THE VALIDITY OF CLASSICAL NUCLEATION THEORY AND ITS APPLICATION TO DISLOCATION NUCLEATION A DISSERTATION SUBMITTED TO THE DEPARTMENT OF PHYSICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Seunghwa Ryu August 2011 © 2011 by Seunghwa Ryu. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- 3.0 United States License. http://creativecommons.org/licenses/by/3.0/us/ This dissertation is online at: http://purl.stanford.edu/rx036ms4124 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Wei Cai, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Douglas Osheroff, Co-Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Paul McIntyre I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. William Nix Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract Nucleation has been the subject of intense research because it plays an important role in the dynamics of most first-order phase transitions. The standard theory to describe the nucleation phenomena is the classical nucleation theory (CNT) because it cor- rectly captures the qualitative features of the nucleation process. However potential problems with CNT have been suggested by previous studies. We systematically test the individual components of CNT by computer simulations of the Ising model and find that it accurately predicts the nucleation rate if the correct droplet free energy computed by umbrella sampling is provided as input. This validates the fundamental assumption of CNT that the system can be coarse grained into a one dimensional Markov chain with the largest droplet size as the reaction coordinate. Employing similar simulation techniques, we study the dislocation nucleation which is essential to our understanding of plastic deformation, ductility, and me- chanical strength of crystalline materials. We show that dislocation nucleation rates can be accurately predicted over a wide range of conditions using CNT with the ac- tivation free energy determined by umbrella sampling. Our data reveal very large activation entropies, which contribute a multiplicative factor of many orders of mag- nitude to the nucleation rate. The activation entropy at constant strain is caused by thermal expansion, with negligible contribution from the vibrational entropy. The ac- tivation entropy at constant stress is significantly larger than that at constant strain, as a result of thermal softening. The large activation entropies are caused by anhar- monic effects, showing the limitations of the harmonic approximation widely used for rate estimation in solids. Similar behaviors are expected to occur in other nucleation processes in solids. iv Acknowledgements First of all, I am very much indebted to my principal adviser, Professor Wei Cai. It is of great fortune for me to work with such a bright and gentle person who I want to follow as a role model both as a scientist and as a gentleman. I have learned how to approach a scientific problem and how to tackle it: under his guidance, my random ideas transformed into a well defined research project, and a seemingly formidable problem into a series of small problems that can be handled systematically. Pro- fessor Cai has also helped me every single step that I need to grow as a scientist, such as writing a concise paper and delivering an insightful presentation. In addition to academic advices, I have also learned the virtues of a gentleman: he has consis- tently shown positive attitude on life, humility in the quest of knowledge, respect on other people, and dedication to his family. I am especially grateful for having many discussions with him on non-academic subjects regarding various aspects of life and being able to listen to his advices. Past four years that I worked with Professor Cai have been one of the most important periods in my life in which I have grown both intellectually and mentally. I owe very special thanks to my co-adviser, Professor Douglas Osheroff, under whom I had worked during the first three years of my graduate study. I had no experience on the experimental physics when I arrived at Stanford, and joined his group in the hope that I could learn a completely new subject under the guidance of a famous Nobel Laureate. Indeed, I have learned a lot from his wizardly expertise and rich experiences on the low temperature physics experiment. I still remember the first moment when I saw the signature of He-3 superfluid transition with full of joy, after several months of struggles to fix the dilution fridge. My experience in v Professor Osheroff’s group has aided and will continue to aid me to communicate and cooperate with experimentalists. I deeply appreciate the generosity he showed me when I decided to leave his group after I realized my natural preference toward theoretical studies. Since then, gratefully, he has been my co-adviser and given me precious advices on research, career, and life in general. His dedication to science education for general public and humble attitude have shown me the way I want to follow when becoming a senior scientist in the far future. I would like to thank Professor William Nix and Paul McIntyre to serve on my thesis committee. The dislocation course that I took from Professor Nix and the kinetic process course from Professor McIntyre have provided me the theoretical basis for the dissertation project. I appreciate Professor Nix for the discussion and valuable assessments on the dislocation nucleation study. He exemplifies the ideal life as a senior professor: he still actively works and enjoys the life at the same time, and willingly shares his valuable time for helping students and young faculties. I would like to thank Professor McIntyre for the invitation to his nanowire group meeting and insightful advices on the nanowire growth simulation project, another branch of my doctoral study. He exemplifies the quality of a real professional: he gives critical assessments on students working in various subjects with his deep and broad understanding in materials science research and organizes collaborations with several groups very efficiently. I also want to thank Professor Evan Reed for serving as the chair for my thesis defense meeting. I am happy to thank two special seniors in our group, Dr. Keonwook Kang and Dr. Eunseok Lee. I was going through a difficult time when I moved to Cai group due to the anxiety from starting a completely new field in the midst of graduate study and the ignorance in computational work. Without their moral support and help on the technical skills on computer simulations, I would have not succeeded in changing my research field so smoothly. I would like to thank all Cai group mem- bers who shared valuable discussions on my project. And many thanks to former lab mates in Osheroff group for the training on the low temperature physics exper- iments and to McIntyre group members for sharing interesting experimental results on semiconductor nanowire growth. vi Besides spending time in the lab doing research, I have been nourished by having good friends and sharing unforgettable memories with them. I would like to thank my fellow KAIST alumni at Stanford, friends in Cornerstone Community Church (special thanks to Dr. Jungjoon Lee), Professor Lew group members, fellow Korean students in physics and mechanical engineering departments, and all other close friends not included in these groups. I have been so comfortable and relaxed with my friends having many trips and parties, playing sports and games, tasting delicious foods and liquors, and going museums and concerts together. Their encouragements and advices on many aspects of life are also priceless. I want to thank my home university, Korea Advanced Institute of Science and Technology (KAIST) and the department of physics where I acquired a solid foun- dation in physics as an undergraduate. Special thanks to my undergraduate adviser, Professor Mahn Won Kim, and Professor Hawoong Jeong for their encouragement and invaluable advices in my career. I appreciate the financial supports from the Stanford Graduate Fellowship and the Korea Science and Engineering Foundation Fellowship, which allowed me to choose research projects more freely. Lastly, I would like to thank my family for all their love, support, and encourage- ment. I do not know how I can repay what I have received from my parents for the rest of my life. The devotion, patience, and responsibility that they have shown in their life have been and will be the source of my strength. I thank my younger brother who kept encouraging me for the past years. I would like to thank my grandmother in heaven who had dedicated her life to her family and showed me what the true love is. During seven years of graduate study, I have gradually realized that I owe every- thing I accomplished to people around me and how important it is to interact well with others.