A New Study on the Structure, and Phase Transition Temperature of Bulk Silicate Materials by Simulation Method of Molecular Dynamics

Abstract

In this paper, the structure and phase transition temperature of bulk silicate materials are studied by the simulation method (SM) of molecular dynamics (MD). In this research, all samples are prepared on the same nanoscale material model with the atomic number of 3000 atoms, for which the SM of MD is performed with Beest-Kramer-van Santen and van Santen pair interaction potentials under cyclic boundary conditions. The obtained results show that both the model size (l) and the total energy of the system (E_tot) increase slowly in the low temperature (T) region (negative T values) at pressure (P), P = 0 GPa. However, the increase of l determines the E_tot value with very large values in the high T region. It is found that l decreases greatly in the high T region with increasing P, and vice versa. In addition, when P increases, the decrease in the E_tot value is small in the low T region, but large in the high T region. As a consequence, a change appears in the lengths of the Si-Si, Si-O, and O-O bonds, which are very large in the high T and high P regions, but insignificant in the low T and low P regions. Furthermore, the structural unit number of SiO₇ appears at T > 2974 K in the high P region. The obtained results will serve as the basis for future experimental studies to exploit the stored energy used in semiconductor devices.

1. Introduction

Today, with the significant development of computer science and materials science for technology, it is possible for researchers to approach materials at the nanoscale. Among the study tools used, the simulation method (SM) of molecular dynamics (MD) is currently the most effective method for studying the structure, phase transition, and determining the phase transition temperature (Tm) of new materials [1]. In the framework of this method, the motion of atoms described by Newton’s law of equations is studied.

In recent years, different scientists have successfully explored the influencing factors such as temperature (T) and pressure (P) on the structure and phase transition process in oxide materials (such as CaSiO₃ [2], MgSiO₃ [3,4], and bulk Fe₂O₃ [5,6]). The obtained results show that when T is rapidly reduced, the material moves to an amorphous state. Conversely, the material moves to a liquid state when T is increased. So a question arises: what will happen with SiO₂ material, and the characteristic quantities of its structure, or with T_m: do these ones follow the same rules as the above materials or not? To answer this question, in this research we have focused on the structural characteristics and T_m of bulk Silica (bulk SiO₂) materials by taking a proper pair interaction potential between the related components. It has been shown that the choice of van Beest-Kramer-van Santen (BKS) potentials introduced in Ref. [7] is the most proper one, because in different modified versions it reproduces the structural properties of bulk SiO₂ well [8]. Furthermore, it describes the dynamical properties of considered materials which are consistent with experimental data obtained before [8,9].

Bulk SiO₂ materials exist mainly in the amorphous (Amor) state as a powder or colloidal and are used widely in life. It is considered as one of the most important materials in the electronic industry. The effects of T and P on the heterogeneous kinetics of bulk SiO₂ material have recently attracted a lot of researchers’ attention, in particular, the influence of T has become one of the focal points of their research [10,11,12,13]. By experimental methods (EMs) and also by SMs, sometimes by the Ab-initio method, authors of many previous publications have determined, among others, the length of links and the link angles in SiO₂ compounds [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]. Some papers have combined the EM with the SM of MD to clarify the change in the structural unit number of SiO₂ when P increases [42,43,44].

Generally speaking, the numerous results obtained before by different methods are very rich, but rather frequently are not consistent one with another. Here a question arises with regard to how the effects of T and P on the structure and phase transition of SiO₂ can be considered systematically. In this research, the answer to this question will be given by considering these effects in the framework of the SM of MD, and for that, as it has been emphasized above, the choice of BKS potentials is the most suitable. Therefore, in this study, the structural characteristics and phase transition of SiO₂ in the high T and P regions have been investigated. The results presented below provide a conclusion that the structural units SiO₄, SiO₅, and SiO₆ in the center of the earth do not exist for SiO₂ material. These are new results which could serve as a basis for future experimental studies.

2. Computational Methods

Initially, the sow randomly 3000 atoms of bulk SiO₂ (1000 atoms Si and 2000 atoms O) into the cube bulk model with the size (1) as expressed in Equation (1):

$$\mathsf{\rho }=\frac{\mathrm{N}}{\mathrm{V}}\to \mathrm{l}=\sqrt[3]{\frac{\mathrm{N}}{\mathsf{\rho }}}=\sqrt[3]{\frac{{\mathrm{m}}_{\mathrm{Si}}{\mathrm{n}}_{\mathrm{Si}}{+\mathrm{m}}_{\mathrm{O}}{\mathrm{n}}_{\mathrm{O}}}{\mathsf{\rho }}}$$

(1)

In this formula m_Si = 26.98154, m_O = 15.999. The model with the force field was expressed by the BKS pair interaction potential (according to the Equation (2)) and a periodic boundary condition in the framework of the SM of MD is proposed [15,16,17,18,19,23,45]:

$${\mathrm{U}}_{\mathrm{rj}}\left(\mathrm{r}\right)=\frac{{\mathrm{q}}_{\mathrm{i}}{\mathrm{q}}_{\mathrm{j}}}{{\mathrm{r}}_{\mathrm{ij}}}{+\mathrm{A}}_{\mathrm{ij}}{\mathrm{e}}^{{-\mathrm{B}}_{\mathrm{ij}}{\mathrm{r}}_{\mathrm{ij}}}{-\mathrm{B}}_{\mathrm{ij}}{\mathrm{r}}_{\mathrm{ij}}{-\mathrm{C}}_{\mathrm{ij}}{\mathrm{r}}_{\mathrm{ij}}^{-6}$$

(2)

whereas n_Si, n_O, ρ, r_ij, q_i, q_j, are molecular weights, the atomic numbers of Si, O and atomic density, distance links, and charges of the atoms i and j, correspondingly. A_ij, B_ij and C_ij are the potential coefficients of the model given in

Table 1. Parameters of the bulk SiO₂ material [46,47].

SiO2	Si-Si	Si-O	O-O
Aij(eV)	0	18,003.5773	1388.773
Bij(Å−1)	0	4.87318	2.76
Cij(eVÅ5)	0	133.5381	175.0
qi,j(e)	-	qSi = +2.4	qO = −1.2

.

By Verlet algorithm [48], one can determine the coordinates, velocity, and energy of atoms in the simulation process (Table 1). The authors create SiO₂ materials by running the 2 × 10⁴ steps recovery statistics NVT (constant atomic number, volume, temperature), and 2 × 10⁴ steps NVP (constant atomic number, volume, pressure) at T = 7000 K. The obtained result shows that atoms do not stick together and when the T is lowered from T = 7000 K to T = 300 K at P = 0 GPa. It can be noticed that the system is stable and reaches equilibrium at T = 300 K, P = 0 GPa. In the next step, both T and P are changed in the following way: first, the T of samples is increased from T = 300 K to T = 500 K, 1500 K, 2500 K, 3000 K, 3500 K, 4500 K, 5500 K, 7000 K at P = 0 GPa; in the next step P is increased from P = 0 GPa to P = 5, 10, 15, 20 GPa at T = 70 K, 300 K, 1273 K, 2974 K, 3500 K. After sample stabilization at the desired T and P, all samples run simultaneously with 5 × 10⁵ steps NVE (constant atomic number, volume, energy) to the moment when the samples achieve equilibrium. To study the heterogeneous kinetics of bulk SiO₂, the samples are analyzed by radial distribution function (RDF) (according to Equation (3)) [48,49,50,51,52,53,54]:

$$\mathrm{g}\left(\mathrm{r}\right)=\frac{\mathrm{V}}{{\mathrm{N}}^2}\langle \frac{{\displaystyle {\sum }_{\mathrm{i}}{\mathrm{n}}_{\mathrm{i}}\left(\mathrm{r}\right)}}{{4\mathsf{\pi }\mathrm{r}}^2\mathsf{\Delta }\mathrm{r}}\rangle$$

(3)

with g(r), V, N, n_i(r), r is RDF, volume, atoms number, and coordinates denoting respectively the links (Equation (4)) [45]:

$$\mathrm{CN}=4\mathsf{\pi }\mathsf{\rho }{\displaystyle \underset{0}{\overset{{\mathrm{r}}_1}{\int }}\mathrm{g}\left(\mathrm{r}\right)}{\mathrm{r}}^2\mathrm{dr}$$

(4)

where CN, r₁ is the average Coordination Number (CN), the first peak position of RDF, and the bond angle. The relationship between the O-Si-O bond angle is used for the link lengths (applied for the links O-O, Si-O, Si-Si), and is computed by the following expression (Equation (5)) [45]:

$$\cos \mathsf{\alpha }=\frac{{2\mathrm{r}}_{\mathrm{Si}-\mathrm{O}}^2{-\mathrm{r}}_{\mathrm{Si}-\mathrm{Si}}^2}{{2\mathrm{r}}_{\mathrm{Si}-\mathrm{O}}^2}$$

(5)

where: α = O-Si-O for the model defined at T and P. Also, during the heating process of SiO₂, it is evaluated according to the Nosé-Hoover formula [55,56].

To confirm the accuracy of the results, our results were compared with those obtained previously under the same T and P conditions. All these results during heating, P change, and model annealing were determined using the Nosé-Hoover formula [55,56], and the Verlet algorithm, and were run on the computer central system of the Institute of Physics, the Department of Physics & Astronomy of Zielona Gora University, Poland.

3. Results and Discussion

3.1. The Structural Characteristic Quantities

To study the structural properties of the bulk SiO₂, we study the bulk SiO₂ at T = 300 K and P = 0 GPa, and the obtained results are shown in Figure 1.

The obtained results show that the bulk SiO₂ at T = 300 K has a cube shape and is composed of two types of atoms: Si, and O (Si atoms are dark blue, and O atoms are red). It can be observed that Si atoms are not homogeneously distributed at the shell, while the O atoms are homogeneously distributed in the core layer (Figure 1a); the structural units number of SiO₂ is SiO₄ (green-blue), SiO₅ (red), SiO₆ (black) (Figure 1b). The parameters of atomic links for the links Si-Si, Si-O, O-O are calculated from the RDF. The links lengths are r_Si-Si = 3.16 Å, r_Si-O = 1.62 Å, r_O-O = 2.64 Å which correspond to the first peak positions of RDF g_Si-Si = 4.47, g_Si-O = 24.76, g_O-O = 4.78 (Figure 1c), whereas the average CNs are CN_Si-Si = 4.11, CN_Si-O = 4.01, CN_O-O = 8.51 (Figure 1d). In addition, the quantities that characterize the structure of bulk SiO₂ also have the structural unit number, and the bond angle between atoms is 2975 atoms SiO₄, 121 atoms SiO₅, 7 atoms SiO₆, and the angles of the links is O-Si-O is 105°. The effect of low T (T < 273 K) corresponds to liquefied gases such as T = 4.22 K (helium), 70 K (nitrogen), 83.8058 K (argon), 90 (oxygen), 194.5 K (carbon), high T (T > 273 K) and P at the respective T values will be studied in detail in the following section.

3.2. Effect of T

3.2.1. High T Region

The results structural characteristic quantities of the bulk SiO₂ are presented in Figure 1,

Table 2. The structural characteristic quantity of bulk SiO₂ at different T values.

T(K)	Links Lengths rij (Å)			First Peak Positions g(rij)			CN
	Si-Si	Si-O	O-O	Si-Si	Si-O	O-O	Si-Si	Si-O	O-O
300	3.16	1.62	2.64	4.47	24.76	4.78	4.11	4.01	8.51
500	3.16	1.62	2.64	4.37	20.69	4.41	4.16	4.02	7.52
1500	3.14	1.64	2.64	3.62	12.72	3.54	4.23	4.02	4.02
2500	3.16	1.62	2.66	3.05	9.72	2.92	4.23	4.03	8.14
3000	3.14	1.62	2.66	3.03	8.85	2.83	4.34	4.02	8.71
3500	3.16	1.64	2.64	2.55	7.41	2.47	4.48	4.12	9.15
4500	3.16	1.62	2.66	2.54	7.14	2.47	4.49	4.12	9.16
5500	3.12	1.62	2.64	2.18	5.79	2.14	4.25	4.06	8.91
7000	3.12	1.56	2.66	1.96	5.31	1.92	3.99	3.96	8.65
Previous Results	rSi-Si	3.155 [15], 3.16 [16], 3.08 [17], 3.13 [18], 3.14 [19], 3.11 [23], 3.12 [21], 3.077 [22]
	rSi-O	1.595 [15], 1.63 [16], 1.62 [17], 1.61 [18], 1.61 [19], 1.60 [23], 1.62 [21], 1.608 [20]
	rO-O	2.59 [15], 2.62 [16], 2.66 [17], 2.65 [18], 2.60 [19], 2.61 [23], 2.65 [21], 2.626 [21]

.

The obtained results show that the bulk SiO₂ has structural characteristic quantities at T = 300 K (Figure 1). When the T increases from T = 300 K to T = 500 K, 1500 K, 2500 K, 3000 K, 3500 K, 4500 K, 5500 K, and 7000 K, then the length (r) of links Si-Si, Si-O, O-O is r_Si-Si, r_Si-O, r_O-O change as r_Si-Si changes (in the range from r_Si-Si = 3.12 Å to r_Si-Si = 3.16 Å), r_Si-O changes (from r_Si-O = 1.56 Å to r_Si-O = 1.64 Å), and r_O-O changes (from 2.64 Å to 2.66 Å at T = 3000 K). Also, the length of the Si-Si, and Si-O bonds decreases greatly at T > 5500 K with r_Si-O = 1.56 Å, which proves that SiO₂ has completely liquefied and has long fracture links which are caused by the size effect caused. The obtained results for r_Si-Si are consistent with the results given by other authors using the SM [12,13,14,15,16,17,18,19,23] and the EM [21,22]. Similarly, one can also see accordance with other results for other links Si-O in link length obtained by SM [15,16,17,18,19,23] and by EM [12,13,14,20,21], whereas for the links O-O by SM [12,13,14,15,16,17,18,19,23] and [20,21] by EM (Table 2). It follows that the effect of T on the link is the length and the number of coordinates are negligible, which is a consequence of the form of g(r). This leads to the question of whether there is any other cause that strongly affects the structure of bulk SiO₂. The obtained results show that in the interval from T = 2500 K to T = 3000 K, g_Si-O decreases slowly, and the r_O-O increases suddenly, so it can be concluded that in this T zone, the phase transition from an amorphous state to a liquid state for bulk SiO₂ has been realized. To study this phase transition, the number of structural units at different T values has been considered. The results are presented in

Table 3. The number of structural units and link angles of bulk SiO₂ at different T values.

T (K)	Structural Units Number			O-Si-O (Degree)	Results (Degree) Obtained Previously
	SiO4	SiO5	SiO6
300	2975	121	7	105	108.3 [15], 109 [17], 107.3 [23] by SM and 109.47 [24], 109.7 [25], 109.4 [26], 109.5 [18] by EM
500	2071	153	7	105
1500	2965	173	21	105
2500	2959	232	0	105
3000	2960	211	0	105
3500	2791	709	74	105
4500	2769	783	49	105
5500	2653	959	119	100
7000	2650	960	64	95

.

When (T) increases from T = 300 K to T = 500, 1500, 2500, 3000, 3500, 4500, 5500, 7000 K, the structure unit number SiO₄ decreases from 2975 atoms to 2650 atoms; whereas for SiO₅ it increases from 121 atoms to 960 atoms. Whereas for SiO₆ change in about from 0 atoms to 119 atoms (Table 3), the link angle of O-Si-O decreases from 105° to 95°. Our results are consistent with the results obtained previously. The links angle for O-Si-O [14,15,17,23] by SM, and by EM [21,24,25,26], are also in agreement with our calculations. The results show a significant influence of T on the link angle and the number of structural units SiO₄, SiO₅, SiO₆. The disappearance of the number of SiO₆ structural units at T = 2500, 3000 K shows that there is a phase transition of the material in this region. To answer this question, the l and total energy of the system (E_tot) at different T values (

Table 4. The l and E_tot of bulk SiO₂ at different T values.

T (K)	l (nm)	Etot (eV)
300	3.440	−53,230
500	3.442	−53,072
1500	3.450	−52,282
2500	3.451	−51,477
3000	3.453	−51,062
3500	3.454	−50,501
4500	3.462	−49,424
5500	3.473	−48,258
7000	3.521	−46,695

) have been also calculated.

The obtained results show the case for the high T region T > 273 K. When T increases, E_tot increases, and with T increasing from T = 300 K to T = 2500 K, the size (l) of the material increases greatly from l = 3.440 nm to 3.451 nm, and when T increases from T = 3000 K to T = 7000 K, l slows down from l = 3.453 nm to l = 3.521 nm (Table 4). The obtained results show that in the high T region, two regions appear, the crystalline state and the liquid state, in which the intersection region between the two liquid states and the crystalline state appears in the T range from T = 2500 K to T = 3000 K [19]. As a consequence, it can be generally said that the effect of T on the heterogeneous kinetics of the considered material is very large. The results obtained show that when T increases at P = 0 GPa, the links length (r) and angle of the links will not change significantly. With the first peak point of RDF g(r), the mean coordinate number tends to decrease, g(r) decreases strongly, and the link Si-O increases. This is the cause that leads to the insignificant change in the number of the structural unit of SiO₄, SiO₅, SiO₆, and the disappearance of structural units. The obtained results could serve as the basis for future experimental studies.

3.2.2. Low T Region

The results of structural characteristic quantities of the bulk SiO₂ at low T values are presented in

Table 5. The structural characteristic quantity of bulk SiO₂ at low T values.

T(K)	Links Lengths rij (Å)			First Peak Positions g(rij)			CN			l (nm)	Etot (eV)
	Si-Si	Si-O	O-O	Si-Si	Si-O	O-O	Si-Si	Si-O	O-O
300	3.16	1.62	2.64	4.47	24.76	4.78	4.11	4.01	8.51	3.439	−53,230
194.5	3.18	1.64	2.64	4.60	28.36	5.00	4.13	4.01	8.41	3.439	−53,312
90	3.2	1.64	2.64	4.63	35.28	5.22	4.12	4.01	10.2	3.439	−53,394
83.8085	3.2	1.64	2.64	4.64	35.81	5.22	4.12	4.01	6.73	3.439	−53,399
70	3.2	1.64	2.64	4.61	37.26	5.27	4.14	4.01	6.73	3.439	−53,410
4.22	3.22	1.64	2.62	4.67	42.51	5.57	4.13	4.00	7.78	3.439	−53,460
The number of structural units and bond angle at low T values
		T(K)	300	194.5	90	83.8085	70	4.22
		SiO4	2975	2974	2970	2969	2970	2974
		SiO5	121	128	144	150	144	133
		SiO6	7	7	7	7	7	7
		O-Si-O (degrees)	105	105	105	105	105	105

.

The obtained results show that with bulk SiO₂ at (T), T = 300 K has structural characteristic quantities (Figure 1). The results obtained in the low T region T < 273 K (negative T values), P = 0 GPa. When the T decreases from T = 300 K to T = 194.5, 90, 83.8085, 70, 4.22 K the lengths links of Si-Si, Si-O, O-O have changed as Si-Si increases (from r_Si-Si = 3.16 Å to r_Si-Si = 3.22 Å), Si-O increases (from r_Si-O = 1.62 Å to r_Si-O = 1.64 Å) and O-O decreases (from r_O-O = 2.64 Å to r_O-O = 2.62 Å); CN changes very little, l is constant value l = 3.439 nm; energy increased (from E_tot = −53,230 eV to E_tot = −53,460 eV); the number of SiO₄, SiO₅, SiO₆ structural units has a constant value, and the O-Si-O bond angle has a constant value of 105° (Table 5) which shows that in this region there is almost no structural change, but there is an increase in energy of the E_tot system. With this, the researchers can use this material in future energy storage devices.

3.2.3. Effects of P

As has been emphasized in the Introduction, other scientists only considered the effect of P at T = 300 K, and there are no research results in the high T area. Therefore, the study on the structural characteristics and phase transition of SiO₂ in the high T and high P regions has also been carried out and presented in this text.

At T = 70 K

The structural characteristic quantities of bulk SiO₂ at T = 70 K with different p values are shown in

Table 6. The structural characteristic quantity of bulk SiO₂ at low T values.

P (GPa)	Links Lengths rij (Å)			First Peak Positions g(rij)			CN			l (nm)	Etot (eV)
	Si-Si	Si-O	O-O	Si-Si	Si-O	O-O	Si-Si	Si-O	O-O
0	3.20	1.64	2.64	4.61	37.26	5.27	4.14	4.01	6.73	3.439	−53,410
5	3.12	1.62	2.62	3.79	35.11	4.58	4.41	4.04	7.57	3.317	−53,347
10	3.06	1.62	2.62	3.64	27.69	4.29	4.82	4.09	8.26	3.232	−53,219
15	3.06	1.62	2.56	3.26	16.54	3.62	5.88	4.34	9.33	3.111	−52,990
20	-	-	-	-	-	-	-	-	-	-	-
The number of structural units and bond angle at low T
			P (GPa)	0	5	10	15	20
			SiO4	2970	2903	2697	1990	-
			SiO5	144	389	894	1725	-
			SiO6	7	35	120	757	-
			O-Si-O (degree)	105	105	105	105	-

.

The results obtained at T = 70 K, P = 0 GPa show that when the P increases from P = 0 GPa to P = 0, 5, 10, 15, 20 GPa the lengths links of Si-Si, Si-O, O-O have changed as Si-Si decreases (from r_Si-Si = 3.20 Å to r_Si-Si = 3.06 Å), Si-O decreases (from r_Si-O = 1.64 Å to r_Si-O = 1.62 Å) and O-O decreases (from r_O-O = 2.64 Å to r_O-O = 2.56 Å); CN increases from CN_Si-Si = 4.14 to 5.88, CN_Si-O = 4.01 to 4.34, CN_O-O = 6.73 to 9.33, l is decreased from l = 3.439 nm to l = 3.111 nm; energy increased (from E_tot = −53,410 eV to E_tot = −52,990 eV); the number of structural units of SiO₄ decreases from 2970 atoms to 1990 atoms, SiO₅ increased from 144 atoms to 1725 atoms, SiO₆ increased from 7 atoms to 757 atoms, and the O-Si-O bond angle has a constant value of 105°, in which the number of SiO₄, SiO₅, and SiO₆ structural units disappear at P = 20 GPa, showing that bulk SiO₂ materials at low T only exist in the region of P < 20 GPa (Table 6), which shows that in this region there is almost no structural change, but there is an increase in energy of the E_tot system. Based on these results, the researchers can use this material in future energy storage devices.

At T = 300 K

The structural characteristic quantities of bulk SiO₂ at T = 300 K with different p values are shown in Figure 2.

The obtained results demonstrate the fact that bulk SiO₂ at T = 300 K, P = 0 GPa has the form of a cube (Figure 2a) with the nanoscale, l = 3.44 nm, and the E_tot is equal to −53,230 eV. The form of RDF gives the lengths of the links (r) of Si-Si, Si-O, O-O equal to r_Si-Si = 3.16 Å, r_Si-O = 1.62 Å, r_O-O = 2.64 Å. These correspond to the heights of RDF g_Si-Si = 4.47, g_Si-O = 24.76, g_O-O = 4.78. The average CNs were calculated by the formula (4) and have the following values: CN_Si-Si = 4.11, CN_Si-O = 4.01, CN_O-O = 8.51, respectively. The number of structural units SiO₄, SiO₅, SiO₆ are correspondingly 1978, 63, and 1, whereas O-Si-O links angle is 105° and Si-O-Si is 140°. When P increases from P = 0 GPa to 5, 10, 15, 20 GPa, the size (l) decreases from l = 3.44 nm to l = 3.33, 3.23, 3.08, 3.03 nm (Figure 2b), which correspond to E_tot increasing from E_tot = −53,230 eV to E_tot = −53,116, −52,921, −52,831, −52,619 eV (Figure 2c), respectively. RDF had the position r slightly changed (from 3.08 Å to 3.16 Å for Si-Si), (1.62 Å to 1.64 Å for Si-O), and (2.50 Å to 2.64 Å for O-O) (Figure 2d), which corresponds to a decrease of g(r) (from 4.47 to 3.21 with Si-Si), (24.76 to 9.90 with Si-O), (4.78 to 3.22 with O-O) (Figure 2e).

The average CNs (4) increased from 4.11 to 13.19 for Si-Si, 4.01 to 5.91 with Si-O, 8.51 to 22.04 with O-O (Figure 2f), while the number of SiO₄ structural units decreased from 2975 atoms to 2906, 1928, 1536, 983 atoms. This number of SiO₅ increases from 121 atoms to 345, 1855, 2070, and 2163 atoms, whereas for SiO₆ it increases from seven atoms to 32, 640, 932, and 1450 atoms. The O-Si-O links angle remains constant at 105°.

The results obtained show that when P increases at T = 300 K, the length (r), g(r), CN, and angle of the links will strongly change. With r_O-O, g_Si-O strongly decreases and CN_O-O, CN_Si-Si strongly increases, and this leads to a sudden decrease in the number of SiO₄ structural units and the sudden increase of SiO₅, SiO₆.

At T = 1273 K

The structural characteristic quantities of bulk SiO₂ at T = 1273 K with different p values are shown in Figure 3.

The results are presented similarly to the previous case of T = 300 K. Namely, bulk SiO₂ at T = 1273 K, P = 0 GPa has the form of a cube (Figure 3a) with the nanoscale, l = 3.45 nm, the E_tot is −52,472 eV; RDF with links length (r) of Si-Si, Si-O, O-O r_Si-Si = 3.14 Å, r_Si-O = 1.64 Å, r_O-O = 2.64 Å corresponding to the height of RDF is g_Si-Si = 3.96, g_Si-O = 13.81, g_O-O = 3.77. The average CNs are CN_Si-Si = 4.21, CN_Si-O = 4.02, CN_O-O = 8.81. When P increases from P = 0 GPa to 5, 10, 15, 20 GPa, (l) decreases from l = 3.45 nm to l = 3.34, 3.22, 3.11, 3.04 nm (Figure 3b) which correspond to the increase of E_tot from E_tot = −52,472 eV to E_tot = −52,427, −52,285, −52,066, −51,983 eV (Figure 3c). RDF has very large change of r from 3.08 Å to 3.16 Å for Si-Si, 1.62 Å to 1.64 Å for Si-O; 2.48 Å to 2.64 Å with O-O (Figure 3d). These correspond to a decrease of g(r) from 3.96 to 2.82 for Si-Si, from 13.81 to 7.30 with Si-O, and from 3.77 to 3.03 with O-O (Figure 3e). The average CN increases from 4.21 to 7.01 with Si-Si, from 4.02 to 4.85 with Si-O, and from 8.81 to 13.13 with O-O (Figure 3f), which corresponds to the decrease in structural units number for SiO₄ from 2970 atoms to 2900, 2571, 1685, 1046 atoms. For SiO₅ this number increases from 147 atoms to 398, 1199, 1961, 2042 atoms, and for SiO₆ it increases from 0 atoms to 36, 205, 881, 1474 atoms. The O-Si-O links angle remains constant at 105°. The results obtained show that when P increases at T = 1273 K, the length (r), g(r), CN, and angle of the links will change. Also, r_O-O, g_Si-O decrease, and CN_O-O, CN_Si-Si increase. This leads to a sudden slow-down decrease in the number of SiO₄ structural units and the slow-down increase of SiO₅, and SiO₆.

At T = 2974 K

The structural characteristic quantities of bulk SiO₂ at T = 2974 K with different values of p are demonstrated in Figure 4.

It follows from these results that bulk SiO₂ at T = 2974 K, P = 0 GPa has the form of a cube (Figure 4a) with the size l = 3.45 nm, E_tot = −51,085 eV. The lengths of the links of Si-Si, Si-O, O-O are r_Si-Si = 3.16 Å, r_Si-O = 1.64 Å, r_O-O = 2.70 Å what corresponds to the height in the peak position of RDF g_Si-Si = 3.06, g_Si-O = 8.75, g_O-O = 2.77. The average CNs are CN_Si-Si = 4.35, CN_Si-O = 4.03, CN_O-O = 8.71. When P increases from P = 0 GPa to 5, 10, 15, 20 GPa, the size l decreases from l = 3.45 nm to l = 3.33, 3.20, 3.11, 3.05 nm (Figure 4b). This corresponds to increase of E_tot from E_tot = −51,085 eV to E_tot = −51,033, −50,882, −50,695, −50,599 eV (Figure 4c). RDF has larger, r changes between 3.10 Å to 3.16 Å for Si-Si, 1.60 Å to 1.64 Å with Si-O, for 2.52 Å to 2.70 Å with O-O (Figure 4d). This corresponds to a decrease of g(r) from 2.58 to 3.06 with Si-Si, 5.42 to 8.75 with Si-O, 2.47 to 2.77 with O-O (Figure 4e). The CN increases from 4.35 to 8.81 with Si-Si, from 4.03 to 4.93 with Si-O, and from 8.71 to 13.32 with O-O (Figure 4f) which corresponds to the decrease in the number of structural units for SiO₄ from 2938 atoms to 2984, 2211, 1434, 961 atoms. This number for SiO₅ increases from 295 atoms to 713, 1660, 2079, 2138 atoms, whereas for SiO₆ it increases from 14 atoms to 111, 413, 1019, 1501 atoms, and SiO₇ it increases from 0 atoms to 72 atoms.

It can be seen that the SiO₇ structure unit number appears at P = 20 GPa; this result is completely consistent with the result of bulk Fe₂O₃ when P is increased at the high T region. The O-Si-O links angle remains constant at 105°. The results obtained show that when P increases at T = 2974 K, the length (r), g(r), CN, and angle of the links will change. Also, r_O-O, g_Si-O decrease and CN_O-O, CN_Si-Si increase; this leads to a sudden slow down decrease in the number of SiO₄ structural units and a very big increase of this number for SiO₅, SiO₆.

At T = 3500 K

The structural characteristic quantities of bulk SiO₂ at T = 3500 K with different values of p are shown in Figure 5.

The calculated results show, that bulk SiO₂ at T = 3500 K, P = 0 GPa has also the form of a cube (Figure 5a) with the nanoscale, l = 3.43 nm. The E_tot is equal to −50,378. The RDF gives the links lengths (r) of Si-Si, Si-O, O-O which are r_Si-Si = 3.12 Å, r_Si-O = 1.64 Å, r_O-O = 2.66 Å. This corresponds to the height of the first peak position of RDF g_Si-Si = 2.62, g_Si-O = 7.62, g_O-O = 2.54. The average CNs are CN_Si-Si = 4.51, CN_Si-O = 4.11, CN_O-O = 9.16. When P increases from P = 0 GPa to 5, 10, 15, 20 GPa, the size (l) decreases from l = 3.43 nm to l = 3.27, 3.17, 3.11, 3.05 nm (Figure 5b). This corresponds to increase of E_tot from E_tot = −50,378 eV to E_tot = −50,313, −50,255, −50,176, −50,078 eV (Figure 5c), relatively. RDF has a very large r changes from 3.04 Å to 3.14 Å for Si-Si, from 1.60 Å to 1.64 Å for Si-O, and from 2.52 Å to 2.66 Å with O-O (Figure 5d). These changes correspond to a decrease of g(r) from 2.73 to 2.43 with Si, from 7.62 to 4.88 with Si-O and from 2.54 to 2.37 with O-O (Figure 5e). The average CNs increase from 4.51 to 10.01 with Si-Si, from 4.11 to 5.19 with Si-O, and from 9.16 to 14.46 with O-O (Figure 5f) which corresponds to the decrease of the number of structural units for SiO₄ from 2820 atoms to 2373, 1788, 1391, 887 atoms. This number for SiO₅ increases from 632 atoms to 1520, 1935, 2100, 2150 atoms, whereas for SiO₆ it increases from 62 atoms to 222, 742, 1014, 1448 atoms, and SiO₇ it increases from 0 atoms to 173 atoms. In which, the appearance of structural units number of SiO₇ at P > 15 GPa with T = 3500 K. The O-Si-O links angle changes from 105° to 100°. The O-Si-O links angle changes from 105° to 100°. It can be concluded that when P increases, l decreases, E_tot increases, r changes, and g(r) decreases with Si-O, but it changes insignificantly for Si-Si, O-O. The CN_Si-O changes in such a way that the number of SiO₄ structural units decreases, whereas for SiO₅, SiO₆ increases with constant links angle O-Si-O equal to 105°. The results obtained show, that when P increases at T = 3500 K, the length (r), g(r), CN, and angle of the links will change. Also, r_O-O, g_Si-O decrease, and CN_O-O, and CN_Si-Si increase. This leads to a sudden slow-down decrease in the number of SiO₄ structural units and the slow-down increase of SiO₅, and SiO₆. When P = 0 GPa and T increase, the numbers of structural units of SiO₄, SiO₅, and SiO₆ have no significant change. When P increases at T = 300, 1273, 2974, 3500 K, the number of structural units SiO₄ decreases, while for SiO₅, SiO₆ increases and there is the largest change at T = 2974 K. This fact proves that at T_m = 2974 K, the largest change in the number of structural units exists and this will be the basis for future experimental studies.

4. Conclusions

In this study, using the SM of MD, the effects of T and P on the heterogeneous kinetics of the bulk SiO₂ (with 3000 atoms at 300 K, 500 K, 1000 K, 1500 K, 2000 K, 2500 K, 3000 K, 3500 K, 4500 K, 5500 K, and 7000 K; at 0 GPa, 5 GPa, 10 GPa, 15 GPa, and 20 GPa with T = 300 K, 1273 K, 2974 K, 3500 K) have been considered. These considerations lead to a conclusion that with bulk SiO₂ (3000 atoms), the choice BKS potentials gives the results consistent with previous both experimental and simulation results. The increase in the T leads to the initial increase in the l. The E_tot increases gradually as the T increases at P = 0 GPa. It follows from the obtained results that for the T range from T = 300 K to T = 2974 K, bulk SiO₂ exists in an amorphous state, whereas for T > 2974 K bulk SiO₂ exists in a liquid state, so the T_m of bulk SiO₂ has been determined as 2974 K. When T increases from P = 0 GPa to P = 5, 10, 15, 20 GPa with T = 300, 1273, 2974, 3500 K calculated the structural units number, which for SiO₄ it decreases, while for SiO₅, SiO₆ it increases, while the number of SiO₇ structural units appears with P > 15 GPa at T = 3500 K, P > 20 GPa at 2974 K. The l of bulk SiO₂ decreases and E_tot increases, g(r) of Si-O decreases, CN of Si-Si, O-O increases strongly with higher T. It follows from these results that for low T, the CN changes very strongly, while T is large, T > 2974 K, CN changes insignificantly. Our results show generally that there is a significant influence of T and P on the structure and phase transition of bulk SiO₂. These are new results which could serve as a basis for future experimental studies.