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ABSTRACT WENG, JAMES. Development of 3-D Diffraction

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ABSTRACT WENG, JAMES. Development of 3-D Diffraction ABSTRACT WENG, JAMES. Development of 3-D Diffraction Techniques for Characterizing Disordered Systems (Under the direction of Dr. James D. Martin). Functional materials owe their properties to features in their crystal structures that are often related to specific, local arrangements of atoms and molecules. This includes breaking of center-symmetry of the overall structure by imposed chemical strains which result from doping, elemental substitution, or multiple molecular orientations. Diffuse scattering is an important identifying feature of the deviation of a material’s lower symmetry short-range structure from its high symmetry long-range structure. Extraction of details of the lower symmetry structure remains a significant challenge. 1-D pair distribution function (PDF) analysis, which provides real-space structural information from diffraction data has previously been a technique of choice for analysis of such low-symmetry structure. However, such analysis necessarily results in the loss of directional information and provides a combination of both the low- and high-symmetry structures in one PDF. In this work a newly developed technique for the characterization of the structure of materials is presented which uses 3-D diffraction data to provide real space structural data of interest. A material agnostic method was developed in order to separate diffuse and bragg scattering, independent of any crystallographic theory, allowing the independent analysis of low and high symmetry structures. The corresponding 3-D analogs to the 1-D PDF calculated from diffuse and bragg scattering data are termed the 3-D-Δ-PDF and 3-D-β-PDF, and contain low and high symmetry structural information and do not result in the loss of directional information. The ability to calculate a 3-D-Δ-PDF provides the ability to resolve long standing structural questions. This is demonstrated with the rotationally disordered system α-CBr4, the structure of which has been the subject of continued controversy since disorder was first observed within the system in 1943[1] and is not resolvable by any existing technique. Analysis of the α-CBr4 system with the newly developed 3-D-Δ-PDF technique clearly resolves the material’s structure with little ambiguity. The ability to calculate a 3-D-β-PDF allows for insight into the structure of materials which are both locally disordered and structurally modulated, such as the ferroelectric perovskite BZN-PT (0.8 PbTiO3-0.2 Bi(Zn2/3Nb1/3)O3), where the structural effects are otherwise impossible to separate by more conventional diffraction techniques. Properties fundamental to the Fourier transform, along with their implications regarding the interpretation of experimental diffraction data, are also explored. In particular, a fundamental limit to the resolution of real space data obtainable from a PDF calculation appears to exist, which cannot be avoided by improvements to experimental setups. An apparent gap in crystallographic theory additionally appears to exist, and new theory appears necessary in order to properly interpret the structure of disordered materials. Finally, a design for a low cost single-pixel x-ray detector is developed which provides a reconstructed 2-D image is outlined. Such a detector could be fit in the beam stop of an x-ray diffractometer in order to provide both an image of the region surrounding the 000 diffraction peak as well as a way to correct for beam intensity fluctuations, making sensitive diffuse scattering measurements more reliable. © Copyright 2021 by James Weng All Rights Reserved Development of 3-D Diffraction Techniques for Characterizing Disordered Systems by James Weng A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Chemistry Raleigh, North Carolina 2021 APPROVED BY: _______________________________ _______________________________ James D. Martin David A. Shultz Committee Chair _______________________________ _______________________________ Paul A. Maggard Jacob L. Jones _______________________________ Christina Hoffman External Member DEDICATION To everyone who hasn’t dedicated a thesis to themselves ii BIOGRAPHY James Weng was born in 1992. This has been widely regarded as a questionable decision. As an undergrad at NC State he fell off of a skateboard a few times. Was in a minor rain storm in Columbia, SC in 2015. Nothing of note has happened since then. He currently lives with his beloved cat Katherine, referred to as “Kitty” for short. iii ACKNOWLEDGEMENTS This work was made possible by funding received through the GO program from Oak Ridge National Labs and flights to travel to the lab were made possible through the Oak Ridge Associated Universities program. Neutron measurements were made possible by and taken with instrumentation available through ORNL, and X-ray measurements were made possible and taken with instrumentation available through Argonne National Lab. Without the support of the National User Facilities at these two labs, this work would not have been possible. Thank you to my advisor Jim; whose tolerance of my working on whatever new harebrained idea of the week was likely critical to the success of this project. Thank you to my advisors at ORNL, Dr. Christina Hoffman and Dr. Ross Whitfield, without whom the instruments used to take these measurements would not exist. Thank you to my group members, Berkley Griffin Hillis and Josh Rickard, who listened to me rant on many occasions about how some paper author didn’t understand “basic” math. Thank you to the SEAS program at NCSU for providing me the opportunity to share my work with other researchers, as well as providing opportunities for collaborative work. Thank you to my committee members: Dr. Christina Hoffman, Dr. David Shultz, Dr. Jacob Jones, and Dr. Paul Maggard for taking the time to read this document and for taking part in my final Defense. iv TABLE OF CONTENTS LIST OF FIGURES ...................................................................................................................... vii CHAPTER 1: Introduction .......................................................................................................... 1 1.1 Motivation ............................................................................................................................. 1 1.2 Prior Work ............................................................................................................................. 3 1.2.1 Plastic crystalline carbon tetrabromide: ......................................................................... 3 1.2.2 BZN-PT (0.8 PbTiO3-0.2 Bi(Zn2/3Nb1/3)O3) .................................................................. 4 1.2.3 Calcia stabilized Cubic Zirconia ..................................................................................... 4 1.3 Summary of Research Presented ........................................................................................... 5 CHAPTER 2: Separation of Bragg and Diffuse Scattering ...................................................... 7 2.2 Introduction ........................................................................................................................... 7 2.2 What is the signal to be measured? ..................................................................................... 13 2.3 KAREN (K-space Algorithmic REconstructioN): .............................................................. 18 2.4 KAREN vs Punch-and-Fill .................................................................................................. 22 2.5 Conclusions ......................................................................................................................... 32 CHAPTER 3: 3D-Δ-PDF – Important Concepts and Experimental Considerations ........... 34 3.1 Introduction to Δ-PDF: ........................................................................................................ 34 3.2 Window Functions: ............................................................................................................. 38 3.3 Reconstruction of 3D X-ray Diffuse Scattering: ................................................................. 46 CHAPTER 4: Plastic Crystalline CBr4 ..................................................................................... 57 4.1 Introduction ......................................................................................................................... 57 4.2 3D neutron diffraction: separating Bragg and diffuse scattering ........................................ 60 4.3 3-D PDF analysis ................................................................................................................ 62 4.4 Local structure and molecular orientations ......................................................................... 64 4.5 Intermediate range order of molecular packing .................................................................. 67 4.6 Outlook and importance of this work .................................................................................. 70 4.7 Methods ............................................................................................................................... 71 4.7.1 Preparation of materials ................................................................................................ 71 4.7.2 3D neutron scattering collection ................................................................................... 72 4.7.3
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