies of odd numbered blocks are greater than the convex hull  
 
 
Figure V.17. DFT calculated energies and structures of PbSe blocks in vacuum with 
varying numbers of monolayers (q). Shown above are visual representations of the relative 
Pb and Se atom positions in the z-axis direction.  
 
created by the even numbered blocks, indicating that it is more favorable to form a mixture 
of adjacent even numbered blocks than an odd numbered blocks. The difference in energy 
between the convex hull and the odd numbered block decreases as the thickness of the odd 
numbered block increases. There is also a general decrease in energy as the thickness of 
the block is increased, which is due to the larger number of internal atoms compared to 
those on the surface. Inter- and intra-layer distortions are observed due to the termination 
of the 3D rock salt structure at the interfaces, as illustrated by the images of each structure 
shown in Figure V.17. Within a monolayer, Pb and Se atoms deviate from the ideal rock 
salt positions by a shift along the z-axis, with the Pb atoms moved to the outside and the 
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Se atoms moved towards the center. There is also a distinct alternation of short and long 
distances between monolayers in the even thickness PbSe blocks, resulting in bilayers. The 
largest puckering occurs in the surface layer, regardless of the thickness of the PbSe block, 
but the distortion in the surface layer decreases in magnitude as the PbSe monolayers 
approach the interior. This reflects the trade-off between the surface reconstruction to lower 
the surface energy and distortions in the interior layers due to the surface reconstruction. 
In blocks with an odd number of monolayers the bulk cannot form bilayers as the surface 
reconstructs resulting in their higher energy relative to the even thickness PbSe layers. 
These energy calculations provide an explanation for the observed as deposited structure 
and the final structures formed. For the q = 1 sample, the energy difference between a 
single PbSe monolayer between VSe2 layers versus ½ the surface being a bilayer and ½ 
without PbSe is high enough that the system reconstructs during the deposition as the atoms 
diffuse on the surface. Annealing results in continued disproportionation of the sample into 
[(PbSe)1+d]2(VSe2)1 and VSe2. High temperatures and long times are required due to the 
significant diffusion distances. For the q = 3 and 5 samples, the energy difference between 
regions with an odd monolayer thickness q versus alternating layers with q-1 and q+1 is 
still large enough to reconstruct the PbSe layer during the deposition. Annealing continues 
the self-assembly of the favored even layer thickness PbSe regions, since the precursor 
already has bilayer nanoarchitecture. For q = 7, the energy difference is not enough to drive 
the system to disproportionate a layer with a thickness of q monolayers into q-1 and q+1 
layers during the deposition.  
 
 
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V.4 Conclusions 
 The data presented in this paper illustrates the importance of the nanoarchitecture 
of precursors in the self-assembly of the precursors and presents surprising evidence for 
significant lateral diffusion of atoms during the room temperature deposition of precursors. 
Precursors with nanoarchitecture close to a specific product self-assemble during the 
deposition and subsequent low temperature annealing via a near diffusionless process. 
Precursors that have a nanoarchitecture that differs from a potential product require longer 
diffusion distances to self-assemble into specific products, which requires higher annealing 
temperatures and longer annealing times. Atoms can undergo long range surface diffusion 
during the deposition process to form more favorable configurations than those targeted 
using the sequence of elemental layers. Surprisingly, even though long range diffusion is 
occurring, the precursors evolve into metastable products rather than completely 
disproportionating. Limiting diffusion via low temperatures restricts the topology of the 
free energy landscape that can be explored, making the structure of the precursor critical 
in determining what products form. 
 In the specific system investigated here, the stability of puckered PbSe bilayers 
drives the lateral diffusion of Pb and Se atoms during both deposition and when annealing 
the films to form coherent bilayers. Precursors with an odd number of PbSe planes (q = 1, 
3, and 5) cannot be prepared with room temperature deposition because long range surface 
diffusion occurs during deposition to form precusors with regions of even number of PbSe 
planes. The higher energy of odd monolayer thick PbSe blocks is associated with the 
inability to retain the puckering distortion found in even monolayer thick blocks. Lowering 
the temperature of the substrate during deposition might decrease surface diffusion enough 
158 
  
to prepare precursors with odd monolayer thick blocks. Similar odd-even alternation based 
on energy differences between even and odd conformations has been observed in self 
assembled alkane monolayers and the melting points and dynamical behavior of alkanes.27–
30 The results obtained herein suggest that calculations on the properties of monolayers and 
thin layers of 3D materials should include the relative energy as a function of thickness to 
aid experimentalists in choosing substrates and synthetic conditions. 
 
V.5 Bridge 
 This chapter builds on the foundation of MER synthesis established from previous 
chapters: the importance of controlling the number of atoms and nanoarchitecture of the 
precursor. We expand this concept in the succeeding chapter by targeting the compound 
[(SnSe2)1+d]1(VSe2)1, another charge density wave material candidate. The new target 
material is closely related to a previously studied, highly kinetically stable compound  
[(SnSe)1+d]1(VSe2)1. In order to drive the self-assembly towards the desired reaction 
pathway, the precursor must be precisely designed so that the SnSe2 compound forms and 
not the SnSe compound.  
159 
  
CHAPTER VI 
 
CONTROLLING THE SELF-ASSEMBLY OF NEW METASTABLE TIN 
VANADIUM SELENIDES USING COMPOSITION AND NANOARCHITECTURE 
OF PRECURSORS 
 
Authorship Statement 
 This chapter has been submitted for publication, with me as the primary author. 
Taryn M. Kam collected x-ray diffraction data. Renae N. Gannon and Dr. Ping Lu collected 
HAADF-STEM data.  Dr. David C. Johnson, my adviser and group leader, and assisted in 
the preparation of this manuscript. 
 
VI.1 Introduction 
 Molecular synthesis is powerful, with chemists being able to perform total 
syntheses of complex molecules through a series of carefully designed steps beginning 
from simple precursors.1 Several important factors have contributed to the development 
and success of this field. One factor is the ability to predict the structure of potential 
kinetically stable compounds using simple bonding rules (the octet rule and the 18-electron 
rule).2,3 A second factor is the diversity of reagents and catalysts that can be used to 
transform a single functional group, allowing a reaction to be possible for a large number 
of substrates. A third factor is the typically homogeneous nature of reacting systems, where 
reactants dissolve in solvents while maintaining their structure. Most of the structure of the 
different reactants is preserved in the product molecules, as targeted reactions break and 
make specific bonds. NMR and other spectroscopies give detailed information about 
speciation, enabling the kinetics of the transformation from reactants to products can be 
investigated.4,5 This has enabled molecular chemists to develop rules based on reaction 
160 
  
mechanisms to modify reaction parameters to control reaction pathways.6 Since 
intermediates in a multistep synthesis can be purified, a sequence of specific reactions can 
be planned using retrosynthetic analysis to synthesize complicated molecules.7 
 In contrast, solid state synthesis is considered “as much art as science”, since the 
process is mainly experience- and intuition-driven.8 This reflects important differences 
between the synthesis of extended structures and molecules. For example, it is much more 
challenging to predict the structure of potential products, because many metallic elements 
can have a variety of oxidation states and coordination numbers.9 The formation of an 
extended structure also involves the repeated formation of specific bonds to form crystals 
with macroscopic amounts of atoms. This self-assembly of the crystal structure cannot be 
done using stepwise reactions. Hence, synthesis approaches are less developed and the 
analytical techniques used to follow reactions often require specialized instrumentation.10 
While the synthesis approach of extended solids using fluids (fluxes, mineralizers, or 
supercritical fluids) as solvents is similar in many respects to molecular synthesis,11–13 the 
reactants typically do not maintain their structure upon dissolution, and very little is 
typically known about the speciation that occurs in the liquid phase.14 Spectroscopy and 
other reaction monitoring methods are also more difficult to implement due to typically 
higher reaction temperatures, opaque fluid phases, and more challenging NMR nuclei.15,16 
Diffusion is the rate-limiting step in the direct reaction of solids at high temperature,17 
where reactions occur at the interfaces between particles. Since many different interfaces 
with different crystallographic orientations are reacting between different elements (A-B, 
B-C, A-C), different reactions will be occurring at different interfaces forming different 
products at different rates.18 Most analytical approaches only provide the sum of all of these 
161 
  
reactions, making kinetic studies challenging. In most reactions to form extended solids, 
high temperatures and long times are typically used, resulting in the formation of only 
thermodynamically stable compounds.19,20 While the importance of solid state reaction 
mechanisms to develop kinetically controlled synthesis approaches has been recognized, 
the field remains understudied.21,22 
 Here we use precursors made of a repeating sequence of Sn|Se|V|Se elemental 
layers to selectively form the metastable solids [(SnSe2)0.80]1(VSe2)1 and SnxV1-xSe2. X-ray 
reflectivity and x-ray diffraction (specular and in-plane) were used to follow the self-
assembly of [(SnSe2)0.80]1(VSe2)1. Laue oscillations observed in the XRR patterns enable 
us to determine the number of unit cells of [(SnSe2)0.80]1(VSe2)1 perpendicular to the 
substrate as a function of annealing temperature.  In-plane XRD patterns enable us to 
independently follow the lateral growth of SnSe2 and VSe2. This data was used to develop 
an atomic scale picture of the reaction mechanism. The proposed reaction mechanism was 
tested by modifying the nanoarchitecture of the initial precursor to synthesize the new 
metastable alloy, SnxV1-xSe2. Using an energy landscape, we rationalized why local 
composition and nanoarchitecture allowed us to discriminate between different reaction 
pathways. 
  
VI.2 Experimental 
 Thin film multilayer precursors were deposited on (100) oriented Si wafers with 
native oxide using a custom-built high vacuum physical vapor deposition (PVD) chamber 
with pressures maintained below 2 x 10-7 torr. Se (Alfa-Aesar, 99.999%) was deposited 
using a Knudsen effusion cell, while V (Alfa-Aesar, 99.7%) and Sn (Alfa-Aesar, 99.98%) 
162 
  
were deposited using 6 keV electron beam guns. More detailed information about the 
instrument setup is found elsewhere.23  The thickness of each element deposited at each 
step was monitored by quartz crystal microbalances found above each elemental source. A 
custom-made LabView code controls the opening and closing of pneumatic shutters to 
control the sequence and amount of each element deposited. 
 The areal density (in atoms/Å2) of each element was measured using x-ray 
fluorescence (XRF) on a Rigaku ZSX Primus II spectrometer. For each sample, the 
background signal was subtracted using the actual measurement from blank substrates as 
described by Hamann and co-workers.24  
 Precursors were annealed on a hotplate in a drybox with an inert atmosphere (O2 < 
0.8 ppm). X-ray reflectivity (XRR) and specular x-ray diffraction (XRD) patterns were 
collected on a Bruker D8 diffractometer equipped with Cu Ka radiation. One piece of 
Precursor I was annealed for 5 minutes at various temperatures to determine the processing 
conditions to form [(SnSe2)0.80]1(VSe2)1. A second piece of Precursor I and Precursor II 
were annealed at the optimum processing conditions. The Kiessig and Laue oscillations 
observed in the XRR pattern were used to calculate the thickness of the film via a modified 
form of Bragg's Law and the size of the coherently scattering domains, respectively. 
Grazing incidence in-plane diffraction (GIXRD) patterns were collected on a Rigaku 
Smartlab diffractometer also equipped with Cu Ka radiation. A model for the position of 
the atomic planes along the c axis was optimized by Rietveld refinement of the specular x-
ray diffraction patterns using the GSAS-II.25 LeBail fitting of the in plane x-ray diffraction 
using the FullProf Suite was used to refine lattice parameters.26  
163 
  
A thin cross-section of the film was prepared with an FEI Helios NanoLabTM 600i 
DualBeam FIB-SEM using standard lift-out procedures. Scanning transmission electron 
microscopy data was collected on FEI TitanTM G2 80-200 STEM with a Cs probe corrector 
and ChemiSTEMTM technology (X-FEGTM and SuperXTM EDS with four windowless 
silicon drift detectors) operated at 200 kV. High angle annular dark field (HAADF) images 
were taken with an electron probe of size (FWHM) of about 0.13 nm, current of ~75 pA, 
convergence angle of 18.1 mrad and using an annular dark-field detector with a collection 
range of 60-160 mrad. 
 
VI.3 Results 
  Two multilayer precursors (I and II) with repeating structure Sn|Se|V|Se were 
deposited. The lattice parameters of bulk VSe2 and SnSe2 were used to calculate the 
required number of atoms in each Sn|Se|V|Se sequence to form Se-M-Se trilayers of both 
VSe2 and SnSe2.27,28 Precursor I used these targets and the Sn|Se|V|Se sequence was 
repeated 41 times. Precursor II contained the Sn|Se|V|Se sequence repeated 82 times, with 
each sequence containing one half the number of atoms needed to form each Se-M-Se 
trilayer. The two precursors containing the same number of atoms but with a different 
nanoarchitecture. The total number of atoms of Sn, V, and Se per Å2 (areal density) were 
measured using XRF and summarize in Table VI.1 along with the targeted values. The 
measured values of Sn and V for both precursors are within error of the target amounts. 
There is a slight excess in the amount of Se in Precursor II. 
 The evolution of a piece of precursor I was followed as a function of annealing 
temperature using XRF, XRR and XRD to determine the conditions to form a single-phase  
164 
  
Table VI.1. Number of atoms per unit area determined using XRF compared to target 
values based on the lattice constants of bulk SnSe2 and VSe2 
 
Repeating Total number of atoms /Å2 Material Units Sn V Se 
Precursor I 41 3.3(1) 4.3(1) 14.6(4) 
Precursor II 82 3.13(9) 4.1(1) 16.6(5) 
VSe2 41 0 4.203(3) 8.406(6) 
SnSe2ref 41 3.256(5) 0 6.52(1) 
 
[(SnSe2)1+d]1(VSe2)1 sample (Figure VI.1). The XRR scan contains Kiessig fringes from 
the interference between the front and the back of the deposited film.30 The spacing of the 
Kiessig fringes yield a film thickness of 550.8(6) Å and the angle where the Kiessig fringes 
can no longer be observed yields a surface roughness of ~6 Å. The number of Kiessig 
fringes observed before the Bragg maxima from the modulation of the electron density in 
the precursor is consistent with the presence of 41 repeating sequences of Sn|Se|V|Se 
layers. The position of the first two Bragg reflections from the Sn|Se|V|Se sequence of 
layers yields a modulation length of 13.5 Å. This is slightly larger than the sum of the c-
axis lattice parameters of bulk VSe2 and SnSe2, 12.247(2) Å, since amorphous layers have 
a lower density than their crystalline counterparts. There is also a broad maximum at ~14° 
suggesting that nucleation and coherent stacking of dichalcogenide layers occurs during 
deposition.  Scherrer analysis of the linewidth suggests that the thickness of the coherent 
stacking is only a few layers thick. The XRR and XRF data indicate that the 
nanoarchitecture of the precursor is close to what was targeted and resembles the desired 
product. 
 
165 
  
 
 
Figure VI.1. Evolution of Sn|Se|V|Se precursor annealed at different temperature steps. (a) 
The number of atoms per Å2 of each element measured by XRF at each temperature step 
and calculated from number of unit cells and a-lattice parameters at RT, 250°C, and 400°C. 
(b) X-ray reflectivity patterns showing the evolution of the overall film structure (c) 
Specular x-ray diffraction showing the evolution of the structure perpendicular to the 
substrate (d) Grazing incidence in-plane x-ray diffraction showing the evolution of the 
structure in the plane parallel to the substrate.  
 
166 
  
 The diffraction data collected on the as deposited precursor is consistent with the 
XRR discussion. The specular XRD pattern contains two narrow Bragg reflections from 
the repeating Sn|Se|V|Se sequence of layers and broad reflections from self-assembly 
occurring during the deposition of the precursor. The broad reflections at ~14 and 28° 
indicate that coherent domains have formed. The in plane XRD pattern contains hk0 peaks 
that can be indexed to two hexagonal unit cells, SnSe2 and VSe2, with a-lattice parameters 
of 3.78(1) and 3.39(1) Å. The peak widths of SnSe2 is narrower than VSe2, indicating that 
there are larger in-plane grains of SnSe2 than VSe2. 
 The data collected between 100 and 300°C show that [(SnSe2)1+d]1(VSe2)1 
gradually self-assembles during this temperature range. The XRF data indicates that there 
is a small decrease in the amount of Se in this temperature range, which results from 
evaporation of Se while annealing. The XRR patterns contain an additional low frequency 
Kiessig oscillation due to the growth of an oxide at the surface of the film. The film 
thickness calculated from the high frequency Kiessig fringes in the XRR indicate that the 
film thickness gradually decreases as annealing temperature increases, which is a 
consequence of both the loss of Se and the increasing density of the film. The first two 
diffraction maxima shift in angle on annealing at 100°C and then increase in intensity and 
become narrower as annealing temperature increases. Laue fringes,31,32 which originate 
from the finite number of unit cells in the coherently diffracting coherent domains of the 
film are clearly visible on the diffraction maxima at 14°, and become closer together as 
annealing temperature increases. This indicates that majority of the coherent domains are 
the identical thickness, which can be calculated from the frequency of the Laue oscillations. 
During the growth process, the low angle Bragg reflections from the artificial layering of 
167 
  
the precursor disappears. The specular XRD patterns confirm the formation of 
[(SnSe2)1+d]1(VSe2)1 and corroborate growth of the coherent domains perpendicular to the 
substrate. Starting at 100°C, long range order starts to develop as additional 00l reflections 
appear at higher angles. These 00l reflections increase in intensity, reaching a maximum at 
250-300°C. The positions of the 00l Bragg reflections yield a c-axis lattice parameter of 
12.69(1) Å, which is slightly larger than the sum of the c-axis lattice parameters of bulk 
VSe2 and SnSe2, 12.247(2) Å, presumably due to the in-plane lattice mismatch preventing 
nesting of one constituent layer in the other. Laue oscillations, indicating a common size 
for the different [(SnSe2)1+d]1(VSe2)1 domains after each annealing temperature, are 
observed on the first several Bragg reflections and will be discussed more fully in the next 
paragraph. The in-plane diffraction patterns reflect the in-plane crystal growth that also 
occurs during annealing. The SnSe2 hk0 reflections exhibited only small changes in peak 
width and intensity, indicating that most of the SnSe2 is crystalline as deposited and the 
crystallite size does not increase during the annealing. The VSe2 hk0 reflections, however, 
noticeable increase in peak intensity and decrease in peak width as annealing temperature 
increases, indicating an increase in the amount of crystalline VSe2 and growth of the in 
plane grain sizes.  
 The characterization data in this temperature range provide a coherent picture of 
the self-assembly of [(SnSe2)1+d]1(VSe2)1 from the as deposited precursor. Figure VI.2a 
contains a closer view of the Laue oscillations visible on the 002 reflection of 
[(SnSe2)1+d]1(VSe2)1 after each annealing temperature. The presence of these oscillations 
indicates that a large majority of the suite of [(SnSe2)1+d]1(VSe2)1 domains at each 
temperature are the identical size and an integral number of unit cells thick, which can be  
168 
  
 
 
Figure VI.2. (a) Laue oscillations coming from the coherent film thickness at different 
temperatures. (b) Kiessig (black circles) and Laue (red circles, left axis) film thickness, and 
the number of unit cells (red circles, right axis) formed at each annealing temperature. The 
size of the coherent domain in the as deposited sample (filled red circle) is estimated from 
the line width of the 002 reflection.  
 
calculated from the spacing of the Laue oscillations. Figure VI.2b graphs the change in the 
size of the domains as a function of annealing temperature. At 250°C, the number of unit 
cells reach its maximum value of 37. The number of unit cells formed is smaller than 
expected due to loss of Se and oxidation at the film surface. The overall film thickness 
(calculated from Kiessig oscillations) decreases by a small amount as the target product 
grows, due to densification of the film as it self-assembles and loss of some Se. The 
difference between the total film thickness and the thickness of 37 unit cells of 
[(SnSe2)1+d]1(VSe2)1 at 250°C is due to an oxide layer on the surface of the film. The areal 
density of Se measure using XRF is consistent with that expected for 37 unit cells of 
[(SnSe2)1+d]1(VSe2)1 at 250°C (solid green line, Figure VI.1a). 
 A growth mechanism consistent with the characterization data is shown in Figure 
VI.3. The most difficult fact to explain is that the majority of the film consists of domains 
of [(SnSe2)1+d]1(VSe2)1 that are exactly the same integral number of unit cells throughout 
the annealing process. One possible explanation is that the coherent domains in the as 
169 
  
deposited film grow out from the substrate film interface as the film is deposited. This 
would provide a common starting point for all of the domains. The domains would stop 
growing as the film is deposited since metal atoms would need to diffuse through a thicker 
layer of amorphous Se and the increasing accumulated roughness as the film becomes 
thicker would decrease the coherence of the later deposited layers. The in plane diffraction 
patterns suggest that most of the SnSe2 forms large 2D grains during the deposition. There 
are fewer and smaller domains of VSe2 and unreacted V|Se layers between the SnSe2 
grains. As the precursor is annealed, the number of unit cells in the coherent domains near 
the substrate increase and an oxide layer forms at the film surface. The coherent domains 
grow at the same rates because the diffusion distances for atoms to arrive at the growth 
fronts are similar as a result of the nanoarchitecture of the precursor. During this process 
lateral growth of existing VSe2 layers in the precursor occurs and additional VSe2 layers 
self-assemble between existing SnSe2 layers as charge transfer between the layers stabilize 
the intergrowth. Excess Se diffuses to the surface and evaporates. The difference in the 
self-assembly behavior of SnSe2 and VSe2 results in an interesting dynamic between lateral 
and perpendicular growth of [(SnSe2)1+d]1(VSe2)1. 
 
 
 
Figure VI.3. Proposed formation and growth mechanism for [(SnSe2)1+d]1(VSe2)1.  
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 Further annealing to 400°C results in the decomposition of [(SnSe2)0.80]1(VSe2)1 as 
Se is lost and [(SnSe)1.15]1(VSe2)1 forms. The XRF data shows a substantial drop in the 
number of Se atoms per Å2 starting at 350°C. This is close to the decomposition 
temperature of bulk SnSe2 to SnSe (340°C).33 Changes in the XRR pattern from 300-400°C 
demonstrate that the SnSe2 layers have indeed decomposed. The decrease in the Kiessig 
fringe amplitude point to a change in the density of the film. The number of unit cells also 
decrease to 32, suggesting that not all of the [(SnSe2)1+d]1(VSe2)1 layers were converted to 
[(SnSe)1.15]1(VSe2)1. This is not at all surprising since SnSe has a higher atomic areal 
density of Sn than SnSe2. The SnSe2 decomposition does not reduce the number of VSe2 
layers, since VSe2 is kinetically stable up to 400°C.34 The VSe2 layers that are not in the 
heterostructure likely exists as small VSe2 grains within the film. The retention of the 
Kiessig fringes in the XRR pattern shown that film remains smooth during this transition. 
The c-axis lattice parameter of 12.02(1) Å after the 400°C anneal is consistent with 
previously reported [(SnSe)1.15]1(VSe2)1.35 The odd order reflections are broader than the 
even order reflections, presumably due to peak splitting from extra planes of VSe2 
separating domains of [(SnSe)1.15]1(VSe2)1 by half of a unit cell’s thickness within the 
interior of the film.36 The in-plane diffraction data supports the formation of SnSe.35 After 
the 350°C anneal, hk0 reflections from VSe2, SnSe2 and SnSe are present. After the 400°C 
anneal the SnSe2 hk0 reflections are no longer present. The a-axis lattice parameter of the 
VSe2 phase is 3.43(1) Å, consistent with previously studied [(SnSe)1.15]1(VSe2)1 (VSe2 a = 
3.414(3) Å).35 SnSe has a square unit cell and an a axis-lattice parameter of 5.94(1) Å, 
which is also consistent with previous reports  for [(SnSe)1.15]m(VSe2)1 (SnSe a = 5.91-5.92 
Å).37 
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 The last phase transition involves the disproportionation and subsequent oxidation 
of [(SnSe)1.15]1(VSe2)1 at temperatures greater than 450°C, even though the sample was 
annealed in a drybox with low oxygen concentration. Another dramatic drop in Se atoms 
per Å2 is observed during this last transition. This transition coincides with an increase in 
oxygen XRF intensity and decrease in Sn atoms per Å2. These stoichiometry changes 
suggest that the disproportionation is accompanied by the oxidation of Sn into volatile 
species. The XRR data shows that the film roughness significantly increases. The 00l peaks 
in the XRD shift to higher angles and broaden starting at 500°C. Odd order 00l reflections 
are completely diminished at 550°C, what remains are 00l reflections coming from a 
structure with a c-lattice parameter of 5.90(1) Å, consistent with some non-stoichiometric 
VSe2 remaining in the film.27 At the highest temperature studied, only hk0 reflections from 
two closely related hexagonal lattices are observed, with a-lattice parameters of 3.46 Å and 
3.52 Å, suggesting that the major phase present is VSe2 with different values of x and y in 
the formula V1+xSnySe2. 
 A second piece of precursor I was annealed at 250°C for 5 minutes based on the 
annealing data and its XRR pattern is shown in Figure VI.4. The Laue oscillations around 
the first order Bragg maximum are consistent with 39 layers of [(SnSe2)1+d]1(VSe2)1 self-
assembling during the anneal. Fewer layers oxidized during this single annealing step 
compared to the sequential annealing done on the first piece of precursor I. The total 
thickness determined from the Kiessig fringes is larger than 39 times the unit cell parameter 
of [(SnSe2)0.80]1(VSe2)1, as two of the deposited precursor layers did not form the intended 
product. We modeled the XRR data using the program GenX to calculate the XRR pattern 
from our proposed structural model.38  
172 
  
 
 
Figure VI.4. (a) XRR modelling of the optimized [(SnSe2)1+d]1(VSe2)1 heterostructure. 
(b) Electron density profile and schematic of the film based on the model. 
 
 
Table VI.2. Thin film layer parameters obtained from XRR modelling (FOM = 0.141). 
 
Layer # Thickness / Density / FU Roughness Interdiffusion layers Å per Å3 x10-2 / Å / Å 
Sn/V 
oxides 1 24.1(6) 1.6(1) 3.4(4) - 
VSe2 39 6.31(4) 1.55(4) - - 
SnSe2 6.38(2) 1.28(4) - - 
SiO2 1 50(20) 1.7(5) 2(1) 4(1) 
 
 The calculated pattern, shown in Figure VI.4, matches the experimental pattern and 
the film parameters in the model are summarized in Table VI.2. The model contained 39 
unit cells of [(SnSe2)0.80]1(VSe2)1 with atomically smooth interfaces between the 
constituents, a rough layer of SiO2 below the [(SnSe2)0.80]1(VSe2)1 block and a rough layer 
of tin/vanadium oxides above it. The thickness of the top oxide layer is approximately 
equal to that of the two missing unit cells, suggesting they were mostly lost to oxidation. 
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A thin interdiffusion region was required in the model to match the experimental pattern, 
which is consistent with a small amount of initially deposited Sn reacting with the SiO2 
surface during deposition. 
 
 
 
Figure VI.5. Rietveld refinement result of the specular x-ray diffraction of 
[(SnSe2)1+d]1(VSe2)1 and the atomic z-plane model of the average structure. 
 
 Rietveld analysis of the specular x-ray diffraction of [(SnSe2)0.80]1(VSe2)1 is shown 
in Figure VI.5. Since only 00l reflections are observed, a Rietveld analysis only provides 
information of the atomic positions of the atomic planes in the heterostructures that are 
parallel to the substrate. To simplify the analysis, a model with V at zero and Sn at half the 
c-axis lattice parameter was used, with a mirror plane at the halfway point. The refined V-
Se distance of 1.54 Å is close to those observed in other VSe2-heterostructures like 
[(SnSe)1+d]1(VSe2)1 (1.48(2) Å),35 [(PbSe)1+d]1(VSe2)1 (1.54 Å),39 [(BiSe)1+d]1(VSe2)1 
(1.52(1) Å),40 and bulk VSe2 (1.57 Å).29 The refined Sn-Se distance (1.59 Å) is close to 
that observed in [(SnSe2)1+d]1(MoSe2)1 (1.57 Å)41 and bulk SnSe2 (1.53 Å).28 The refined 
van der Waals gap of 3.21 Å is larger than those observed in either VSe2 or SnSe2, but 
smaller than the gap found in  [(SnSe2)1+d]1(MoSe2)1 (3.35(1) Å).41 The large van der Waals 
gap is a consequence of the large difference between the in-plane lattice parameters of 
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VSe2 and SnSe2, which prevents the Se atoms on either side of the van der Waals gap from 
nesting in between the Se atoms of the adjacent layers. 
 
 
Figure VI.6. LeBail fit of the grazing incidence in-plane x-ray diffraction pattern of the 
optimized [(SnSe2)1+d]1(VSe2)1 heterostructure. 
 
 A LeBail fit of the in-plane x-ray diffraction data of the second piece of Precursor 
I is shown in Figure VI.6. All reflections can be indexed as hk0 reflections from to two 
different hexagonal unit cells. The calculated a-axis lattice parameter for the SnSe2 
constituent (3.79(1) Å) is only slightly lower than what is observed for bulk SnSe2 (3.811 
Å),28 and in [(SnSe)1+d]1(MoSe2)1 (3.81 Å).41 The calculated a-axis lattice parameter for 
the VSe2 constituent (3.39(1) Å) is between the bulk value for stoichiometric VSe2 (3.358 
Å),29 and that reported for [(SnSe)1+ ]1(VSe2)1 (3.414 Å).35d  The difference in the in plane 
lattice parameters results in a stoichiometry of [(SnSe2)0.80]1(VSe2)1.  
 HAADF-STEM data was obtained on a cross section of the [(SnSe2)0.80]1(VSe2)1 
film from the second annealed piece of precursor I to obtain information about the relative 
orientation of the dichalcogenide layers. Figure VI.7a contains an image of the entirety of 
the film, which shows that the film is homogenous and smooth, consistent with the 
modelling of specular XRD and XRR. There are 38 layers of [(SnSe2)0.80]1(VSe2)1 clearly 
175 
  
visible, with another layer occasionally found at the top or bottom of the film. A closer 
look of the  
 
 
Figure VI.7. HAADF-STEM image of the  (a) entirety and (b) large section of the film 
shows that it consists of [(SnSe2)0.80]1(VSe2)1. 
 
film at higher magnification, Figure VI.7b, contains alternating dark and bright layers that 
can be identified as VSe2 and SnSe2, respectively, since heavier elements appear brighter 
in HAADF-STEM data.42 There are noticeably dark regions between at the interfaces of 
176 
  
the SnSe2 andVSe2 layers due to the van der Waals gap between the two constituents. The 
inset of Figure VI.7b shows a region of layers with high atomic resolution that happen to 
show zone axis views of both constituent layers. Only the <110> and <12!0> orientations 
of the two constituents are clearly resolved in the images. Both the VSe2 and SnSe2 layers 
exhibit octahedral coordination, which is consistent with the bulk structures of SnSe2 and 
VSe2. It is apparent from the microscopy data that there is a large degree of turbostratic 
disorder and lack of long range order in the heterostructure. A close inspection of the 
entirety of the cross section reveals that there are no large grains containing multiple 
repeating units crystallizing with a consistent orientation. Qualitative analysis of Figure 7b 
gives an estimated grain size of 5 nm, smaller than the grain sizes observed from other 
heterostructures that have long range order.43 These features can be traced to the large 
lattice mismatch and weak interaction between the constituents. 
 
 
 
Figure VI.8. EDX elemental analysis of a section of the film showing atomic plane position 
of the elements. 
 
 More information on the elemental distribution of the atoms within the layers was 
collected by EDX analysis of a small section of the film (Figure VI.8). The elemental EDX 
map confirms that there are alternating atomic layers of Sn and V separated by Se. 
However, there are regions where there are V-intensity in the Sn positions and vice versa. 
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Since the unexpected intensities are not uniform across the analyzed region, it is likely due 
to inhomogeneous cross substitution (e.g. VSe2 replacing SnSe2 or vice versa) across layers 
rather than homogenous alloying (e.g. SnxV1-xSe2) within the layers. Substitutional defects 
of this type have been observed in non-stoichiometric [(SnSe)1+d]1(VSe2)1 when there are 
deliberate variations in global composition.44 Homogenous alloys like 
[(SnSe)1+d]1(TaxV1+xSe2)1[(SnSe)1+d]1(VyTa1-ySe2)1 have clearly resolved V intensity peaks 
in Ta positions and vice versa.45 In [(SnSe2)0.80]1(VSe2)1, we speculate this result comes 
from variations in local composition that are difficult to control during the deposition 
process. 
 The data presented above on precursor I and the mechanism for growth prompted 
us to prepare precursor II to probe the relative importance of composition versus 
nanoarchitecture on product formation. We intended precursor II to have the same 
composition as precursor 1 but half the initial modulation length of the deposited sequence 
of Sn|Se|V|Se layers. Our question was, “what would form from this precursor?”. Only 
short range diffusion would be required to form the metastable alloy SnxV1-xSe2 and 
roughly twice that diffusion distance would be required to form the metastable compound 
[(SnSe2)0.80]1(VSe2)1,. Alternatively, small domains of VSe2 interwoven with larger 
domains of SnSe2 might form, or Se might segregate enabling the thermodynamically 
stable compound [(SnSe)1.15]1(VSe2)1 to form. Based on the data from precursor I, we 
expected SnSe2 would nucleate first, but the formation of large in plane grains of SnSe2 
would be inhibited by increasing concentrations of vanadium atoms at the growth front.  
 Figure VI.9 contains diffraction data on precursor II. The experimental modulation 
length of the layering in the as deposited precursor II was 7.27 Å, close to the c-axis lattice  
178 
  
 
Figure VI.9. Synthesis of a new SnxV1-xSe2 alloy. (a) Specular x-ray diffraction of a 
precursor with half the number of required atoms per layer (b) In-plane x-ray diffraction of 
the tin and vanadium diselenide alloy showing the presence of alloys with two different 
values of x. 
 
parameters of tin and vanadium diselenides. Figure VI.9a contains the specular and in plane 
diffraction patterns of precursor II after it was annealed at 250°C. The specular diffraction 
pattern contains 4 reflections that can be indexed as 00l reflections, yield a c-axis lattice 
parameter of 6.23(1) Å. The 110 reflection from the in-plane diffraction pattern (Figure 
VI.9b) of this sample is split suggesting the products are a vanadium rich and a tin rich 
dichalcogenide alloy. Vegard’s law can be used to estimate the composition of the majority 
components from the resulting a-axis lattice parameters of a = 3.49(1) and 3.75(1) Å. The 
calculated compositions of the two phases observed are Sn0.86V0.14Se2 and Sn0.29V0.71Se2. 
We suggest that SnSe2 nucleates and grows, but incorporates some V due to the increasing 
concentration of V at the growth front. The increased concentration of V results in the 
nucleation of the vanadium rich dichalcogenide. These events occur randomly results in 
the random intergrowth of the two alloys rather than a precisely layered nanoarchitecture.  
 
VI.4 Discussion 
 Traditional materials synthesis approaches have few parameters that can be used to 
control a reaction pathway to a specific product, instead relying on changing the system  
179 
  
 
 
Figure VI.10. Schematic of the free energy landscape of tin vanadium selenides. 
 
conditions (temperature, pressure, composition) to make the desired product 
thermodynamically stable. The results presented herein indicate that both the local 
composition and nanoarchitecture of precursors, which controls the initial distribution of 
atoms, provides a means to choose between different self-assembly pathways. An energy 
landscape provides a useful tool to visualize key aspects reaction pathways and Figure 
VI.10 contains an energy landscape consistent with the results of our study. Figure VI.10 
shows the two kinetically stable phases formed in this study, [(SnSe2)0.80]1(VSe2)1 and Sn1-
xVxSe2 exists as local minima and the misfit layer compound [(SnSe)1.15]1(VSe2)1 as the 
thermodynamic global minimum. Three different starting points are shown, corresponding 
to precursors I and II, and precursor A containing less Se with the nanoarchitecture 
designed to form the misfit layer compound [(SnSe)1.15]1(VSe2)1. As the layers in precursor 
I self-assemble to form [(SnSe2)1+d]1(VSe2)1, the free energy drops as the system falls into 
the local minima (solid black line from site I). The formation of SnSe2 during the 
deposition, facilitated by the local composition and nanoarchitecture of precursor I, selects 
180 
  
this reaction pathway. Precursor II, while having the same overall composition, has a 
nanoarchitecture that does not provide enough Sn in any single elemental layer to form 
large grains of SnSe2. When SnSe2 nucleates, the growth front quickly becomes enriched 
in V, resulting in the formation of the metastable alloy, Sn1-xVxSe2 (black dash dot line 
from site II). Precursor A, reported by Atkins and coworkers, had a nanoarchitecture 
similar to precursor I, containing alternating Sn and V rich layers, but ~25% less Se. This 
precursor forms [(SnSe)1.15]1(VSe2)1, as there was not sufficient Se to nucleate SnSe2 
during the deposition. There are large activation barriers between the different products 
initially formed because it would be necessary to create regions with the local composition 
required to nucleate the different alternatives, and this would require long range solid state 
diffusion which has a high activation energy.35 The importance of local composition is also 
seen in a paper by Falmbigl and coworkers, which involved the reaction of a Sn|Se|V|Se 
precursor with a nanoarchitecture similar to that of precursors I and A, but with an 
intermediate amount of Se.46 In this precursor, annealing at 100°C resulted in the 
simultaneous crystallization of SnSe2, SnSe, and VSe2 and all of these exhibited significant 
in-plane grain growth between 100-300°C. The simultaneous formation of all three 
constituents suggests that the difference between the nucleation barriers for the three 
phases is small and controlled by the local Sn and Se composition.  
 
VI.5 Conclusions 
 In this work, in-plane diffraction measurements and Laue oscillations present in x-
ray reflectivity scans of a designed precursor as it evolved into a metastable heterostructure, 
enabled us to determine the absolute size of the growing crystal as a function of 
181 
  
temperature. This data provided insights into the self-assembly mechanism and defined 
optimum processing conditions to form a new kinetically stable misfit layer compound, 
[(SnSe2)0.80]1(VSe2)1, with minimum oxidation. Controlling the local composition of the 
precursor enabled [(SnSe2)0.80]1(VSe2)1 to preferentially form over [(SnSe)1.15]1(VSe2)1. 
Preparing a precursor with the same overall composition but different nanoarchitecture 
resulted in the formation of a new kinetically stable SnxV1-xSe2 alloy instead of 
[(SnSe2)0.80]1(VSe2)1. The different reactions encountered from annealing studies of closely 
related multilayer systems were discussed in terms of an energy landscape as an effort to 
rationalize the different self-assembly pathways observed. The results show that 
nanoarchitecture and local composition are complementary design parameters to direct the 
self-assembly of new kinetically stable compounds along different reaction pathways in 
the energy landscape. 
 
 
  
182 
  
CHAPTER VII 
 
CONCLUSIONS AND SUMMARY 
 
Authorship Statement 
 This chapter was written with the editorial assistance of my advisor, Dr David C. 
Johnson. 
 
VII.1 Concluding Remarks 
 As the existing paradigm of solid state synthesis shifts from serendipitous discovery 
to materials-by-design, the need for synthesis planning has become more increasingly 
apparent. This dissertation focused on understanding the self-assembly behavior of 
Modulated Elemental Reactants (MER) synthesis in order to uncover new aspects and 
consequential factors that go beyond the generally accepted simple mechanism. 
 The first chapter introduced the concept of an energy landscape applied to bulk 
systems, molecular systems, solid interfaces, and eventually, ultrathin layers. We 
emphasize the need to study reaction mechanisms in order to explore more reaction 
pathways in an energy landscape. Chapter II discussed important structural and 
compositional techniques essential to guiding the deliberate synthesis of heterostructures. 
A novel method of analyzing and utilizing XRF data based on manual background 
correction and thin film limit considerations is introduced. Two new methods of calibrating 
XRF intensities and converting values to atom density (in atoms per square Angstrom) are 
presented. XRF and XRD would later be demonstrated as foundational methods for MER 
synthesis. Chapter III shed light on a fundamental requirement of misfit layered compounds 
and ferecrystalline heterostructures: the presence of a strong interaction between 
183 
  
constituent layers. A strong interaction exists if a thick rock salt layer (PbSe) crystallizes 
crystallographically aligned on transition metal dichalcogenide layers (VSe2). This 
approach serves as a test to determine the compatibility of two layered constituents as a 
heterostructure or misfit layer compound.  
 As Chapter III addressed the compatibility of PbSe and VSe2 as a combined 
heterostructure, Chapter IV discussed the synthesis of [(PbSe)1+d)]m(VSe2)1 
heterostructures, where m = 1, 2, 3, 4, as potential charge density wave materials. The 
synthesis was driven by the ability to precisely control the number of atoms and 
nanoarchitecture of a designed precursor, guided by XRF and XRD. It was determined that 
the distinct charge density wave behavior in VSe2 heterostructures is strongly influenced 
by the identity of the intervening constituent rather than VSe2-separation. This worked also 
highlighted the importance of having the correct number of atoms in the precursor and 
presented alternate pathways in the energy landscape when this condition is not met. 
Chapter V built on the foundations established in Chapter III and IV by using designed 
precursors to investigate the limit of the interaction between PbSe and VSe2 by targeting 
the synthesis of [(PbSe)1+d]q(VSe2)1 where q = 1 - 11 and the number of PbSe monolayers. 
The designed precursors exhibited vastly different self-assembly behaviors depending on 
the number of PbSe monolayers targeted. Unexpected room temperature lateral diffusion 
of atoms was observed for precursors with q = 1, 3, and 5, all of which were targeted to 
form PbSe monolayers. DFT calculations further demonstrated that the low temperatures 
rearrangements were driven by the stability of PbSe bilayers over monolayers. 
 Finally, Chapter VI described the synthesis of new metastable compounds 
[(SnSe2)1+d]1(VSe2)1 and SnxV1-xSe2, by precisely controlling the nanoarchitecture of the 
184 
  
precursor and using XRR and XRD reaction monitoring the elucidate the growth 
mechanism from the precursor to the target product. 
 
VII.2 Outlook 
 Overall, the goal of this work is to establish foundations for a toolbox of methods 
and concepts for rational synthesis planning of heterostructures via modulated elemental 
reactants. So far, we recognize the following ideas and methods as valuable tools in for 
rational synthesis. 
1. X-ray Fluorescence (XRF) 
 The ability of measure the number of atoms on a film with submonolayer 
accuracy opens up multiple opportunities in the thin film community. The 
convenience, low-cost, and non-destructive approach make it suitable to investigate 
compositional evolution of films made by various deposition methods. At the 
moment, active collaborations with groups with expertise in atomic layer 
deposition are ongoing as an effort to make the method more widespread. 
2. Compatibility Test 
 The compatibility test based on crystallographic alignment when combined 
with XRF, provides a quick and systematic approach for preliminary testing of new 
materials. Additionally, it also acts as a means for synthesizing crystallographically 
aligned rock salt films. As of the time of writing, the thermodynamic counterpart 
of PbSe-VSe2 has been confirmed, consistent with the compatibility test. 
 
 
185 
  
3. Precise Precursor Design 
 One of the most important and consequential aspects of MER synthesis is 
the design of the precursor. This work has demonstrated how the number of atoms 
and the modulation length can dictate the reaction pathway and impact the reaction 
product. The renewed emphasis in the precursor have contributed to recent 
successes in the group such as a synthesis of the very first three layer rock salt 
heterostructure. The ability to precisely control these two parameters have allowed 
us to test and investigate the generally accepted MER mechanism and reveal 
consequential features that were previously overlooked. 
4. Energy Landscape 
 In the synthesis of heterostructures, the energy landscape framework helps 
motivate the exploration of reaction pathways by traversing the experimental 
parameter space. Being cognizant of activation barriers that trap local minima 
containing metastable products helps one make logical experimental decisions. 
Computational tools that can predict kinetically stable structures as local minima 
can expedite synthesis. 
These tools potentially move us closer to the ultimate goal of mechanistic solid state 
synthesis. The more we develop and establish new tools to guide synthesis planning, the 
closer we get to more deliberate chemistry and the less we have to rely on serendipity. 
  
186 
  
APPENDICES 
A. SUPPLEMENTAL MATERIAL TO CHAPTER IV 
 
 
 
Figure A.1. Plot of c-lattice parameter of the [(PbSe)1+δ]m(VSe2)1 heterostructures and m, 
showing that the lattice parameter increases linearly as a PbSe bilayer is added to the 
repeat unit.  
 
 
 
 
 
 
 
 
 
 
 
187 
  
Table A.1: Rietveld refinement results from GSAS analysis of the [(PbSe)1+δ]3(VSe2)1 
heterostructure  
Parameter Value 
Atom Fractional Coordinate (occ) 
      V (1.00) 0 
      Se (1.00) 0.6385(6) 
      Pb (0.517) 0.18246(7) 
      Se (0.517) 0.2053(2) 
      Se (0.517) 0.2965(2) 
      Pb (0.517) 0.31638(9) 
      Pb (0.517) 0.43339(9) 
      Se (0.517) 0.4510(2) 
Uiso 0.026(1) 
Profile coefficients: Histogram type 1 
      U 8.6(2) x 102 
      V -1.0 x 100 
      W 4.9(2) x 101 
      X 1.549(9) x 101 
Rp 0.0955 
 
 
  
188 
  
B. SUPPLEMENTAL MATERIAL TO CHAPTER V. 
 
 
Figure B.1 In plane x-ray diffraction patterns of the annealed q = 1 and 3 precursors.  
  
189 
  
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