HYBRID COMPUTATIONAL MODELING OF THERMOMAGNETIC MATERIAL SYSTEMS A Thesis Presented to The Academic Faculty by Sookyung Kim In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in Material Science and Engineering School of Material Science and Engineering Georgia Institute of Technology May, 2017 Copyright c 2017 by Sookyung Kim HYBRID COMPUTATIONAL MODELING OF THERMOMAGNETIC MATERIAL SYSTEMS Approved by: Prof. Hamid Garmestini, Advisor Prof. Chaitanya S. Deo School of Material Science and School of Mechanical Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Prof. Seung Soon Jang Dr. Lorin Benedict School of Material Science and Physical and Life Sciences Directorate Engineering Lawrence Livermore National Lab. Georgia Institute of Technology Prof. Richard Fujimoto Dr. Mohammad A. Khaleel School of Computational Science and Energy and Environmental Sciences Engineering Directorate Georgia Institute of Technology Oak Ridge National Lab. Date Approved: Nov 11, 2016 To my Mom and Dad iii ACKNOWLEDGEMENTS First and foremost, I want to give my regard and thank to advisor Hamid Garmestani. It has been a great honor and privilege for me to be his student. I still remember the moment that I first visit Georgia Tech to meet him and talk about my previous research projects on DFT in Columbia University. He gave me a chance to present my previous research works, and understood my ambition to continue my study. I know it would not be easy for him to give an opportunity to me, who already went through tough time in Ph.D program from another school. However, he trusted me and accepted me as his student by dealing with all difficulties and obstacles without any condition, just because he trusted my ambition to continue research. Since that moment, he has taught me, both consciously and unconsciously with unconditional support, how good material research is done. I appreciate all his contributions to finish my Ph.D. successfully. He was the first person in academia who puts such a strong trust on me. Because he trusted me, I have been able to have faith in myself even in hard time. He is really a person who changed my life. Thank you, Prof. Garmestani. The collaborators in Lawrence Livermore National Laboratory have contributed im- mensely to my thesis work in spin thermodynamic simulation using Heisenberg Model. The magnetism group in LLNL has been a source of good advice and collaboration. I am especially grateful to Dr. Lorin Benedict and Dr. Mike Surh in LLNL who stuck it out to solve difficult research questions with me, and teach me how to solve the difficult problems in material physics step by step. We worked together on the spin dynamic simulations for about one and half years. Dr. Benedict supported magnetic research project in my summer internship at LLNL as the PI. With brilliant mind in physics, and enthusiasm, he guided my research in every way. I very much appreciated his enthusiasm, intensity, willingness to advise my research and support development of my research career in every way. Dr. Surh always stuck it out to difficult research questions and patiently guided me how to solve those problems. The joy and enthu- siasm I had for research discussion with him was contagious and motivated me to pursue post-doc position in LLNL after Ph.D program. I want to thank Dr. Surh for being such a great mentor and excellent example he has provided as a scientific iv role-model. In regards to the MnBi and MnSb project, I thank Dr. Kim Ferris at Pacific Northwest National Laboratory and Dr. Dongsheng Li (formerly at PNNL). They gave me advice on DFT work in early stage of the rare-earth replacement material development project. My fundamental knowledges on computational chemistry has been owing from Dr. Ferris a lot. He taught me the key physical concepts in DFT, and shared with various lessons he learned in his long research career. I would like to thank for his effort and time that he puts to nurture me as a scientist. In my later work of GPU parallelization of Heisenberg model, I am particularly in- debted to Prof. Richard Fujimoto and Robert Lee. Prof. Fujimoto guided the com- puting side of my thesis work by sharing some of his insights. I very appreciated his support and willingness to allow me to use the computing resources such as Georgia Tech GPU clusters. Robert Lee wrote the initial GPU code to parallelize Monte-Carlo spin simulation using Ising model. He also provided relevant support for Heisenberg model in GPU programing and his insight on high performance computing. It was my pleasure to work with him as a team in Modeling and Simulation class. For this dissertation I would like to thank my committee members: Prof. Seung Soon Jang, Prof. Richard Fujimoto, Prof. Chaitanya S. Deo, Dr. Mohammad A. Khaleel and Dr. Lorin Benedict for their time, interest, helpful feedbacks, and insightful questions. Lastly, I would like to express my gratitude and love to my family for all their love and encouragement. Words cannot express how grateful I am to, my mother, and father for all of the sacrifices that they have made on my behalf. They raised me with a love and supported me in every way, spiritually and financially, throughout long years of my education even from South Korea. For my brother and sister who always in my heart encouraged me to do my best even during tough times in the Ph.D. pursuit. And most of all for my beloved husband Joonseok Lee whose faithful support during the all stages of this Ph.D. is so appreciated. Finding him and getting married with him is one of the best outcomes from years of graduate education. I would like to express my love and deep appreciation to him. Sookyung Kim Georgia Institute of Technology December, 2016 v Contents DEDICATION .................................. iii ACKNOWLEDGEMENTS .......................... iv LIST OF TABLES ............................... x LIST OF FIGURES .............................. xi SUMMARY .................................... xv I INTRODUCTION ............................. 1 II THERMOMAGNETIC PROPERTIES OF MNBI USING COLD- SMEARING METHOD .......................... 9 2.1 Motivation................................9 2.2 Theoretical Backgrounds........................ 11 2.2.1 Rare-earth replacement magnetic materials.......... 11 2.2.2 Density Functional Theory................... 12 2.3 Computational Methods......................... 15 2.4 Results.................................. 16 2.4.1 Predicted crystal structure parameters for MnBi and related compounds............................ 18 2.4.2 Thermomagnetic properties of MnBi and MnSb........ 20 2.5 Discussions................................ 22 III COMPUTATIONAL STUDY OF RARE-EARTH SUBSTITUTES (FE1−X COX )2B. USING HEISENBERG MONTE CARLO MOD- ELING .................................... 24 3.1 Motivation................................ 24 vi 3.2 Theoretical backgrounds........................ 26 3.2.1 Theory of magneto-crystalline anisotropy........... 26 3.2.2 KKR-CPA calculation...................... 28 3.2.3 Obtaining Coupling Coefficient Jij from KKR-CPA calculation 31 3.2.4 Monte-Carlo Method...................... 32 3.2.5 Heisenberg Model........................ 33 3.3 Computational Methods......................... 34 3.3.1 KKR-CPA calculation...................... 35 3.3.2 Monte Carlo simulation using Full Spin MC ......... 35 3.3.3 Obtaining TC from Monte Carlo simulation.......... 49 3.4 Results.................................. 49 3.4.1 Output analysis from Monte Carlo simulation......... 49 3.4.2 Results for (F e1−xCox)2B .................................. 52 3.5 Discussion................................ 54 IV CALCULATING MAGNETIC CONTRIBUTION OF STACKING FAULT ENERGY IN STAINLESS STEEL USING LSF-MC SIM- ULATION .................................. 57 4.1 Motivation................................ 57 4.2 Theoretical Background......................... 58 4.2.1 SFE in Stainless Steel...................... 58 4.2.2 Fe-Cr-Ni system......................... 62 4.2.3 Magnetic Entropy Contribution................ 63 4.2.4 Magnetic Hamiltonian: LSF model............... 66 vii 4.3 Computational Method......................... 67 4.3.1 DFT for obtaining J(m) .................... 68 4.3.2 Monte-Carlo simulation..................... 71 4.4 Material Design Framework for Fe-Cr-Ni system........... 72 4.4.1 Inputs.............................. 72 4.4.2 Algorithmic Steps........................ 73 4.4.3 Output.............................. 74 4.5 Results.................................. 74 4.5.1 Ab-initio molecular dynamic calculation............ 74 4.5.2 Size and alloy configuration dependence on DFT....... 75 4.5.3 Dependence of DFT-functional on SFE............ 77 4.5.4 J (i)(m) .............................. 78 4.5.5 Stacking Fault Energy...................... 80 4.6 Discussion................................ 82 V GPU IMPLEMENTATION ON MONTE-CARLO SIMULATION USING ISING MODEL .......................... 87 5.1 Motivation................................ 87 5.2 Backgrounds............................... 89 5.2.1 GPGPU computing....................... 89 5.2.2 Monte-Carlo for many-particle simulations on GPUs..... 90 5.2.3 GPU memory scheme...................... 90 5.2.4 Monte Carlo simulation based on Ising model......... 92 5.3 Computational Method......................... 92 viii 5.3.1 Checkerboard algorithm..................... 92 5.3.2 Memory scheme......................... 94 5.3.3 Random Number Generator.................. 96 5.4 Results.................................