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First-Principles Calculations of Electric Field Gradients in Complex Perovskites

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First-Principles Calculations of Electric Field Gradients in Complex Perovskites W&M ScholarWorks Dissertations, Theses, and Masters Projects Theses, Dissertations, & Master Projects 2007 First-principles calculations of electric field gradients in complex perovskites Dandan Mao College of William & Mary - Arts & Sciences Follow this and additional works at: https://scholarworks.wm.edu/etd Part of the Condensed Matter Physics Commons Recommended Citation Mao, Dandan, "First-principles calculations of electric field gradients in complex perovskites" (2007). Dissertations, Theses, and Masters Projects. Paper 1539623330. https://dx.doi.org/doi:10.21220/s2-qn95-r722 This Dissertation is brought to you for free and open access by the Theses, Dissertations, & Master Projects at W&M ScholarWorks. It has been accepted for inclusion in Dissertations, Theses, and Masters Projects by an authorized administrator of W&M ScholarWorks. For more information, please contact [email protected]. FIRST-PRINCIPLES CALCULATIONS OF ELECTRIC FIELD GRADIENTS IN COMPLEX PEROVSKITES Dandan Mao Jingzhou, Hubei, China Master of Science, The College of William and Mary, 2001 Bachelor of Science, Peking University, 1999 A Dissertation presented to the Graduate Faculty of the College of William and Mary in Candidacy for the Degree of Doctor of Philosophy Department of Physics The College of William and Mary August 2007 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT Various experimental and theoretical work indicate that the local structure and chemical ordering play a crucial role in the different physical behaviors of lead- based complex ferroelectrics with the ABO 3 perovskite structure. First-principles linearized augmented plane wave (LAPW) with the local orbital extension method within local density approximation (LDA) are performed on structural models of P b (Z r 1/ 2T i 1/ 2) 0 3 (PZT), Pb(Sc 1/ 2Ta 1/ 2) 0 3 (PST), Pb(Sc 2/ 3W 1/ 3) 0 3 (PSW), and P b (M g i/ 3N b 2/ 3) 0 3 (PMN) to calculate electric field gradients (EFGs). In order to simulate these disordered alloys, various structural models were constructed with different imposed chemical orderings and symmetries. Calculations were carried out as a function of B-site chemical ordering, applied strain, and imposed symmetry. Large changes in the EFGs are seen in PZT as the electric polarization rotates between the tetragonal and rhombohedral directions. The onset of polarization rotation in monoclinic Cm symmetry strongly correlates with the shearing of the TiC >6 octahedron, and there is a sharp change in slope in plots of Ti EFGs versus octahedral distortion index. The same changes in EFGs and the BC >6 shearing corresponding to the change of off-centering direction are also seen in PST. In PSW and PMN, the calculated B cation EFGs showed more sensitivity to the surrounding nearest B neighboring environments. Calculated B atom EFGs in all alloys are considerably larger than those inferred from the NMR measurements. Based on comparisons with experiments, the calculated results are interpreted in terms of static and dynamic structural models of these materials. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with with permission permission of the copyrightof the copyright owner. Further owner. reproduction Further reproductionprohibited without prohibited permission. without permission. TABLE OF CONTENTS Acknowledgements ....................................................................................................viii List of T ables .......................................................................................................... x List of Figures .......................................................................................................... xiv Chapter 1 Introduction ................................................................................................ 2 1.1 Ferro electrics .................................................................... 2 1.2 Lead-based complex perovskites ................................................... 6 1.3 N M R quadrupole in te ra c tio n ........................................................................ 11 1.4 Electric field gradient (E FG ) .................................................................... 19 2 Methodology ....................... 23 2.1 Density functional theory ( D F T ) ................................................................. 23 2.1.1 Hohenberg and Kohn theorems .................................................... 25 2.1.2 Kohn-Sham th e o ry ..................... 26 2.1.3 Widely used exchange-correlation approxim ations .................. 29 2.1.4 Solving the Kohn Sham equations with basis s e t ...................... 31 2.2 DFT applications to periodic systems ....................................................... 31 2.2.1 Structural relaxation ........................................................................ 32 2.2.2 k-point sam pling ...............................................................................33 2.2.3 Plane wave basis functions for crystals .......................................34 2.2.4 LAPW basis functions .....................................................................39 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.3 Computation of electric field gradients ................................................... 42 3 Structural dependence of EFGs in P Z T ......................................... 47 3.1 Sim ulation p ro c e d u re .....................................................................................48 3.2 Structural models and comparison with experimental pair distri­ bution functions ...............................................................................................49 3.3 EFG results and simulated NMR spectra ................................................54 3.4 Discussion .........................................................................................................71 3.4.1 Lead off-centering and lone-pair contributions to the EFG 71 3.4.2 Ti and 0 calculated EFGs and possible structural anisotropy in P Z T .................................................................................................. 76 4 EFG calculations in PST, PSW, and PM N .............................. 87 4.1 Sim ulation p ro c e d u re .................................................................................... 8 8 4.2 Structural pair distribution function results ............................................92 4.2.1 P S T ..................................................................................................... 92 4.2.2 P S W ..................................................................................................... 95 4.2.3 P M N .................................................................................... 98 4.3 EFG results ...................................................................................................100 4.3.1 P S T ................................................................................................... 100 4.3.2 P S W ................................................................................................... 105 4.3.3 P M N ...................................................................................................108 4.4 Structural sensitivity of calculated E F G s ............................................. 109 4.4.1 EFGs and off-centerings of B atom s .......................................... 110 4.4.2 Pb off-centering and O EFGs in P S T .......................................115 4.5 Simulated NMR spectra ........................................................................... 120 4.5.1 Manifestation of EFGs on measured NMR spectra .................120 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.5.2 B atom NMR spectra comparison between simulations and experiments .............................. 130 5 Conclusion .......................................................................................................134 A ppendix A Nuclear quadrupole central peak powder patterns ............................138 Bibliography................................................................................................................. 143 V i t a .................................................................................................................................. 157 vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To Mom and Dad v ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS I would like to express my gratitude to Dr. Henry Krakauer, under whose supervision this project was conducted, for his guidance, patience, and support during the tenure of this work. I would also like to extend special thanks to Dr. E. J. Walter for his encour­ agement and assistance on all aspects of this project. Furthermore, I would like to thank the rest of my committee members, Dr. S. Zhang, Dr. G. Hoatson, Dr. R. Void, and Dr. I. Novikova for careful reading and helpful comments on much of this manuscript. I am also very grateful for my colleagues and group mates, Dr. Z. Wu, Dr. W. Purwanto, Dr. M. Suewattana, Hendra Kwee, and Dan Pechkis for their support and assistance. Finally, I would like to acknowledge my family and all of my friends for their
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