SOLID STATE PHYSICS FOR THE STRUCTURE OF URANIUM OXIDE AND ZINC ARSENIDE by Lydia S Harris A senior thesis submitted to the faculty of Brigham Young University - Idaho in partial fulfillment of the requirements for the degree of Bachelor of Science Department of Physics Brigham Young University - Idaho December 2019 Copyright c 2019 Lydia S Harris All Rights Reserved BRIGHAM YOUNG UNIVERSITY - IDAHO DEPARTMENT APPROVAL of a senior thesis submitted by Lydia S Harris This thesis has been reviewed by the research committee, senior thesis coor- dinator, and department chair and has been found to be satisfactory. Date Lance J Nelson, Advisor Date David Oliphant, Senior Thesis Coordinator Date Evan Hansen, Committee Member Date Todd Lines, Chair ABSTRACT SOLID STATE PHYSICS FOR THE STRUCTURE OF URANIUM OXIDE AND ZINC ARSENIDE Lydia S Harris Department of Physics Bachelor of Science Material properties are based on the structure of the material. Two ways to determine the structure of a material are a computational search for the ground state structures, and an experimental look using X-ray diffraction. In this work, these two ways are described and utilized to find the structure of two materials, uranium dioxide and zinc arsenide. Experimental techniques such as X-ray diffraction are used in order to better understand existing materials, but computational searches can be used in materials discovery. The consequences of using computational techniques is that new alloys with desirable properties can be discovered using inexpensive computer resources, however, the existence of such alloys must be validated experimentally. ACKNOWLEDGMENTS I would like to thank my parents, family, and friends for their support in my life, a.k.a. getting me through all the things that aren't schooling. As far as schooling is concerned, I would like to thank Richard Hatt for converting me to the pure science of physics and for inviting me to repent of disliking coding. I have grown greatly as a physicist in my classes under the guidance of many professors in the physics department at BYU-Idaho. Special thanks to Evan Hansen, Lance Nelson, and Jon Johnson for helping me learn to do research in many different fields using many different techniques. These experiences have been helpful in my development as a physicist and for building my resume. This helped me to get the two internships I was able to complete: the first at the Idaho National Laboratory with Lance Nelson and the second at BYU with John Colton. Another thanks to Lance Nelson for helping me out by reading and editing my thesis, as well as the other students that did the same. For anyone reading this far, I may as well also offer my unsolicited advice: start research as soon as possible in your physics career. It's great for your resume and especially for your development. Don't be afraid to ask for help from your peers and professors on homework and in life. And remember, physics is hard, but worth doing. Contents Table of Contents xi List of Figures xiii 1 Introduction1 1.1 Finding the Structure...........................1 1.1.1 Experimentally..........................2 1.1.2 Computationally.........................3 1.1.3 Verification............................4 1.2 Three Problems..............................4 1.2.1 Ag-Au \Toy Problem"......................4 1.2.2 Uranium Oxide Ground State Search..............5 1.2.3 Crystalline Structure of Zinc Arsenide.............5 2 Methodology7 2.1 Computational Methods.........................7 2.1.1 Density Functional Theory....................7 2.1.2 Machine Learning for Exhaustive Searches........... 10 2.2 Experimental Methods.......................... 19 2.2.1 Symmetries in Crystals...................... 19 2.2.2 X-ray Diffraction......................... 24 2.2.3 Single Crystal XRD........................ 26 2.2.4 Powder XRD........................... 27 3 Experiments 33 3.1 Ag-Au................................... 33 3.2 Uranium Oxide.............................. 34 3.2.1 DFT and Uranium........................ 34 3.3 Zinc Arsenide............................... 39 3.3.1 Collecting and Analyzing Data................. 40 4 Results and Discussion 43 4.1 Ag-Au................................... 43 4.2 Uranium Oxide.............................. 46 xi xii CONTENTS 4.3 Zinc Arsenide............................... 49 4.3.1 Initial P-XRD Results...................... 49 4.3.2 Single Crystal XRD Results................... 49 4.3.3 Later Powder XRD Results................... 51 4.3.4 DFT results............................ 52 5 Conclusion 55 5.1 Metals................................... 55 5.2 Uranium Dioxide Potential........................ 56 5.3 Zinc and Cadmium Arsenide....................... 57 Bibliography 59 A Zinc Arsenide Structural Information 65 B VASP settings 75 List of Figures 1.1 A convex hull (in green) for an A-B system. Blue points indicate phases that are not on the hull and therefore unstable. Red points indicate stable phases. Figure from Ref [10]....................2 2.1 Iterative workflow to solve a transcendental equation..........9 2.2 Comparison of atomic wave functions of Mn using the PAW method (solid line) with the exact result (bullets) for a given energy and angular momentum. Shown also are their differences magnified by a factor of 10 (dash-dotted line), and their pseudo wave functions (dashed line). Figure from Ref [2]............................ 11 2.3 The ith atom's neighborhood is made up of each atom within some Rcut of itself. The total energy E is made up of the contributions from individual neighborhoods. The energy contribution, Vi, of neighbor- hood ni depends on the separation between atoms i and j, rij, and a discrete variable, zj, that represents the species of the atom in the neighborhood (I or II in this illustration). Figure from Ref [8].... 13 2.4 Simple 2-dimensional visualization of configuration space vs. energy with a best fit \line". Each configuration is on the x-axis with it's corresponding energy on the y-axis. In reality this graph would be N+1 dimensional, where N is the number of basis functions Bα (n).. 14 2.5 An illustration of the filling of configuration space. As more structures are added to the training set, finer details present themselves in the model.................................... 17 2.6 Active learning during relaxation. If MTP extrapolates too much (γ ≥ γtsh), the configuration is added to the pre-selected set, and MTP predicts the energies, fores, and stresses of the configuration. If a second threshold is reached (γ ≥ Γtsh), relaxation is terminated and no predictions are completed. Figure from Ref [8]............ 18 2.7 Anti-fluorite structure of oxides such as Li2O or Na2O......... 20 xiii xiv LIST OF FIGURES 2.8 Structure of Zn3As2 proposed by Dr. Campbell, isomorphic to struc- ture of Cd3As2 given in Ref [1], a 25% cation deficient 2x2x4 anti- fluorite structure, referred to in this work as SymSG-A. Note that va- cancies accounting for the zinc (grey) deficiencies can be seen in several places.................................... 20 2.9 A crystal from each of the 230 space groups. Figure from Ref [35]... 23 2.10 Low background sample holder for powder X-ray diffraction scans... 29 2.11 Cone of diffracted light that is recorded in P-XRD. Figure from Ref [23]. 30 3.1 Preferred structure of UO2, the fluorite structure with uranium (blue) atoms located on the face centered cubic sites, and oxygen (red) atoms located on the simple cubic sites..................... 35 3.2 Two equivalent structures, with different directions for the layers. No- tice that on the right, every \1" atom lies in an uncircled layer, but on the left side, \1" atoms lie in both circled and uncircled layers. Choos- ing the correct direction preserves the layers and makes them able to be modeled as anti-ferromagnetic..................... 37 3.3 An example of a super periodic structure (right) of the unit cell (left). The structures are equivalent, but are represented by different lattice and basis vectors.............................. 38 4.1 Convex hull of Ag-Au system as determined by 294 high-throughput ab initio calculations. The 50% concentration structure is the B10 structure shown in Fig 4.2. Figure from Ref [6]............. 44 4.2 The B10 crystal structure. It is similar to the fcc crystal structure. It is the structure of Ag-Au at 50% concentration. Figure from Ref [6]. 44 4.3 Convex hull of Ag-Au system as determined by the ML potential relax- ation of 38,109 structures. This convex hull has shallow ground states that were not found in the high-throughput search of the same system shown in Fig 4.1. This may be due to fitting errors (this fitting has a mean absolute error of 0.8 meV/atom), as a few meV would place some of these structures above the convex hull. The training set for this model had 1556 configurations in it................. 45 4.4 One plane of a derivative fluorite structure with 2:1 oxygen (red) to uranium (blue) stoichiometry. Shown also are the forces on these atoms calculated by VASP (solid pink arrows) and predicted by the ML po- tential (dashed black arrows)....................... 48 4.5 Powder XRD data for 99.9% (blue) and 99.999% (red) pure Zn3As2.. 50 4.6 Powder XRD data for 99.999% pure Zn3As2 (red) fit to the structure obtained from SC-XRD analysis (green peaks, blue profile)....... 53 Chapter 1 Introduction The crystalline structures of materials give them their properties. Some of these prop- erties include strength, hardness, heat and electrical conduction, magnetic properties, and even color. This means that there is great power in knowing the structure of a material because it determines their properties. Searching for materials with specific properties is easier if their structures are already known. 1.1 Finding the Structure Materials science is the study of materials and their properties. With recent increases in computing power, a large part of this science has become theoretical and computa- tional, but experimental validation is still necessary to verify the results.