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HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY MASTER’S THESIS Structural Simulation of MgSiO3 under High Pressure Condition NGUYEN HOANG ANH anh.nh211326m@sis.hust.edu.vn Supervisor: Ph.D., Associate Prof Nguyen Van Hong Department: Computational Physics School: Engineering Physics HANOI – 06/2023 HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY MASTER’S THESIS Structural Simulation of MgSiO3 under High Pressure Condition NGUYEN HOANG ANH anh.nh165736@sis.hust.edu.vn School of Engineering Physics Department of Computational Physics President of the committee Supervisor (Sign and write full name) (Sign and write full name) Pham Khac Hung Nguyen Van Hong HANOI – 06/2023 Acknowledgement I would like to express my sincere gratitude and appreciation to all those who have contributed to the completion of my master's thesis on Structural Simulation of MgSiO3 under High Pressure Without their support, guidance, and encouragement, this endeavor would not have been possible First and foremost, I extend my heartfelt thanks to my thesis supervisor, Associate Professor Nguyen Van Hong, for his unwavering guidance, invaluable expertise, and constant support throughout this research journey His dedication, patience, and commitment to excellence have been instrumental in shaping my understanding of molecular dynamics simulation and refining the quality of this thesis I am truly grateful for his mentorship and the opportunities he has provided I would also like to extend my deepest appreciation to my family for their unconditional love, encouragement, and understanding Their unwavering support, belief in my abilities, and sacrifices have been a constant source of motivation for me Their presence and words of encouragement have kept me going during the challenging times, and for that, I am forever grateful I am indebted to my friends and classmates who have stood by my side throughout this academic journey Their camaraderie, motivation, and intellectual discussions have played a significant role in shaping my ideas and enhancing my thesis Their friendship has brought joy and inspiration to my life, and I am grateful for their presence Furthermore, I would like to express my gratitude to the Hanoi University of Science and Technology for providing me with the resources, facilities, and environment conducive to research and learning The academic community, including the professors, researchers, and staff, has contributed to my growth as a scholar and provided me with opportunities for collaboration and intellectual development Last but not least, I would like to acknowledge the countless researchers and scientists whose work and contributions have paved the way for advancements in molecular dynamics simulation Their dedication to expanding the boundaries of knowledge in this field has been a source of inspiration for my own research Abstract In this study, models were constructed for both MgSiO3 glass at 600K and MgSiO3 liquid at 3000K However, because the behavior of the fundamental SiO x and MgOy units in both substances under compression is not different They all tend to rearrange more tightly to increase the coordination number and increase the polymerization of the network In light of this, we study the local structure of both states However, because of limited research time, we limit our investigation on ring statistics and related things to a singular material type: MgSiO liquid The pressure range examined in this study spans from to 200 GPa The characteristics of the microstructure in this ternary material have been investigated in many works In spite of that, the effects of pressure on the -Si-O- network, especially ring statistics and ring-related phenomena under compression, have not been completely investigated In this work, the local structure of MgSiO3 glass and liquid are performed to evaluate the reliability of these models as well as visualize the influence of pressure on the short-range order The ring statistics is analyzed in MgSiO3 liquid to add more information on the intermediate-range order, to explain why the second peak of Si–Si pair radial distribution function splits into sub-peaks at 200 GPa and show a close relationship between the formation of large rings and the formation of Mg-rich regions The variation of Qn distributions and Voronoi on the ring is also clarified to provide additional insights about the rings under compression Declaration My name is Nguyen Hoang Anh, a master student of the 2021A–Physics Engineering class, School of Engineering Physics; student ID: 20211326M My supervisor is Associate Prof Nguyen Van Hong I declare that all contents presented in the thesis are the results of my study The data stated in the thesis is completely truthful and accurately reflecting the actual simulation measurement results All information quoted is subject to intellectual property regulations; references are transparently listed I have full responsibility for the contents outlined in this thesis Author of the thesis (Sign and write full name) Nguyen Hoang Anh TABLE OF CONTENTS LIST OF ABBREVIATIONS AND SYMBOLS i LIST OF FIGURES ii LIST OF TABLES iv INTRODUCTION CHAPTER OVERVIEW 1.1 Silica structure 1.2 Structure of ternary MgO-SiO2 models CHAPTER METHODOLOGY 11 2.1 Construction 11 2.1.1 Molecular dynamics simulation 11 2.1.2 Interatomic potential 16 2.1.3 Constructing silicate model 17 2.2 Model analysis 18 2.2.1 The radial distribution function 18 2.2.2 Coordination number and bond length 19 2.2.3 Ring statistics 20 2.2.4 Voronoi diagrams 21 CHAPTER RESULT AND DISCUSSION 23 3.1 Local structure of MgSiO3 23 3.2 Ring analysis 34 3.3 Mg-rich region 38 3.4 Voronoi diagrams 39 CONCLUSION 44 REFERENCES 45 APPENDIX 50 LIST OF ABBREVIATIONS AND SYMBOLS MD Molecular dynamics PRDF Pair radial distribution function RDF Radial distribution function CN Coordination number BO Bridging oxygen NBO Non bridging oxygen FO Free oxygen SRO Short-range order IRO Intermediate-range order RMC Reverse Monte Carlo DFT Density functional theory OG Oganov i LIST OF FIGURES Figure 1-1 Ternary MgO-SiO2 network, circles are color-coded to determine the type of species Gray is silicon atom; white is oxygen atom; orange circles are Mg atoms 8 Figure 2-1 The illustration of ݤݚPRDF 18 Figure 2-2 Ring visualization a) 7-fold Si ring at GPa b) 8-fold Si ring at GPa The atoms are color-coded Black rigid spheres are O species, cyan ones represent Si atoms 20 Figure 3-1 The PRDFs of MgSiO3 glass .23 Figure 3-2 The PRDFs of MgSiO3 liquid 24 Figure 3-3 comparison between this study and previous work [33,55] The structure factor of Si-O and O-O for MgSiO3 glass (top), the overall RDF and structure factor for MgSiO3 liquid (bottom) 25 Figure 3-4 The dependance of Si and Mg CNs on pressure 26 Figure 3-5 Visualization of Mg and Si CNs of the models at different pressures of MgSiO3 glass The Mg atoms (big spheres), 3-coordinated Si atoms (small spheres), and Si-O coordinated polyhedron are color-coded to denote the CN, where black/gray represents 3-fold, cyan for 4-fold, green for 5-fold, dark blue for 6-fold and magenta for 7-fold or higher 27 Figure 3-6 Visualization of Mg and Si CNs of the models at different pressures of MgSiO3 liquid The Mg atoms (big spheres), 3-coordinated Si atoms (small spheres), and Si-O coordinated polyhedron are color-coded to denote the CN, where black/gray represents 3-fold, cyan for 4-fold, green for 5-fold, dark blue for 6-fold and magenta for 7-fold or higher 28 Figure 3-7 The PRDFs of Si-O and O-O in MgSiO3 glass (top) and liquid (bottom) 29 Figure 3-8 The PRDF of Si-Si in MgSiO3 liquid .31 Figure 3-9 The bond angle distribution (left) and bond length distribution within each type of SiOx (x = 6, 7, 8) units 32 Figure 3-10 The change in the fraction of SiOx units under compression 33 ii ݦ ˲ ݦݤ ˲ ݦݤéW Velocity of Verlet algorithm is given by: ݦݨé ݦ ݦݨ ݦ > ݦݙ@ ݦݙ ݦ ݟ 2.6 The MD program uses the Verlet algorithm The coordinate of ݦݛǾ atom at the time ݦݗ ݦis determined through its coordinates at times ݦand ݦݗ ˲ ݦfollowing as: 12 ݦݗ ݦ ݛݤ ݦݗ ˲ ݦ ݛݤ ˲ ݦ ݛݤ ݦݗܿ ݦ ݛ ݛݟ 2.7 Velocity at time ݦis calculated through coordinates at times ݦݗ ˲ ݦand ݦݗ ݦ by the expression: