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

TẠP CHÍ KHOA HỌC − SỐ 8/2016

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THE INFLUENCE OF TEMPERATURE ON THE

MICROSTRUCTURE AND THE PHASE TRANSITION PROCESS

OF THE SiO₂BULK 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 SiO₂bulk 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 BeestꢀKramerꢀvan 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, SiO₂bulk model,

Molecular Dynamics

1. INTRODUCTION

In recent years, the oxide materials Al₂O₃, SiO₂, Fe₂O₃, GeO₂... are widely used in

many industries, of which SiO₂is used to manufacture the semiconductor materials. Some

methods have been developed to study SiO₂such 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 [1ꢀ8].The experiment method using Xꢀray

diffraction has identified the average angle of the couplings SiꢀOꢀSi is 151⁰[9] and 144⁰

[10]; Zachariasen predicted the microstructure of SiO₂with the amorphous state and the

liquid state is mainly SiO₄structure unit [11] which has been determined through the Xꢀray

diffraction technique of Mozzi and Warren [12].The simulation method using the

1

Nhꢁn bài ngày 19.8.2016; gꢂi phꢃn biꢄn và duyꢄt ñăng ngày 15.9.2016

Liên hꢄ tác giꢃ: Nguyꢅn Chính Cương; Email: nccuong@hnue.edu.vn

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TRƯỜNG ĐẠI HỌC THỦ ĐÔ Hꢀ NỘI

molecular dynamics model has determined the average angle of the couplings SiꢀOꢀSi is

145⁰[13], while the average angle of the couplings OꢀSiꢀO is 109.5⁰[14], 109.47⁰[13, 14]

and the average length of the couplings SiꢀSi, SiꢀO, OꢀO 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 SiO₂by the Molecular

Dynamics (MD) Simulation method, pair interaction potential and the van BeestꢀKramerꢀ

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.

q_iq_je²

+ A_ije^{−B r}− B_ijr_ij−C_ijr_ij⁻⁶

ij ij

(1)

U_rj(r) =

r

ij

Including: A_ij, B_ijand C_ijare the potential coefficients of the model; qi, qj are the

charges of the two atoms i and j; r_ijis the distance between the i^thatom and the j^thatom;

U_ij(r) is the interaction energy between the i^thatom and the j^thatom which is shown in

Table 1

Table 1. The parameters in the SiO₂bulk model.

Factor

SiꢀSi

SiꢀO

OꢀO

A_ij(eV)

0.0

Bij (Å^ꢀ1)

0.0

Cij (eVÅ⁵)

0.0

qij (e)

18003.5773

1388.773

4.87318

2.76

133.5381

175.0

q_si=+2.4

q_o=ꢀ1.2

The SiO₂bulk 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 2.10⁴steps by the

BKS pair interaction potential and periodic boundary conditions so that the atoms

TẠP CHÍ KHOA HỌC − SỐ 8/2016

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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 5.10⁵NVE 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 SiO₂bulk 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 SiO₂bulk sample (3000 atoms) at the temperature 300K.

The result in Figure 1 shows that the SiO₂bulk 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

300

500

1000

1500

2000

2500

3000

3500

Temperature (K)

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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TRƯỜNG ĐẠI HỌC THỦ ĐÔ Hꢀ NỘI

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 SiO₂bulk 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 SiO₂bulk 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

r_{ij (Å)}

SiꢀO

g_ij

Z_ij

Temperature

(K)

SiꢀSi

OꢀO

SiꢀSi

SiꢀO

OꢀO

4.75

4.50

3.87

3.50

3.20

2.94

2.71

2.47

SiꢀSi

4.16

4.17

4.18

4.15

4.2

SiꢀO

OꢀSi

OꢀO

300 K

500 K

3.18 1.64 2.64 4.53 24.72

3.18 1.62 2.64 4.43 20.54

3.16 1.62 2.64 4.01 15.55

3.16 1.62 2.64 3.63 12.60

3.14 1.62 2.66 3.31 11.00

3.18 1.62 2.66 3.07 9.64

3.16 1.62 2.68 2.85 8.52

3.18 1.62 2.66 2.59 7.46

4.02 2.01 7.51

4.02 2.01 7.50

4.02 2.01 7.46

4.01 2.01 7.45

4.02 2.01 7.50

4.02 2.01 7.59

4.03 2.01 7.68

1000 K

1500 K

2000 K

2500 K

3000 K

3500 K

4.2

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From Figure 2 and Table 3 we can see the SiO₂bulk 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 SiꢀSi changed around 1.2

%, increased insignificantly in the coupling OꢀO and changed slightly in value with the

coupling SiꢀO. This result is consistent with previous simulation results (at the normal

pressure, the couplings SiꢀSi, SiꢀO, OꢀO 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 SiꢀO did not depend on the

temperature and there always existed a close order in the coupling SiꢀO. The first peak

height of radial distribution function of the coupling SiꢀO 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 SiꢀSi and OꢀO. This indicates

that there were influences of the temperature on the length of the couplings SiꢀSi, SiꢀO, Oꢀ

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 SiꢀO 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 SiO₂bulk model

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TRƯỜNG ĐẠI HỌC THỦ ĐÔ Hꢀ NỘI

Table 4. The coordination numbers 4, 5 and 6 of the samples at different temperatures

300

1973

75

500

1972

67

1000

1968

78

1500

1963

121

7

2000

1965

94

2500

1960

104

1

3000

1897

253

17

3500

1786

436

29

Temperature (K)

4

5

6

Coordination

number

0

1

0

3

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 SiꢀOꢀSi (Figure 3d) existed in the SiO₂model. 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 OꢀSiꢀO in SiO₂model

Temperature

300

105

140

500

105

140

1000

105

1500

105

2000

105

2500

105

3000

105

3500

105

(K)

OꢀSiꢀO

(degree)

SiꢀOꢀSi

(degree)

145

Table 5 showed that when the temperature was increased, the distribution of the angle

of the couplings SiꢀOꢀSi changed slightly from 140⁰to 145⁰, the angle of the couplings Oꢀ

SiꢀO 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 SiꢀOꢀSi measured

in experiment is 151⁰[1], 144⁰[2], 144⁰[3]; the distribution of angle of SiꢀOꢀSi in

simulation is 152⁰[6], 145⁰[7] and the distribution of angle of OꢀSiꢀO 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 SiO₂bulk model.

Research results are shown in Table 6 and Figure 4.

TẠP CHÍ KHOA HỌC − SỐ 8/2016

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Table 6. The energy of the model at different temperatures

Temperature

(K)

300

500

1000

1500

2000

2500

3000

3500

ꢀ53230.411 ꢀ53074.651 ꢀ52680.729 ꢀ52279.583 ꢀ51872.542 ꢀ51472.907 ꢀ50985.287 ꢀ50383.735

Energy (eV)

Figure 4. The phase transition temperature of the SiO₂model

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 SiO₂bulk 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 SiO₂sample 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 BeestꢀKramerꢀvan Santen (BKS) pair interaction potential

with parameters to simulate the SiO₂sample (3000 atoms) have given the consistent results

with the previous experiment and simulation results.

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TRƯỜNG ĐẠI HỌC THỦ ĐÔ Hꢀ NỘI

−

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 SiꢀSi, SiꢀO, OꢀO in the

models.

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ꢁNH HƯꢂNG CꢃA NHIꢄT Đꢅ LÊN VI CꢆU TRÚC

VÀ QUÁ TRÌNH CHUYꢇN PHA CꢃA MÔ HÌNH KHꢈI SIO₂

Tóm tꢁt: Bài báo này nghiên cꢂu sꢃ ꢄnh hưꢅng cꢆa nhiꢇt ñꢈ lên vi cꢉu trúc và quá trình

chuyꢊn pha cꢆa mô hình khꢋi SiO₂. Mô hình khꢋi này ñưꢌc xây dꢃng vꢍi 3000 nguyên tꢎ

(1000 nguyên tꢎ Si và 2000 nguyên tꢎ O) ꢅ nhiꢇt ñꢈ (300 K, 500 K, 1000 K, 1500 K, 2000

K, 2500 K, 3000 K và 3500 K) và ꢅ áp suꢉt 0Gpa bꢏng phương pháp mô phꢐng ñꢈng lꢃc

hꢑc phân tꢎ, vꢍi thꢒ tương tác cꢓp van BeestꢀKramerꢀvan Santen (BKS) và ñiꢔu kiꢇn biên

tuꢕn hoàn. Các kꢒt quꢄ nghiên cꢂu cho thꢉy các mꢖu có sꢋ phꢋi vꢗ 4 là chꢆ yꢒu, khi tăng

nhiꢇt ñꢈ thì mꢖu có sꢋ phꢋi vꢗ 4 giꢄm dꢕn, sꢋ phꢋi vꢗ 5 và 6 tăng dꢕn.

Tꢘ khoá: Nhiꢇt ñꢈ, vi cꢉu trúc, quá trình chuyꢊn pha, mô hình khꢋi SiO₂, ñꢈng lꢃc hꢑc

phân tꢎ.