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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: MgSiO3 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 MgSiO 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 Figure 2-1 The illustration of ݚݤ PRDF 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 MgSiO 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 SiO x units under compression 33 ii Figure 3-11 Ring statistics at different pressures a) n-fold Si-O ring, b) n-fold TO ring 34 Figure 3-12 Si-Si-Si distance distribution on different types of rings at 200 GPa 36 Figure 3-13 Qn distribution of different ring sizes at different pressures 38 Figure 3-14 Cyan, black and red spheres are Si, O and Mg atoms respectively, the yellow path is 10-fold ring a) Ring with surrounding oxygen atoms b) Mg-rich region inside the ring 39 Figure 3-15 Characteristic of Voronoi polyhedrons of rings: average volume of SiVoronoi (a) and O-Voronoi (b) Voronoi on rings under compression 40 Figure 3-16 Voronoi on rings a) 6-fold ring at 50 GPa b) 6-fold ring at 200 GPa Cyan and gray polyhedrons correspond for Voronoi centered by Si and O atoms 40 Figure 3-17 The snapshot of Voronoi of 6-fold Si-O rings at a) GPa, b) 50 GPa, c) 100 GPa, d) 200 GPa 42 Figure 3-18 The mean Si-O-Si angle on rings at GPa 43 iii at 200 GPa, the 9-fold ring fraction surpasses others, which will impact the IRO of the -Si-O- network This phenomenon is particularly utilized to explain the splitting peak observed in the second peak of the Si-Si PRDF ϭϮ ϭϬ ϰͲĨŽůĚƌŝŶŐ ϱͲĨŽůĚƌŝŶŐ ϲͲĨŽůĚƌŝŶŐ ϴ ϲ ϰ Ϯ &ƌĂĐƚŝŽŶ;йͿ Ϭ ϭϮ ϭϬ ϴ ϲ Ϯϱ ϯϬ ϯϱ ϰϬ ϰϱ ϱϬ ϱϱ ϲϬ ϲϱ ϳϬ ϳϱ ϳͲĨŽůĚƌŝŶŐ ϴͲĨŽůĚƌŝŶŐ ϵͲĨŽůĚƌŝŶŐ Ϯϱ ϯϬ ϯϱ ϰϬ ϰϱ ϱϬ ϱϱ ϲϬ ϲϱ ϳϬ ϳϱ ϭϬͲĨŽůĚƌŝŶŐ ϭϭͲĨŽůĚƌŝŶŐ Ϯϱ ϯϬ ϯϱ ϰϬ ϰϱ ϱϬ ϱϱ ϲϬ ϲϱ ϰ Ϯ Ϭ ϭϮ ϭϬ ϴ ϲ ϰ Ϯ Ϭ ϳϬ ϳϱ ŝƐƚĂŶĐĞ;Ϳ Figure 3-12 Si-Si-Si distance distribution on different types of rings at 200 GPa To simplify, we examine the bond length distribution between a Si atom on a ring and its second nearest Si atoms on the same ring, which we refer to as the SiSi-Si distance distribution This distribution is heavily influenced by specific ring structures (refer to Figure 3-12) Rings with 4, 5, and members exhibit a Gaussian-shaped distribution, with peak values at 4.1, 4.8, and 4.7 Å, respectively The Si-Si-Si distance distribution is narrower in 4-fold rings compared to 5-fold and 6-fold rings, as measured by the full width at half maximum (FWHM) In contrast, the Si-Si-Si distance distribution in 10-fold and 11-fold rings significantly deviates from that of smaller rings, indicating that larger rings are more flexible in terms of their topology The construction of large rings involves multiple Si-O 36 paths, enabling the SiOx units within these rings to arrange themselves more freely while minimizing the cohesive energy of the overall configuration Conversely, low-fold rings, such as 2-fold and 3-fold rings, are formed by stretching the Si-O bond length and adjusting the Si-O-Si and O-Si-O bond angles to optimize the increased energy [18] The energy constraint has a greater impact on smaller rings compared to larger ones Higher-fold rings exhibit more diverse shapes compared to smaller rings As a result, the Si-Si-Si distance distribution in larger rings does not follow a Gaussian shape Despite its asymmetric nature, the Si-Si-Si distance distribution of the 9-fold ring exhibits a distinct peak at approximately 5.3 Å Figure 3-11 illustrates the distribution of ring sizes, indicating that at 200 GPa, the 9-fold rings are significantly more prevalent compared to other ring sizes They account for nearly 24% of the rings, while the second most dominant type, the 11-fold rings, only represents around 15% This combination of dominance in proportion and the high peak position of the Si-Si-Si distance distribution in the 9-fold rings influences the Si-O PRDF Under compression, the second peak of the Si-Si PRDF tends to shift towards lower values (see Figure 3-8) At 200 GPa, this second peak splits into two subpeaks The first subpeak is located at approximately 4.6 Å, while the second subpeak is around 5.3 Å The extensive formation of 9-fold rings is responsible for this phenomenon of the second peak splitting into two subpeaks at 200 GPa The smaller subpeak corresponds to a reduction in the average bond length between interacting atoms, similar to what occurs at pressures below 200 GPa The higher subpeak corresponds to the sharp peak observed in the Si-Si-Si distance distribution To gain a better understanding of the rings, Figure 3-13 presents the distributions of Qn (where n represents the number of BOs) under compression At GPa, the Qn distribution of 2-fold and 3-fold rings exhibits peaks at n = (as shown in Figure 3-13.a) In 2-fold rings, the value of Q3 is approximately equal to the value of Q5, at around 27% The fraction of Q3 in 2-fold rings is higher compared to other ring sizes For rings with or more members, Q3 represents the highest proportion Across different rings at the same pressure, the distribution of Qn is generally similar, except for the Qn distribution on the 11-fold ring at 100 GPa (as depicted in Figure 3-13.c) The shift of the peak in the Q n distribution, 37 from or at ambient pressure to or at pressures of 50 GPa or higher, indicates that rings have a tendency to merge or fuse together under compression &ƌĂĐƚŝŽŶ;йͿ ϰϬ ϯϬ ϮϬ ϭϬ ƌŝŶŐϮ ƌŝŶŐϯ ƌŝŶŐϰ ƌŝŶŐϱ ƌŝŶŐϲ ƌŝŶŐϳ ƌŝŶŐϴ ƌŝŶŐϵ ƌŝŶŐϭϬ ƌŝŶŐϭϭ ϰϬ &ƌĂĐƚŝŽŶ;йͿ ƌŝŶŐϮ ƌŝŶŐϯ ƌŝŶŐϰ ƌŝŶŐϱ ƌŝŶŐϲ ƌŝŶŐϳ ƌŝŶŐϴ ƌŝŶŐϵ ƌŝŶŐϭϬ ƌŝŶŐϭϭ ϱϬ ϯϬ ϮϬ ϭϬ Ϭ Ϭ ϭ Ϯ ϯ ϰ ϱ ϲ ϳ ϴ ϵ ϭϬ ϭ Ϯ ϯ ϰ ϱ YŶ ϲ ϳ ϴ ϵ ϭϬ ϳ ϴ ϵ ϭϬ YŶ a) GPa b) 50 GPa ϱϬ ƌŝŶŐϮ ƌŝŶŐϯ ƌŝŶŐϰ ƌŝŶŐϱ ƌŝŶŐϲ ƌŝŶŐϳ ƌŝŶŐϴ ƌŝŶŐϵ ƌŝŶŐϭϬ ƌŝŶŐϭϭ ϯϬ ϮϬ ϭϬ ƌŝŶŐϮ ƌŝŶŐϯ ƌŝŶŐϰ ƌŝŶŐϱ ƌŝŶŐϲ ƌŝŶŐϳ ƌŝŶŐϴ ƌŝŶŐϵ ƌŝŶŐϭϬ ƌŝŶŐϭϭ ϯϬ &ƌĂĐƚŝŽŶ;йͿ &ƌĂĐƚŝŽŶ;йͿ ϰϬ ϮϬ ϭϬ Ϭ Ϭ ϭ Ϯ ϯ ϰ ϱ ϲ ϳ ϴ ϵ ϭϬ ϭ Ϯ ϯ ϰ ϱ ϲ YŶ YŶ c) 100 GPa d) 200 GPa Figure 3-13 Qn distribution of different ring sizes at different pressures 3.3 Mg-rich region The analysis of ring statistics also provides insight into the heterogeneity observed in MgSiO3 When large rings form within the Si-O network, there are no silicon atoms present inside these rings due to the absence of shortcut paths [51] Consequently, the region enclosed by these large rings exhibits a high density of oxygen atoms, creating a negatively charged area (as depicted in Figure 3-14.a) To neutralize this charge, Mg2+ ions are drawn inward, resulting in the formation of an Mg-rich region (shown in Figure 3-14.b) The spatial distribution of Mg2+ ions 38 within the material is non-uniform, contributing to its heterogeneity As pressure increases, there is a higher proportion of large Si-O rings (as indicated by the ring statistics in Figure 3-11.a), enhancing the capacity to capture Mg atoms In other words, the heterogeneity of MgSiO3 intensifies with increasing pressure a) b) Figure 3-14 Cyan, black and red spheres are Si, O and Mg atoms respectively, the yellow path is 10-fold ring a) Ring with surrounding oxygen atoms b) Mg-rich region inside the ring 3.4 Voronoi diagrams To elucidate the arrangement of atoms within the Si-O network, an analysis of Si- and O-Voronoi volume distributions on the rings was conducted Figure 3-15 illustrates the variation in Voronoi volumes on specific rings with pressure Figure 3-16 provides an example of Si- and O-Voronoi volumes on a 6-fold ring at pressures of 50 and 200 GPa, while the spatial distribution of Voronoi volumes on the 6-fold ring is displayed in Figure 3-17 39 Ϭ'WĂ ϭϬϬ'WĂ ϭϴ ϮϬ'WĂ ϮϬϬ'WĂ ϱϬ'WĂ ^ŝsŽƌŽŶŽŝ ϭϲ ϭϰ ϭϮ ϭϬ ϴ ϲ ϰ Ϯ ϰ ϲ ϴ ^ŝͲKƌŝŶŐƚLJƉĞ ϭϬ ϭϮ sŽůƵŵĞŽĨKsŽƌŽŶŽŝƉŽůLJŚĞĚƌŽŶƐ;ϹͿ sŽůƵŵĞŽĨ^ŝsŽƌŽŶŽŝƉŽůLJŚĞĚƌŽŶƐ;ϹͿ ϮϬ ϮϬ Ϭ'WĂ ϭϬϬ'WĂ ϭϴ ϮϬ'WĂ ϮϬϬ'WĂ ϱϬ'WĂ KsŽƌŽŶŽŝ ϭϲ ϭϰ ϭϮ ϭϬ ϴ ϲ ϰ Ϯ ϰ ϲ ϴ ϭϬ ϭϮ ^ŝͲKƌŝŶŐƚLJƉĞ a) b) Figure 3-15 Characteristic of Voronoi polyhedrons of rings: average volume of Si-Voronoi (a) and O-Voronoi (b) Voronoi on rings under compression a) b) Figure 3-16 Voronoi on rings a) 6-fold ring at 50 GPa b) 6-fold ring at 200 GPa Cyan and gray polyhedrons correspond for Voronoi centered by Si and O atoms At GPa, the Si-Voronoi volume ranges from 7.50 to 7.76 Å In contrast, OVoronoi volumes at ambient pressure strongly depend on the ring type and are significantly larger than Si-Voronoi volumes At GPa, the O-Voronoi volume increases from approximately 13 Å to nearly 16 Å as the ring size expands from 40 to members However, for rings larger than size 6, the O-Voronoi volume decreases with increasing ring size The O-Voronoi volume for the 11-fold ring is around 14.3 Å The variation in O-Voronoi volume with ring size can be attributed to the distortion of SiOx units and their arrangements on the ring At ambient pressure, the distribution of O-Si-O bond angles peaks at around 109° [56] Geometrically, smaller rings have internal O-Si-O angles in SiOx units that are smaller than 109°, resulting in greater distortion of the SiOx units Besides the distortion of SiOx units, the arrangement of SiOx units on the rings through shared Si atoms also influences the volume of O-Voronoi The O-centered Voronoi volume of smaller rings (size ≤ 5) is primarily affected by the distortion of SiO4 units In contrast, for larger rings, the atoms have greater flexibility to arrange themselves into highly symmetric SiOx units, which helps reduce the system's energy [18] Consequently, SiOx units on larger rings (size > 5) experience less distortion There is a relationship between the Si-O-Si angle and the O-Voronoi volume (as observed in Figure 3-15.b and Figure 3-18) Notably, the average O-Voronoi volume is proportional to the mean Si-O-Si angle The observation that the mean Si-O-Si angle reaches a value of 148.2° and then gradually decreases to 137.5° corresponds to the decrease in O-Voronoi volume when the ring size exceeds six Therefore, the average O-Voronoi volume in 6-fold rings is greater than in other rings At pressures of 20 GPa or higher, the average Voronoi volumes of atoms of the same type on different rings tend to converge to a similar value Si atoms are surrounded by O atoms, while O atoms form bonds with both Mg and Si atoms Additionally, the mean Si-O bond length is shorter than the mean Mg-O bond length under the same pressure conditions [22] Consequently, the average distance from the center point of Si-Voronoi is shorter than that of O-Voronoi As a result, O-Voronoi exhibits a larger volume than Si-Voronoi Specifically, at pressures of 50, 100, and 200 GPa, the Si-Voronoi volumes are 6.7, 6.1, and 4.8 Å respectively, while the O-Voronoi volumes are 9.0, 7.8, and 6.0 Å respectively As pressure increases, the number of edge-sharing and face-sharing bonds increases (see Table 3-2), the model size decreases due to compression, and the polymerization of the Si-O network intensifies Atoms become densely packed, and the rings connect to one another, sometimes overlapping (as shown in Figure 3-14.a where a 2-fold ring overlaps a 10-fold ring, and in Figure 3-17 where 6-fold 41 rings merge under compression) As a result, Voronoi volumes of the same type on different rings tend to converge to an average value a) GPa b) 50 GPa c) 100 GPa d) 200 GPa Figure 3-17 The snapshot of Voronoi of 6-fold Si-O rings at a) GPa, b) 50 GPa, c) 100 GPa, d) 200 GPa 42 DĞĂŶŶŐůĞ;ĞŐƌĞĞͿ ϭϱϬ ϭϰϬ ϭϯϬ ϭϮϬ ϭϭϬ ϭϬϬ ϭ Ϯ ϯ ϰ ϱ ϲ ϳ ϴ ϵ ϭϬ ϭϭ ϭϮ ZŝŶŐƚLJƉĞ Figure 3-18 The mean Si-O-Si angle on rings at GPa 43 CONCLUSION We conducted a comprehensive investigation into the structural changes of MgSiO3 glass and liquid under compression at a temperature of 600K and 3000 K, respectively The behavior of the structure of the two systems under compression is quite similar In general, as pressure increases, there is an observable rise in the CN for both Si and Mg atoms The first peaks of Si-O in MgSiO glass and liquid shift to the right then shift to the left under compression and the ones of O-O PRDFs only shift to the left In MgSiO3 liquid, the Si-Si and O-O PRDFs exhibit rapid transformations under pressure, while the Si-O PRDF remains relatively stable This can be attributed to the formation of edge- and face-sharing linkages and an increase in the average CN of Si atoms Notably, at a pressure of 200 GPa, the system is predominantly characterized by 9-fold rings, leading to a sharp peak in the Si-Si-Si distance distribution at approximately 5.3 Å Simultaneously, Si-O linkages experience contraction due to the high pressure, resulting in the splitting of the Si-Si PRDF peak into two subpeaks at 4.6 Å and 5.3 Å The formation of these large rings at high pressures sheds 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and Nguyen Van Hong Study the structure of MgSiO3 system under compression by using ring statistics and Voronoi diagrams Physica Scripta, March 2023, doi: 10.1088/1402-4896/acc5b7 Nguyen Hoang Anh, Nguyen Hung Son and Nguyen Van Hong Pressureinduced glassy networks of enstatite (MgSiO3) and forsterite (Mg2SiO4) VNU Journal of Science: Mathematics Physics, March 2023, doi: 10.25073/25881124/vnumap.4767 50