Local structure of liquid SiO₂ under temperature

LOCAL STRUCTURE OF LIQUID SiO2 UNDER TEMPERATURE N.T.Nhan, V.V.Hung, P.K.Hung, P.H.Kien and T.V.Mung Hanoi National Pedagogic University Hanoi University of Technology Abstract. The molecular dynamic simulation has been conducted to study the behavior of void and void clusters in liquid silica under temperature. We focused on two kinds of void aggregation: void cluster and void tube. The evolution of structural changes of silica under temperature has been analyzed through coordination number, angle distribution and void characteristics. It was found that there is a large void tube composed of 91% O-void spread over simulation shell. The temperature dependence of different kinds of void seems to be very week in comparison with pressure. 1 Introduction Liquid and amorphous silica have been studied intensively for the past decays from both exper- iment and computer simulation due to their enormous technological applications and anomalous properties [1-9]. The diffusivity anomaly was predicted by Waffs and later it had been verified experimentally [2]. Subsequent molecular dynamic (MD) simulations showed that silica has two distinct amorphous states, denoted as high-density amorphous (HDA) and low-density amorphous (LDA). Direct experimental evidence for the transition from LDA to HDA silica phases with dis- continuous volume change of 20% had only recently reported [16]. Danienl J. investigated the amorphous-amorphous transformation in silica glass by MD method and concluded that this tran- sition liked the first-order phase transition known to occur in water and it took place in pressure range between 3 and 5 GPa [13]. The thermo-mechanical conditions for those transitions and the relationship between local microstructure and certain anomalies are studied in [17,18]. According to [17] the transitions can be reversible or irreversible depending on the pressure and temperature at which ones take place. The characteristics feature of network-forming fluids SiO2 is the presence of a large number of voids. Obviously, the behavior of theses voids is responsible for diffusivity as well as for local atomic arrangement. However, as far as we know, the problem of voids has been investigated very little. Several works have been found, but they focus only on the analyzing of radii distribution of voids [11,19,20]. Therefore the goal of the present study is to show the temperature dependence of void and void aggregation in silica liquid. 2 Calculation method Classical molecular dynamic simulation has been carried out in the cubic box with periodic boundary condition for 999 atoms (333 Silicon and 666 Oxygen atoms). We have adopted the van Beest, Kramer and Santen potential, which is still simple and reproduce a number of experimental properties in liquid and glass states. The form of this potential is Uij = qiqj rij + Aijexp(−Bijrij)− Cij r6ij (1) Where the effective charges are qsi = 2.4e and qo = −1.2e; A, B and C are parameterized constant, which can be found in [15]. The long-range Coulomb interactions are calculated with the standard Ewald summation technique. We used the velocity version of Verlet algorithm to integrate 1 the equation of motion. MD time step is equal to 0.4 fs. The initial configuration was generated by random placing all atoms in a cubic box with sizes of 23.7  A under the constraint that the distance between any atom pair is bigger than a specified value. This configuration is heated to 5000 K at ambient pressure and thermalized over 50,000 steps using velocity and coordinate scaling. Then, the sample is cooled to 2500 K during 20,000 steps. Next, system is allowed to reach equilibrium for 100,000 steps without any disturbance. With this well-equilibrated SiO2 liquid we prepared 7 systems at temperature from 2500 to 6000 K and with density of 3 g/cm 3 . The radial distribution functions, coordination number and angle distributions have been calculated for every run during 10,000 last steps. In order to improve statistics all the positional and angular characteristics have been calculated by averaging over last 1000 configurations separated by 10 steps. The void is defined as a sphere that can be embedded in the model without intersection with any atomic spheres. The radius of Si and O are 1.46 and 0.73  A respectively. To calculate the void, for every ith atoms (i=1,2,..,N) we take all set of three neighbor atoms; the atoms are considered as neighbors of ith atom if the distance between them is less than 11  A. Then a void sphere is inserted in contact with these four atomic spheres. If the inserted void is overlapped with any atom, we remove it from system. Thereby, we have obtained a set of voids, which are not intersected with any atom, but can overlapped with each other. Next step is removing small voids that almost located inside another void. To remove them, we randomly generate several millions points in simulation shell. For every ith void, we determine the number of point n0, which locate inside ith void. Then the number of point n1 locating in both ith void and other bigger voids is calculated. We remove ith void if the relation n1/n0 bigger than 0.95. Two kinds of void aggregation are examined: void cluster(VC) and void tube(VT). First one is a set of voids consisted of a central void and several smaller voids overlapped with central void. The second contained the number of voids with radius bigger than radius of oxygen atom. Besides, every void in VT must overlapped at least with one adjacent void by sharing circle with radius also bigger than oxygen radius. Obviously, from viewpoint of the diffusion mechanism the VT may serve as a path along which the oxygen can travel free. 3 Result and discussion Fig.1 shows the pair radial distribution functions (PRDF) for model at 3000 K and ambient pressure. These PRDFs are very close to ones for BKS silica models reported in [24]. The plot of pressure versus temperature is displayed in Fig.2. A minimum is appeared at 4000 K and indicates an isobaric density maximum. This minimum is already observed with some discrepancy in another MD simulation [18]. The discrepancy probably related to the different sizes of system. The model in [18] contained only 450 atoms. Regarding to various temperatures the PRDF strongly changes that the height of individual peaks and minima become more pronounced at low temperature. More detailed changes in structure with temperature can be found in coordination number distribution, which is depicted in Fig.3. As shown from this Figure, four-coordinated silicon monotony decreases with temperature, whereas the five and six-coordinated in contrast increases. It is clear that most fourfold-silicon is replaced by fivefold-silicon with increasing temperature. We can notice that the curves corresponding to SiO4 and SiO5 fraction have two regions where the rapid and gradual replacing four- by five-coordinated silicon occurs. It is interesting to note that the first region cor- responds to first branch of graph in Fig.2 where pressure decreased with temperature. More details about short-range order under temperature can be inferred from bond-angle distribution. From Fig.4 it can be seen that the O-Si-O angle distributions become broader as temperature increases. The major change observed here is a decrease in the height of main peak with temperature. Two adjacent SiOx (x=4,5 and 6) are linked to each other through common oxygen, which we denoted as " bridge oxygen". The connectivity of two adjacent SiOx (x=3,4,5,6) is described by Si-O-Si angle distributions strongly depending on temperature. The position of main peak shifted to smaller angle and at high temperature a second peal appeared (see Fig.4d). It is evidence that the system changes from a mostly corner-sharing tetrahedral network to a network, which contains also fivefold and sixford units linked to each other by the corners as well as by the edges and/or faces. This trend can be also inferred from Table 1. 2 Distance, r/  A Figure 1. The RDFs for amorphous and liquid SiO2 at 3000 K Figure 2. Pressure vs temprature for silica liquid Table 1. The distribution of "bridge oxygen" in silica liquid at 3 g/cm 3 m is number of oxygens that two neighbor units SiOx are bonded to. m Temperature (K) 2506.26 2996.27 3470.26 4012.8 4468.4 5071.73 5959.47 1 93.79 92.79 91.66 90.01 86.10 85.90 83.73 2 6.00 6.94 8.08 9.65 13.16 13.37 15.35 3 0.21 0.27 0.26 0.34 0.74 0.73 0.91 The temperature seems to weaker influence on voids. Table 2 showed that the number of S-voids increased, whereas the number of O-voids decreased, but the change is not so systematic. Here O-void and S-void are the void with radius bigger than oxygen and silicon atom respectively. Similar tendency also observed for other characteristics such as the proportion of simulation shell volume for void and number of voids in largest VT, which contains 68% all O-voids. It mean that this void tube is spread over whole system. Table 2. The characteristics of VC and VT for silica liquid. VV ,VOV , VSV and V LVT are volume proportion of all voids, O-void, S-void and largest VT; N VT , N VC are the number of VT and VC; N LVT is number of voids in largest VT; N SV , N OV is number of S-void and O-voids Temperature (K) 2506.26 2996.27 3470.26 4012.8 4468.4 5071.73 5959.47 V V 0.4333 0.4336 0.4298 0.4307 0.428 0.4295 0.4236 N SV 240 391 534 862 781 850 942 N OV 3209 3298 3152 3070 3077 3030 3008 V OV 0.3991 0.3986 0.3944 0.3924 0.3901 0.3888 0.3779 N VC 1129 1119 1175 1195 1234 1254 1309 N VT 216 239 232 214 242 212 221 V LVT 0.2737 0.2509 0.2123 0.2814 0.2771 0.2592 0.2497 N LVT 2190 2034 1686 2196 2199 2042 1999 4 Conclusions The MD results for 7 models at temperature from 2500 to 6000 K showed the density anomalies in silica liquid. The major structural change with temperature is a transformation from tetrahedral network structure to system where the proportion of five- and six-coordinated silicon is essential. The two adjacent basic units are linked to each other mainly by corners at low temperature, but 3 Figure 3. Dependence of SiO4,SiO5 and SiO6 fraction on temperature for silica liquid Degree Figure 4. The angle distribution at ambient pressure. a) for O-Si-O in SiO4; b) for O-Si-O in SiO5; c) for O-Si-O in SiO6 and d) for Si-O-Si also by edges and/or faces as pressure increased. The increasing temperature shifts positions of main peak of O-Si-O distribution to smaller angle and second peak appeared. Furthermore, we found that in the range of temperature where pressure decreased under constant density there 4 exits significant replacing of fourfold by fivefold silicon with temperature. The temperature influence on void and void aggregation seems to be very weaker in comparison with pressure. In the temperature range considered we found very large VT containing about 70% all O-voids and spreading over whole system. 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