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Local Crystal Structure of Bi-Based Perovskites Solved by RMC Modeling

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Local Crystal Structure of Bi-Based Perovskites Solved by RMC Modeling Local crystal structure of Bi-based perovskites solved by RMC modeling Thesis submitted in accordance with the requirements of the University of Liverpool for the degree of Doctor in Philosophy by Robert Jan Szczecinski April 2013 Local crystal structure of Bi-based perovskites solved by RMC modeling The local structure investigation by Reverse Monte Carlo modeling and comparison to average crystallographic structure of Bi-based perovskite materials are presented in this thesis. This novel technique using neutron total scattering is applied in search of possible short-range correlations between atoms to understand complex structure of these materials. Chapter One gives an introduction into perovskite structure and its properties. Chapter Two describes the difference between periodic and aperiodic crystals, which average crystallographic structure has been adopted by materials presented in this thesis. It also describes the total scattering and Pair Distribution Functions used in Reverse Monte Carlo modeling. The next chapters describe the local and average structure investigated during this thesis. Chapter Three describes the local and average perovskite structure of BiTi3/8Fe1/4Mg3/8O3 at various temperatures, where local structure analysis revealed particular displacements and correlations of A site and B site cations not captured by average crystallographic structure. Chapter Four compares local structure derived from RMC modeling and average incommensurate and commensurate crystallographic structures of Bi2Mn4/3Ni2/3O6 at room and high temperatures respectively, demonstrating importance of recognizing the length- scale of the probe used for structural characterization. Chapter Five describes the work on BiFe0.6Mn0.4O3 perovskite which was investigated by traditional crystallography to determine the modulated behavior and distorted structure of this material. The last Chapter 6 contains main conclusions from all experimental chapters. i Acknowledgments This research project would not have been possible without the support of many people. Firstly I would like to thank my supervisors Prof. Matthew Rosseinsky and Dr. John B. Claridge for all their help and guidance throughout this PhD. Many thanks to all members of MJR group, in particular Sam and Phil who helped me a lot in preparing and analyzing PDF data. I would like to also thank Natasha, Alicia, and Umut. It was big pleasure to share office with You! Frantisek thanks for the hot chocolate breaks when we chatted most of time about running and cycling. Thanks to the brilliant beamline scientist Dr. Matthew G. Tucker at ISIS. Last but not least I would like thank my parents for unwavering support and my wife Malwina for being with me throughout this time. ii The work presented in this thesis was carried out by myself, except where stated, at the Chemistry Department, University of Liverpool between May 2009 and April 2013 under the supervision of Prof Matthew J. Rosseinsky and Dr. John B. Claridge. This work has not been submitted for any other degree at this or any other university. Robert J Szczecinski April 2013 iii Contents Page Abstract ................................................................................................................... i Acknowledgements..................................................................................................ii Declaration..............................................................................................................iii Chapter 1. Introduction 1.1 Introduction and Thesis Aim ......................................................................... 1 1.2 Perovskite structure ....................................................................................... 2 1.2.1 Ferroelectricity and ferroelectric materials ................................................... 4 1.2.2 Magnetic ordering ....................................................................................... 11 1.3 References ................................................................................................... 15 Chapter 2. Methods 2.1 Principles of Diffraction .............................................................................. 21 2.1.1 Bragg’s Law ................................................................................................ 21 2.1.2 Powder diffraction ....................................................................................... 22 2.1.3 Diffraction intensity .................................................................................... 23 2.1.4 Systematic absences and the crystal systems .............................................. 24 2.1.5 Commensurate and incommensurate structures .......................................... 27 2.1.6 X-ray Diffraction ......................................................................................... 33 2.1.7 Neutron Diffraction ..................................................................................... 35 2.1.7.1 Reactor Source ......................................................................................... 35 2.1.7.2 Spallation Source .................................................................................... 36 2.1.8 The difference between X-rays and neutrons.............................................. 37 iv 2.1.9 X-ray and neutron diffractometers .............................................................. 38 2.1.9.1 Laboratory X-ray diffractometer - Panalytical X’PERT PRO ................. 38 2.1.9.2 Neutron Powder Diffraction Experiments ............................................... 39 2.1.9.2.1 POLARIS Diffractometer at ISIS, Oxford, UK ..................................... 39 2.1.9.2.2 GEM Diffractometer at ISIS, Oxford, UK............................................. 40 2.1.10 Transmission Electron Microscopy (TEM) ............................................. 41 2.1.10.1 TEM experiments.................................................................................. 42 2.1.11 Structural analysis .................................................................................... 43 2.1.11.1 Profile matching .................................................................................... 43 2.1.11.2 Rietveld refinement .............................................................................. 43 2.2 Introduction to total scattering and Reverse Monte Carlo modeling .......... 46 2.3 Total scattering and Reverse Monte Carlo modeling .................................. 47 2.3.1 Diffuse and total scattering – reciprocal space ........................................... 47 2.3.2 Pair Distribution function – real space ........................................................ 49 2.3.2.1 Useful information from PDF .................................................................. 50 2.3.2.2 Data collection and analysis ..................................................................... 52 2.3.3 Reverse Monte Carlo modeling .................................................................. 56 2.3.3.1 Constraints .............................................................................................. 60 2.3.3.1.1 Distance windows constraints .............................................................. 60 2.3.3.1.2 Bond Valence Sum (BVS) constraints ................................................. 61 2.3.3.1.3 Interatomic potentials........................................................................... 62 2.3.3.2 RMC files ................................................................................................. 63 2.4 References .................................................................................................. 67 Chapter 3. Local and crystallographic average structure of BiTi3/8Fe1/4Mg3/8O3 (BTFM) in various temperatures v 3.1 Crystallographic average structure of BTFM at room temperature ............ 72 3.2 Local structure of BTFM at room temperature (RT) .................................. 74 3.2.1 Generation of RMC model .......................................................................... 74 3.2.2 Analysis of the pair distribution function ................................................... 78 3.2.3 Analysis of A and B site cation displacements ........................................... 83 3.2.4 Analysis of A and B site correlations .......................................................... 92 3.2.5 B site cation ordering .................................................................................. 99 3.2.6 Conclusions ............................................................................................... 100 3.3 Crystallographic average structure of BTFM at low temperature (10K) .. 101 3.4 Local structure at LT ................................................................................. 104 3.4.1 Generation of RMC model ........................................................................ 104 3.4.2 Analysis and comparison of pair distribution function between LT and RT data ............................................................................................................ 106 3.4.3 Analysis and comparison of A and B site displacements between LT and RT data ...................................................................................................... 112 3.4.4 Analysis and comparison of A and B site displacement correlations between LT and RT data ........................................................................... 115 3.4.5 Comparison of nearest neighbours between LT and RT - B site cation
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