The influence of temperature on the microstructure and the phase transition process ofof the SiO₂ bulk model

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THE INFLUENCE OF TEMPERATURE ON THE 
MICROSTRUCTURE AND THE PHASE TRANSITION PROCESS 
OF THE SiO2 BULK MODEL 
Nguyen Chinh Cuong1, Nguyen Trong Dung 
Hanoi University of Education 
Abstract: This paper studies the influence of temperature on the microstructure and the 
phase transition process of the SiO2 bulk model. This bulk model is constructed with 3000 
atoms (1000 Si atoms and 2000 O atoms) at temperatures 300K, 500K, 1000K, 1500K, 
2000K, 2500K, 3000K and 3500K and at the pressure 0GPa by the Molecular Dynamics 
Simulation method with the van Beest-Kramer-van Santen (BKS) pair interaction 
potential and periodic boundary conditions. Research results showed that almost the 
samples had the coordination number 4. When the temperature was increased, the 
number of samples with the coordination number 4 decreased while number of samples 
with the coordination number 5 and 6 increased. 
Keywords: Temperature, microstructure, phase transition process, SiO2 bulk model, 
Molecular Dynamics 
1. INTRODUCTION 
In recent years, the oxide materials Al2O3, SiO2, Fe2O3, GeO2... are widely used in 
many industries, of which SiO2 is used to manufacture the semiconductor materials. Some 
methods have been developed to study SiO2 such as the experiment method, the theory 
method and the simulation method. The obtained results have shown the polymorphism of 
the material and the influence of temperature and pressure on the microstructure and the 
phase transition process of the material [1-8].The experiment method using X-ray 
diffraction has identified the average angle of the couplings Si-O-Si is 1510 [9] and 1440 
[10]; Zachariasen predicted the microstructure of SiO2 with the amorphous state and the 
liquid state is mainly SiO4 structure unit [11] which has been determined through the X-ray 
diffraction technique of Mozzi and Warren [12].The simulation method using the 
1 Nhận bài ngày 19.8.2016; gửi phản biện và duyệt đăng ngày 15.9.2016 
 Liên hệ tác giả: Nguyễn Chính Cương; Email: nccuong@hnue.edu.vn 
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molecular dynamics model has determined the average angle of the couplings Si-O-Si is 
1450 [13], while the average angle of the couplings O-Si-O is 109.50 [14], 109.470 [13, 14] 
and the average length of the couplings Si-Si, Si-O, O-O at the pressure 0GPa is 3.07 Å, 
1.59 Å, 2.61 Å [8], 3.08 Å, 1.6 Å, 2.6 Å [5], 3.11 Å, 1.56 Å, 2.50 Å [14], 3.12 Å, 1.62 Å 
and 2.65 Å [13, 14] and transition temperature 2973K (from solid to liquid state) [16]. The 
results showed that there were differences between the experiment method and the 
simulation method both in terms of the coupling length and the coupling angle. In order to 
clarify this issue, we studied the microstructure, the phase transition process of the SiO2 
bulk model under the influence of the temperature, the pressure and determining the phase 
transition temperature of the model. The obtained results will support the experimental 
measurements in order to increase the applicability of the material in practice. 
2. RESEARCH METHOD 
To study the microstructure and the phase transition process of SiO2 by the Molecular 
Dynamics (MD) Simulation method, pair interaction potential and the van Beest-Kramer-
van Santen (BKS) pair interaction potential were used [17], in which we mainly used the 
BKS pair interaction potential. In this paper, we used the Molecular Dynamics Simulation 
method with BKS pair interaction potential in the form (1) and periodic boundary 
conditions. 
ij ij
2
B ri j 6
rj ij ij ij ij ij
ij
q q e
U (r) A e B r C r
r
− −= + − −
(1) 
Including: Aij, Bij and Cij are the potential coefficients of the model; qi, qj are the 
charges of the two atoms i and j; rij is the distance between the ith atom and the jth atom; 
Uij(r) is the interaction energy between the ith atom and the jth atom which is shown in 
Table 1 
Table 1. The parameters in the SiO2 bulk model. 
Factor Aij (eV) Bij (Å-1) Cij (eVÅ5) qij (e) 
Si-Si 0.0 0.0 0.0 
Si-O 18003.5773 4.87318 133.5381 qsi=+2.4 
O-O 1388.773 2.76 175.0 qo=-1.2 
The SiO2 bulk model with 3000 atoms (1000 Si atoms and 2000 O atoms) was initially 
put randomly in a cubic box. It was run with the statistical recovery of 2.104 steps by the 
BKS pair interaction potential and periodic boundary conditions so that the atoms 
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(molecules) were not stuck together. After that, the temperature was increased to 300K, 
500K, 1000K, 1500K, 2000K, 2500K, 3000K and 3500K at the pressure 0GPa to reach the 
expected value. All samples were run simultaneously with 5.105 NVE steps until the model 
reaching to the stable state. The obtained samples were analyzed through the shape, the 
size, the energy, the radial distribution functions, the coordination number, the distribution 
angle, the length of the coupling and the phase transition temperature through the 
relationship between the energy and the temperature of the samples. 
3. SIMULATION RESULTS 
The SiO2 bulk model (3000 atoms) was simulated by the Molecular Dynamics (MD) 
method with the BKS pair interaction potential and periodic boundary conditions. The 
result on the shape of the sample at the temperature 300K is shown in Figure 1. 
Fig. 1. The shape of the SiO2 bulk sample (3000 atoms) at the temperature 300K. 
The result in Figure 1 shows that the SiO2 bulk model at the temperature 300 K had 
the cubic shape and nano scale with the existence of the two atoms: Si and O. Si atoms are 
red and the O atoms are blue. When the temperature was increased from 300 K to 500 K, 
1000 K, 1500 K, 2000 K, 2500 K, 3000 K and 3500 K, the size of the samples are shown 
in Table 2. 
Table 2. The size of the samples at the different temperatures 
Temperature (K) 300 500 1000 1500 2000 2500 3000 3500 
The size (nm) 3.4399 3.4430 3.4502 3.4538 3.4584 3.4436 3.4315 3.4246 
Table 2 shows that when the temperature was increased from 300K to 2000K, the size 
of the model increased from 3.4399 nm to 3.4584 nm; in the temperature range from 
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2000K to 3500K, the size of the model reduced from 3.4584 nm to 3.4246nm. This 
indicates that the temperature range from 2000K to 3000K are the phase transition range of 
the model from the amorphous state to the liquid state. 
The microstructure of the SiO2 bulk model continues to be studied at different 
temperatures, the results are shown in Figure 2 and Table 3. 
Figure 2. The radial distribution function (RDF) of the SiO2 bulk samples 
at the temperature 300 K 
Table 3. The position, the height and the average coordination number 
of the radial distribution function at different temperatures 
rij (Å) gij Zij Temperature 
(K) Si-Si Si-O O-O Si-Si Si-O O-O Si-Si Si-O O-Si O-O 
300 K 3.18 1.64 2.64 4.53 24.72 4.75 4.16 4.02 2.01 7.51 
500 K 3.18 1.62 2.64 4.43 20.54 4.50 4.17 4.02 2.01 7.50 
1000 K 3.16 1.62 2.64 4.01 15.55 3.87 4.18 4.02 2.01 7.46 
1500 K 3.16 1.62 2.64 3.63 12.60 3.50 4.18 4.02 2.01 7.46 
2000 K 3.14 1.62 2.66 3.31 11.00 3.20 4.15 4.01 2.01 7.45 
2500 K 3.18 1.62 2.66 3.07 9.64 2.94 4.15 4.02 2.01 7.50 
3000 K 3.16 1.62 2.68 2.85 8.52 2.71 4.2 4.02 2.01 7.59 
3500 K 3.18 1.62 2.66 2.59 7.46 2.47 4.2 4.03 2.01 7.68 
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From Figure 2 and Table 3 we can see the SiO2 bulk model at temperatures 300K, 
500K, 1000K, 1500K, 2000K, 2500K, 3000K and 3500K with the height of the first peak 
of the radial distribution function predominates. When the temperature was increased, the 
first peak position of radial distribution function of the coupling Si-Si changed around 1.2 
%, increased insignificantly in the coupling O-O and changed slightly in value with the 
coupling Si-O. This result is consistent with previous simulation results (at the normal 
pressure, the couplings Si-Si, Si-O, O-O have the length of 3.07 Å; 1.59 Å; 2.61 Å [8], 
3.08 Å; 1.6 Å; 2.6 Å [5], 3.11 Å; 1.56 Å; 2.50 Å [12], 3.12Å; 1.62Å; 2.65Å) [13, 14] 
respectively. This indicates that the distance of coupling Si-O did not depend on the 
temperature and there always existed a close order in the coupling Si-O. The first peak 
height of radial distribution function of the coupling Si-O at temperatures 300K had the 
greatest value. When temperature was increased, the first peak height of the radial 
distribution function decreased gradually. Similarly, the first peak position and height of 
the radial distribution function decreased in the couplings of Si-Si and O-O. This indicates 
that there were influences of the temperature on the length of the couplings Si-Si, Si-O, O-
O which led to the heterogeneity of the microstructure of the SiO2 bulk model. In addition, 
in the temperature range from 2000K to 3000K, the first peak height of the radial 
distribution function of the coupling Si-O tended to slow down the decrease. It shows that 
in this temperature range, the SiO2 bulk model had the phase transition process from an 
amorphous state to a liquid state. 
To study this in detail, we analyzed the coordination number of the samples at 
different temperatures. The results can be seen in Figure 3 and Table 4 
Figure 3. The coordination number in the SiO2 bulk model 
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Table 4. The coordination numbers 4, 5 and 6 of the samples at different temperatures 
Temperature (K) 300 500 1000 1500 2000 2500 3000 3500 
4 1973 1972 1968 1963 1965 1960 1897 1786 
5 75 67 78 121 94 104 253 436 
Coordination 
number 
6 0 1 0 7 3 1 17 29 
The results in Figure 3 and Table 4 shows that, the coordination number 4 (Figure 3a), 
the coordination number 5 (Figure 3b), the coordination number 6 (Figure 3c) and the 
couplings Si-O-Si (Figure 3d) existed in the SiO2 model. When the temperature was 
increased, the coordination number 5 and 6 increased while coordination number 4 
decreased (Table 4). In the temperature range from 2000K to 3000K, the coordination 
number 4 decreased quickly while the coordination number 5 and 6 increased quickly. It 
indicates that in this temperature range, the sample tended to gradually change from the 
crystalline state to the liquid state. The results shown in Table 5 which illustrates the 
distribution of the angle between the two atoms Si and O. 
Table 5. The distribution of angle of the couplings O-Si-O in SiO2 model 
Temperature 
(K) 
300 500 1000 1500 2000 2500 3000 3500 
O-Si-O 
(degree) 
105 105 105 105 105 105 105 105 
Si-O-Si 
(degree) 
140 140 145 145 145 145 145 145 
Table 5 showed that when the temperature was increased, the distribution of the angle 
of the couplings Si-O-Si changed slightly from 1400 to 1450, the angle of the couplings O-
Si-O between the Si atoms and the O atoms was 1050. These results are completely 
consistent with the previous research results: the distribution of angle of Si-O-Si measured 
in experiment is 1510 [1], 1440 [2], 1440 [3]; the distribution of angle of Si-O-Si in 
simulation is 1520 [6], 1450 [7] and the distribution of angle of O-Si-O in simulation is 
109.50 [12], 109.470 [13, 14]. In other words, the distribution of the angle between the 
atoms Si, O depends strongly on the temperature. 
In addition, we can determine the phase transition temperature of the SiO2 bulk model. 
Research results are shown in Table 6 and Figure 4. 
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Table 6. The energy of the model at different temperatures 
Temperature 
(K) 
300 500 1000 1500 2000 2500 3000 3500 
Energy (eV) -53230.411 -53074.651 -52680.729 -52279.583 -51872.542 -51472.907 -50985.287 -50383.735 
Figure 4. The phase transition temperature of the SiO2 model 
Results in Table 6 and Figure 4 show that when the temperature was increased, the 
energy of the samples decreased gradually. Particularly, at temperature range from 2000K 
to 3000K the energy of the SiO2 bulk model decreased strongly. The phase transition 
temperature of the model was 2787.6K corresponding to the energy level of - 51265.3. 
This result is entirely consistent with the simulation results 2973K [16]. Basing on the 
above mentioned research and analysis results, we can determine that the influence of 
temperature on the microstructure and the phase transition process of the model is 
significant. 
4. CONCLUSION 
By using the Molecular Dynamics method, the influence of temperature on the 
microstructure, the diffusion and the phase transition temperature of the SiO2 sample with 
3000 atoms at temperatures 300K, 500K, 1000K, 1500K, 2000K, 2500K, 3000K and 
3500K was studied and analyzed. The obtained results are following: 
− The selection of the van Beest-Kramer-van Santen (BKS) pair interaction potential 
with parameters to simulate the SiO2 sample (3000 atoms) have given the consistent results 
with the previous experiment and simulation results. 
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− When the temperature is increased, the size of the model increases then decreases, 
the energy of the model increases and the phase transition temperature of the model is 
determined as 2787.6K. 
− In the temperature range from 300K to 2787.6K, the model exists in the amorphous 
state with the structure of the bulk materials and this has been shown in the previous 
works. 
− There is the influence of temperature on the microstructure and the phase transition 
process of the model. 
− There are differences on the microstructure of the couplings Si-Si, Si-O, O-O in the 
models. 
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ẢNH HƯỞNG CỦA NHIỆT ĐỘ LÊN VI CẤU TRÚC 
VÀ QUÁ TRÌNH CHUYỂN PHA CỦA MÔ HÌNH KHỐI SIO2 
Tóm tắt: Bài báo này nghiên cứu sự ảnh hưởng của nhiệt độ lên vi cấu trúc và quá trình 
chuyển pha của mô hình khối SiO2. Mô hình khối này được xây dựng với 3000 nguyên tử 
(1000 nguyên tử Si và 2000 nguyên tử O) ở nhiệt độ (300 K, 500 K, 1000 K, 1500 K, 2000 
K, 2500 K, 3000 K và 3500 K) và ở áp suất 0Gpa bằng phương pháp mô phỏng động lực 
học phân tử, với thế tương tác cặp van Beest-Kramer-van Santen (BKS) và điều kiện biên 
tuần hoàn. Các kết quả nghiên cứu cho thấy các mẫu có số phối vị 4 là chủ yếu, khi tăng 
nhiệt độ thì mẫu có số phối vị 4 giảm dần, số phối vị 5 và 6 tăng dần. 
Từ khoá: Nhiệt độ, vi cấu trúc, quá trình chuyển pha, mô hình khối SiO2, động lực học 
phân tử.