HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

MASTER’S THESIS
Structural Simulation of MgSiO3
under High Pressure Condition

NGUYEN HOANG ANH


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

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 3 liquid. The
pressure range examined in this study spans from 0 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 2
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 ................................................................................................ 1
CHAPTER 1. OVERVIEW ................................................................................... 4
1.1. Silica structure ......................................................................................................... 4
1.2. Structure of ternary MgO-SiO2 models ................................................................ 7
CHAPTER 2. 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 3. 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 0 GPa. b) 8-fold Si ring at 0 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


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) 0 GPa, b) 50 GPa,
c) 100 GPa, d) 200 GPa. ............................................................................................... 42 
Figure 3-18. The mean Si-O-Si angle on rings at 0 GPa. ......................................... 43

iii


LIST OF TABLES
Table 2-1. Parameters of OG potential....................................................................... 16
Table 3-1. The first peak position of PRDFs, the CN of MgSiO 3 glass (a) and
MgSiO3 liquid (b), at 0 GPa ......................................................................................... 26
Table 3-2. The number of corner-(Nc), edge-(Ne), face-sharing (Nf) network per the
number of Si atoms at different pressure, corresponding with the mean bond
length of them, corner-, edge-, face-sharing bond length of MgSiO 3 glass (a) and
MgSiO3 liquid (b). .........................................................................................................30

iv


INTRODUCTION

1. Problem Statement
Silica and magnesium silicate play a crucial role in high technologies such as

microelectronics technology, porous ceramic membranes, refractory brick,
biomedical glass, etc. They are also one of the most popular constituents of the
Earth’s crust and mantle. Because of this great significance in materials science and
geosciences, the structural properties of silica, magnesium silicate and materials
with chemical formulas close to them in both the glass and liquid states (‫ݪ‬MgO –
 ˲ ‫
ݪ‬SiO2) have been extensively studied in many decades. Silica and magnesium

silicate attract the interest of researchers and have been investigated by both
experimental methods such as X-ray diffraction, nuclear magnetic resonance
(NMR), etc., and by simulation methods like density function theory (DFT). Silica
and silicate are formed by fundamental structural units, with silica being SiO x units
and with silicates being SiOx and MgOy units. These basic units link to each other
via common O atoms. In MgSiO3, the structural transition occurs drastically under
compression but does not much vary with temperature. This structural change is
mainly due to the fact that at high pressure, the atoms tend to be more tightly
packed, and the influence of Mg2+ ions also changes strongly with pressure.
Nonetheless, the comprehension of how pressure and temperature impact the
microstructure of MgSiO3 remains restricted and poses a significant obstacle,
particularly when it comes to the intermediate range order (IRO) of such materials.
Given the unexplored characteristics associated with this, the purpose of this study
is to contribute additional insights into the structural network of these materials.

2. Scope of the study
The research objects are to study MgSiO 3 in two states, namely glass (at 600 K)
and liquid (at 3000 K), under various pressure conditions. The pressure range for
MgSiO3 glass and liquid is 0-200 GPa.

3. Research methods
The thesis employs the following methods and techniques:

-

Model construction: molecular dynamics (MD) simulation – MgSiO 3 glass
and MgSiO3 liquid systems are constructed by MD simulation at 600 K,
1


ranging from 0 to 200 GPa with periodic boundary condition for all three
dimensions. The interatomic Oganov (OG) potential has been applied for
simulating structure. The code is written in C language.
-

Structural analysis method: the local structure (short-range order (SRO))
and IRO are clarified through radial distribution function (RDF),
coordination number (CN), ring statistics, Qn distribution and Voronoi
diagrams.

-

Visualization technique: the models are visualized by MATLAB, OriginLab.

4. The scientific and practical significance of the topic
The thesis presents a comprehensive examination of the microstructure of
MgSiO3 glass and liquid under varying pressure conditions, with a particular focus
on the ring statistics of the network structure. Additionally, this research aims to
address specific issues which could prove beneficial for future investigations.
Enstatite and forsterite, which are two-component magnesium silicates, are
widely used in technology and scientific fields, and they also constitute the primary
materials found in the Earth's mantle. Hence, gaining a better understanding of the
structure and dynamics of silicate systems holds significant importance for

technological advancements, particularly in high-tech industries and geoscience.
This knowledge can enable better control and prediction of natural phenomena
occurring in the Earth's crust, mantle.

5. New contributions of the thesis
The investigation of the IRO of MgSiO3 through ring statistics is considerably
deficient. Consequently, this study aims to contribute to the understanding of ring
statistics and various related aspects mentioned earlier, such as the splitting peak
of the second peak Si-Si PRDF, the Mg-rich region, heterogeneity, Voronoi
diagrams, and the distribution of Qn values on the rings.

6. The structure of the thesis
The thesis consists of three main chapters as follows:
Chapter 1 – Overview: presents a general understanding of the system. The results
are indicated and cited from the previous investigations.

2


Chapter 2 – Methodology: describes how to build the systems, algorithms,
computational techniques, and structural analysis as well as visualization in certain
cases.
Chapter 3 – Results and discussion

3


CHAPTER 1. OVERVIEW
Silica and two-component silicate materials, such as MgO-SiO2, hold
significant importance in various fields including geology, geophysics, and

microelectronics technology, etc. [1,2]. Extensive research is being conducted
using experimental and simulated methods to understand their properties and
optimize technological processes. Among the key areas of focus, the
microstructure characteristics of these materials have garnered significant
attention from scientists. This chapter provides a general overview of silica and
silicate materials. MgSiO3 can be regarded as SiO2 doped with MgO, where the Mg
cations act as both network formers and modifiers [3–5]. The structure gradually
transitions from SiO2 to SiO2 doped with MgO. Therefore, this section introduces
the SiO2 structure to enhance comprehension of these material types. Investigating
the microstructure of MgSiO3 as it varies with pressure can aid in understanding
the atomic origins of various physical properties, including crystal-melt
partitioning, elasticity, viscosity, and density of silicate glass and melts [6]. The
changes of the structure occur continuously throughout the entire range of
compression.

1.1. Silica structure
Silica, the simplest oxide among silicon compounds, is widely present inside
the Earth, often found in the form of white sand or quartz [7]. Despite its
straightforward chemical composition, SiO2 holds immense significance in
semiconductor technology, materials science, and geoscience, etc. Numerous
studies have been conducted on this material under ultrahigh pressures and
temperatures to create extreme computer-simulated environments resembling
Earth's conditions. Simulation methods offer notable advantages as they allow
exploration of a wide range of pressure and temperature conditions without
limitations.
To analyze the microstructure of SiO2, as well as other materials, the RDF (‫)
ݤݚ‬
plays a crucial role. In experimental methods, ‫
ݤݚ‬is obtained by transforming the
total structure factor (‫ )

݊݌‬measured through methods such as neutron scattering
or X-ray diffraction. The scattering factor (݊) is determined using the formula
৷‫ݠݛݥ‬৯
৲, where ৲ represents the wavelength and the scattering angle is denoted

4


as ৯ [8]. In atomistic simulations, analyzing the RDF only requires the atomic
coordinates.
The phase transition temperatures for the melt-crystal system range from 1673
to 1823 K, while for the melt-glass system, they fall between 1247 and 1533 K [9].
The changes in structural order during the phase transition result in variations in
density. Melted silica has a density of approximately 2.2 g/cm3, but when it
transforms into a solid state, the density ranges from 2.2 to 2.5 g/cm3 for vitreous
silica and 2.3 to 4.6 g/cm3 for crystalline silica.
Glass silica exhibits a continuous random-network structure, first introduced
by Zachariasen [10]. The arrangement of atoms in the system serves as a
distinguishing feature to differentiate between the SRO of glass, the long-range
order of crystals, and the disordered amorphous or liquid state. The author
proposed that silica glass consists of fundamental structural units comprising a
silicon (Si) atom surrounded by three, four, or five oxygen (O) atoms. However,
the most prominent units are the tetrahedrons formed by Si atoms and four
neighboring O atoms, resulting in a mean CN of the system of about 4. When Si
atoms possess CNs other than 4, it introduces asymmetry to the system, leading to
an increase in total energy. In order to achieve the most stable state for the material,
the energy must be minimized.
Through the RDF, we can determine the SRO and IRO of the structure. The
results measured by previous experimental and simulated methods are similar
[11]. The MD results of S. K. Mitra [12] indicate that the spatial structure in SiO 2

glass contains fundamental SiO4 units at ambient pressure. These units link to each
other forming the continuous random network. The O-Si-O bond angle
distribution has the maximum value close to 109.5 p, which is expected for a regular
tetrahedron. The mean distance between an arbitrary Si atom and nearest O atoms
in that tetrahedron is approximately 1.6q0.1 Å. The CN of Si-O pair is 4q0.1. The
IRO of silica glass depends on the change of Si-O-Si angle and Si-Si distance, where
Si-O-Si can be considered as the linkage angle between two adjacent structural
units. The Si-O-Si angles are in the range of 120p–180p through neutron scattering
method, the peak position is located at 144p [13].
The experimental work [14] using X-ray diffraction method reveals that the OSi-O bond angle distribution has a maximum angle at 109.3(3)p, with the root
mean square value of 4.2(3)p. The Si-O-Si bond angle distribution is quite broad
and reach the maximum value at 180p. The peak of this bond angle distribution is
5


147p, being identical to the result in the research of T.Wu et al. [15]. The average
bond length of Si-O, O-O, Si-Si has also shown in this work are 1.59 Å, 2.61 Å and
3.07 Å, respectively. These values are in decent agreement with the investigation of
F. Mauri et al. [16]. The Si-O-Si bond angle distribution concentrates from 130pto
180p and has a peak in the angle interval of 140-155p. Besides, the fundamental
units SiO4 link together by the corner-sharing bond (one common O atom, this O
atom also known as bridging oxygen atom). There are no edge-sharing and facesharing linkages in the same condition.
The IRO of SiO2 is analyzed through the distribution of Si-Si-Si, O-O-O, O-SiSi, O-O-Si angles. By using the Reverse Monte Carlo (RMC) method, Kohara et al.
stated the peak of Si-Si-Si bond angle distribution is nearly at 60p(3-fold ring of Si)
and 80p-150p (4-fold to the 8-fold ring of Si) [17]. To analyze SiO2-type covalent
structure, J. P. Rino and colleagues defined that the ring size is the shortest path
(convenient way) between two neighboring O atoms of the given Si atom. This
shortest path does not include the given Si atom [18]. Si-Si-O, O-O-O, O-O-Si
angle have corresponding peaks at 15p, 60p, 40p. They pointed out the size of the
ring is in a range from 3-fold to 10-fold, while 6-fold size appears the most in both

liquid and glass states. However, the size could be broader.
In the simulation method, R. G. Della Valle and H. C. Andersen [19] proved
the computing results are not much dependent on the model size. The mean bond
length of Si-O, O-O, Si-Si are 1.645 Å, 2.694 Å and 3.184 Å respectively; and
corresponding CNs are 4.0, 6.0 and 4.0. The calculated O-Si-O is 109.5 p, rather
similar to the aforementioned results in experimental works [16–18]. A high
amount of those angles is found because the potential energy of system depends
on more on O-Si-O angle than on Si-O-Si angle. In addition to analysis
microstructure of vitreous silica at ambient pressure, research on the change of the
structure at extreme condition is necessary. The microstructure of SiO2 changes
drastically as a function of pressure. The structural phase transits from SiO4 to SiO6
through SiO5 unit when compressing [20]. The formation of SiO6 units is the most
significant in the range 8 – 40 GPa.
In conclusion, at ambient pressure, SiO4 units link to each other through one
common atom (conner-sharing bond) and form silica network. At higher pressure,
the average CN of Si-O increases, or the model creates 5-fold, 6-fold, or higherfold coordinated Si because the atoms are highly packed. Previous studies also
proved that the size of the model does not significantly affect results of
6


microstructure. The changes of the structure depend less on temperature and more
on compression.

1.2. Structure of ternary MgO-SiO2 models
In SiO2, at ambient pressure, the SiO4 tetrahedrons link to each other through
one common O atom and create a continuous random network [10]. This O atom
is known as bridging oxygen (BO). O atom only links to one Si atom called nonbridging oxygen (NBO). O atom, which does not link to any Si atoms, is free
oxygen (FO). At 0 GPa, silica glass mostly consists of BO, the percentage of NBO
is very little and there is no FO [7]. The change of microstructure doped MgO into
pure silica (magnesium silicate) has been indicated in experimental as well as

simulation studies. The evolution of detail composition-dependent structure in
MgO-SiO2 glass has been regularly investigated by neutron and X-ray diffraction.
The first peak of Si-O PRDF is nearly located at 1.64 Å. The Si-O CN is 4.0 [21]
and almost unchanged compared to pure vitreous silica. Meanwhile, the O-Si-O
bond angle in SiO4 units is 105p for MgSiO3 and approximately 106p for Mg2SiO4
[22]; it is smaller than the one in silica glass (about 109 p). This change is
insignificant (around 2% altering) when MgO is doped. The coordinated O-Si is
1.35 at ambient pressure, much smaller than the one in pure silica glass. This is
attributed to the broken O-Si bonds that cause the transformation of BO to NBO
and the creation of Si-NBO-Mg linkages. Qn is given to clarify the relation between
Si-O and O-Si CN (n is the number of BO, can be in any coordination state). At
ambient pressure, Q1, Q2, Q3 are dominant in MgSiO3 glass, taking up about 80%
of total Qn. In particular, the proportions of NBO, BO, and FO are 62%, 37% and
0% at zeros pressure [6]. While M. C. Wilding et al. [23] have shown the
corresponding percentages are 68.8%, 27.3% and 3.4%. Under densification, the
rate of high-order Qn species increases, which leads to a better connecting ability
of the -Si-O- network. As a result, the doped component (Mg-O) causes light effect
on the fundamental structural units, but strong effect on the linkages between
them. Thus, Si and O species are considered as network formers, while Mg species
are network modifiers (Figure 1-1) or even network formers in some cases.

7


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.

The experimental methods investigating the molecular structure of glasses are
commonly nuclear magnetic resonance, X-ray diffraction, X-ray absorption,

neutron scattering, vibrational spectroscopy, and Raman spectroscopy. For X-ray
diffraction data, C. D. Yin and coworker pointed out that the mean CN for Mg-O
is 4.5 for MgSiO3 – enstatite, 5.0 for Mg2SiO4 – forsterite [24]. In MgSiO3, Mg
species have 6-fold coordination (4 neighboring O atoms at 2.08 Å and 2
neighboring O atoms at 2.50 Å) or 4-fold coordination (4 neighboring O atoms at
2.04 Å). Si-O, Mg-O and O-O bond lengths are corresponding 1.64 Å, 2.0 and 2.69
Å by neutron investigation [21]. While, with X-ray method, the Si-O, Si-Si, SiMg/Si distances are 1.64 Å, 2.74 Å and 3.2 Å, respectively [25]. The position of the
first peak in Mg-O PRDF is 2.0 Å, which has an asymmetric shape but has a drastic
high-r tail. That is attributed to the wide distribution of Mg-O bonding distance
and the distortion of magnesium coordination polyhedron. The CN of Mg-O was
determined from the integrating the pair correlation function with integration
limits taken as the minima on either side of the Mg-O peak. Mg-O CN in MgSiO3
is interval 4.5 q 0.1 with MgSiO3 (mixture of coordinated MgO3 and MgO4). This
8