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Atomistic Materials Modeling of Complex Systems: Carbynes, Carbon Nanotube Devices and Bulk Metallic Glasses

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ATOMISTIC MATERIALS MODELING OF COMPLEX SYSTEMS: CARBYNES, CARBON NANOTUBE DEVICES AND BULK METALLIC GLASSES DISSERTATION Presented in Partial Ful¯llment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Weiqi Luo, M.S., B.S. ***** The Ohio State University 2008 Dissertation Committee: Approved by Professor Wolfgang Windl, Adviser Professor Katharine M. Flores Adviser Professor John E. Morral Graduate Program in Professor William F. Saam Materials Science and Engineering °c Copyright by Weiqi Luo 2008 ABSTRACT The key to understanding and predicting the behavior of materials is the knowledge of their structures. Many properties of materials samples are not solely determined by their average chemical compositions which one may easily control. Instead, they are profoundly influenced by structural features of different characteristic length scales. Starting in the last century, metallurgical engineering has mostly been microstructure engineering. With the further evolution of materials science, structural features of smaller length scales down to the atomic structure, have become of interest for the purpose of properties engineering and functionalizing materials and are, therefore, subjected to study. As computer modeling is becoming more powerful due to the dramatic increase of computational resources and software over the recent decades, there is an increasing demand for atomistic simulations with the goal of better understanding materials behavior on the atomic scale. Density functional theory (DFT) is a quantum mechanics based approach to calculate electron distribution, total energy and interatomic forces with high accuracy. From these, atomic structures and thermal effects can be predicted. However, DFT is mostly applied to relatively simple systems because it is computationally very demanding. In this thesis, the current limits of DFT applications are explored by studying relatively complex systems, namely, carbynes, carbon nanotube ii (CNT) devices and bulk metallic glasses (BMGs). Special care is taken to overcome the limitations set by small system sizes and time scales that often prohibit DFT from being applied to realistic systems under realistic external conditions. In the first study, we examine the possible existence of a third solid phase of carbon with linear bonding called carbyne, which has been suggested in the literature and whose formation has been suggested to be detrimental to high-temperature carbon materials. We have suggested potential structures for solid carbynes based on literature data and our calculations and have calculated their free energies by DFT as a function of temperature (0 – 4000 K) and pressure (0-180 kbar). We propose and verify a simplified approach to calculate the phonon density of states (DOS) to allow a fast calculation of free energies. We found that all carbyne structures have higher free energies than graphite in the whole temperature and pressure range of this investigation, making pure (carbon-only) carbynes at most meta-stable. The inclusion of impurities was studied as well and may be the key for a stable carbyne phase. For CNT devices which have been suggested to eventually replace current Si technology, there is currently no equivalent for the highly used Si process modeling methods (“Technology Computer Aided Design” (TCAD)). We suggest accelerated DFT molecular dynamics (MD) simulations as a method for process modeling and apply it to study the contact formation between CNTs and metal contacts consisting of Ti, Pd, Al, and Au. The temperature accelerated dynamics (TAD) technique was adopted to overcome the time limitations of MD simulations in general, which are especially severe for the computationally demanding DFT MD simulations. We found that CNTs undergo a structural transformation when brought into contact with certain metal electrodes (here, iii Ti and Al). This resulted in a dramatic decrease in electrical conductance of the device. We also show that the transformation depends on the size of CNTs due to the size- dependent elastic energy and on the electrode materials due to the electronegativity- dependent charge transfer. In the last study, DFT was used in conjunction with classical MD simulations to predict the electron density of a Cu46Zr54 BMG structure modeled by a 1000-atom cell. Whereas DFT is capable to calculate the electron distribution in the cell, it is too slow to simulate melting and structural relaxation, which we handle by classical MD within the Embedded Atom Method. We propose a new model to analyze the open volume distribution based on the electron density and compare it with the traditional hard sphere model. Results from both models agree well, while the former allows a significantly better physical insight into the open volume distribution. As an additional plus, its results can be connected to experimental results by techniques such as Positron Annihilation Spectroscopy (PAS). iv To My Parents v ACKNOWLEDGMENTS I joined the group with limited background knowledge and encountered numerous problems during my studies. Prof. Windl carried me through all the difficulties since my first day in the group. My work wouldn’t have been possible without his endless support. More importantly, as an advisor, he always inspired me with enlightening ideas and always gave me generous help and encouragement. As a teacher, he often explained sophisticated physics to me in simple and precise language. My most sincere thanks go to him first. I am grateful to Prof. Morral and Prof. Flores, who gave me excellent advice and supported me. Moreover, they introduced me to the experimental world and made it possible for me to connect simulations to experiments. I wish to thank my fellow students, Tao Liang, Ashwini Bharathula, Naveen Gupta, Ryan Paul, Ning Zhou, Yuan Zhang, Karthik Ravichandran, Dipanjan Sen, Lanlin Zhang and Anupriya Agrawal who helped me in solving research problems and gave me a lot of laugh in my student life. They gave me very good memories during the past three years. This work was supported by the National Science Foundation and Semiconductor Research Cooperation. I am thankful for the computer time awarded by the Ohio Supercomputer Center, with which most of my simulations were performed. vi VITA 2002……………. B.S., Fudan University Shanghai, China 2005……………. M.S., Ohio State University Columbus, OH 2005-present…… Graduate Research Associate Ohio State University Columbus, OH FIELDS OF STUDY Major Field: Materials Science and Engineering vii TABLE OF CONTENTS Page Abstract............................................................................................................................... ii Dedication........................................................................................................................... v Acknowledge .....................................................................................................................vi Vita.................................................................................................................................... vii List of Tables ...................................................................................................................... x List of Figures................................................................................................................... xii Chapters: 1. Introduction..................................................................................................................... 1 1.1 Computational Materials Science ....................................................................... 1 1.2 Atomistic Modeling............................................................................................ 4 1.3 Motivation and Organization of This Thesis ...................................................... 6 2. An Introduction to the Density Functional Theory......................................................... 8 2.1 The Schrödinger Equation and Wave Functions .............................................. 10 2.2 Born-Oppenheimer Approximation.................................................................. 12 2.3 Many-Body Wave Functions ............................................................................ 13 2.4 The Variational Method.................................................................................... 13 2.5 Hartree-Fock Approximation............................................................................ 16 2.6 The Exchange and Correlation Hole................................................................. 27 2.7 The Thomas-Fermi Model ................................................................................ 30 2.8 The Hohenberg-Kohn Theorem and Kohn-Sham Approach............................ 31 2.9 Approximate Exchange-Correlation Functionals............................................. 35 2.10 Pseudo Potentials.............................................................................................. 38 3. The Structure and Stability of Carbynes....................................................................... 41 3.2 Structure and Stability of Carbynes .................................................................. 46 3.2.1 Crystal Structure of Carbyne in Previous Work ....................................... 46 viii 3.2.2 Computational Method............................................................................. 54 3.2.3 Kasatochkin-Type Carbyne.....................................................................
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