The short and intermediat range orders in a model of amorphous silica under compression

170 JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2017-0046 Mathematical and Physical Sci. 2017, Vol. 62, Iss. 8, pp. 170-175 This paper is available online at THE SHORT AND INTERMEDIAT RANGE ORDERS IN A MODEL OF AMORPHOUS SILICA UNDER COMPRESSION Nguyen Thi Thu Ha and Mai Thi Lan School of Engineering Physics, Hanoi University of Science and Technology Abstract. The change of short and intermediate range orders in a model of amorphous silica at 500 K in the 0-100 GPa pressure range is investigated using molecular dynamics simulation. The pressure dependence of the bond length, bond angle and coordination distribution is analysed in detail. The transformation from tetrahedral to octahedral network structure and corresponding structural unit transition from SiO4 to SiO6 is found under compression. At pressure greater then 20 GPa, most of the structural units are SiO6 and silica tend to transform from an amorphous phase to a crystal phase at high pressure. Moreover, the results also show that the first peak spliting of Si-Si PRDF under compression is caused by the redistribution of Si-O-Si bond angles in the process of structural unit transition and the main densified mechanism of silica is a change of intermadiate order. Keywords: Short and intermediate range orders, phase transition, crystalline, simulation, silica. 1. Introduction Silica is one of the abundant components of the Earth and is an important application material. It is a material of common interest in past decades. Recently, polymorphism and structural transformation under high pressure have been of great importance not only in physics but also in materials science and geophysics [1, 2]. The experimental works [2-5] show that coordination of Si atoms increases from 4 to 6 with compression. The results in this work [4] show that a structural transformation occurs in the 8 - 28 GPa pressure range. At ambient pressure, the first peaks of Si-Si, Si-O and O-O PRDFs are determined at 3.07 Ǻ, 1.59 and 2.61 Ǻ, respectively. The first peak position of Si-O PRDF increases from 1.59 Ǻ to 1.64 Ǻ under compresion up to 28 GPa and it is about 1.66 Ǻ at higher pressure. At 42 GPa, the O-Si-O bond angle in glass silica is found at about 96 o which is intermediate between the tetrahedral and octehedral values of 109.5 and 90 o , respectively. In the works [2, 5], the authors also investigated pressure dependence of the Si-O-Si bond angle. The Si-O-Si bond angle is around 145 o at ambient pressure and decreaces to 130 o as compression to 10 GPa [2]. The results in this work [6] also show that the Si-O-Si bond angle decreases from 146.36 o to 129.49 o under compression in the 0 - 12.7 GPa pressure range. In addition, by using molecular dynamic simulation, the authors have shown that a structural transformation occurs strongly in the 15 - 25 GPa pressure range [7-9]. Received February 17, 2017. Accepted July 29, 2017. Contact Nguyen Thi Thu Ha, email: hahuy197808@gmail.com The short and intermediat range orders in a model of amorphous silica under compression 171 In a recent work [6], the model of amorphous silica is constructed using an ab initio method consisting of 1296 atoms. The authors confirmed that the Si-O bond length increases suddenly in pressure range occuring structural transformation. This result agrees with the previous work [7] showing that the Si-O bond lengths be long to SiO4, SiO5 and SiO6 units are different. Moreover, the work [6] also showed that the first peak position for Si–Si pairs shifts to the left under compression in the 0-23.8 GPa pressure range. At higher pressure, the first peak position of the Si–Si pair shifts strongly to the right and the distribution become more broad. The changes of O- Si-O and Si-O-Si bond angles with compression is also describled in the work [6]. The authors confirmed that the first peaks of O-Si-O and Si-O-Si bond angle distribution are about 108 o and 146 o at zero pressure, respectively. The O-Si-O bond angle distribute around 90 o while the Si-O-Si bond angle distribution tends to split into two peaks around 126 o and 96 o under compression to 79.8 GPa. In the work [9], the authors also showed the change of Si-O-Si bond angle with pressure and confirmed that the bond angle distribution decreases under compression and this relates to the change of intermediate range order structure. In this paper, the structural transformation of amorphous silica under compression is investigated. The effect of pressure on short and intermediate range orders will be clarified. A relation between the structure and the Si-O-Si bond angle distribution as well as the first peak spliting of Si-Si PRDF is also discussed in detail. 2. Content 2.1. Calculation method Amorphous silica models at different pressure (in the pressure range from 0 to 100 GPa) consisting of 1666 Si and 3332 O atoms are contructed by molecular dynamic simulation with Beest–Kramer–van Santen (BKS) potential and periodic boundary conditions [10, 11]. To integrate the equation of motion, Verlet algorithm is used with time steps of 0.478 fs. Initially, all atoms are placed randomly in a simulation box and heated to 6000 K to remove initial configuration. After that the sample is cooled to 5000, 4000, 3000, 2000, 1000 and finally to 500 K. Next, the sample is relaxed in an isothermal–isobaric (NPT) condition for a long time (10 7 time steps) to get equilibrium state. The structural data of considered models is determined by averaging more than 1000 configurations during the last 10 4 time steps. 2.2. Rerult and discussion Figure 1 displays pair radial distribution functions (PRDFs) of Si-Si, Si-O and O-O pairs. It can be seen that at ambient pressure, the first peaks of PRDFs are very sharp. This demonstrates that Figure 1. Pair radial distribution functions gSi-Si (r), gO-O (r) and gSi-O at different pressure. 0 2 4 6 2 3 4 5 6 7 0 5 10 15 20 g S i-S i(r ) g O -O (r ) 0GPa 15GPa 20GPa 100GPa g S i-O (r ) r(Å) 0 2 4 6 8 10 Nguyen Thi Thu Ha and Mai Thi Lan 172 short range order structure or local structure in amorphous silica is more ordered at low pressure. The positions of these peaks are 3.14, 1.60 and 2.60 Ǻ corresponding to Si-Si, Si-O and O-O PRDFs which is in good agreement with the results in the experimental work [4]. At higher pressure (15 GPa), the height of the first peaks decreases. This shows that the short range order structure is significant and dependent on pressure. At pressure greater than 20 GPa, the PRDFs have many peaks which show the formation of crystal structure. This means that under compression, amorphous silica tends to transform into a crystaline structure (Figure 2). It can be seen that network structure tends towards crystalline formation. To clarify short range order structure, we investigated structural unit transformation and the change of Si-O length under a pressure of 0-100 GPa. Evolution of structural unit transformation in silica is presented in Figure 3. It can be seen from Figure 3 that at ambient pressure, the number of SiO4 structural units with tetrahedral network structure is greater than 95%. Under compression, there is a transition from a tetrahedral to octahedral network structure corresponding to structural unit transition from SiO4 to SiO6 via SiO5. This structural unit transition is always accompanied by the transition from OSi2 to OSi3 linkages as shown in Figure 4. At high pressure (greater than 20 GPa), the number of SiO6 structural units is over 94% and that of OSi3 linkages is over 89%. This indicates that the coordination number of both Si and O atoms increaces under compression. Investigating the change in Si-O average bond length of SiOx (x = 4, 5, 6) structural units under the influence of pressure, we found that the bond lengths are almost unchanged and are approximately 1.6 Ǻ, 1.64 Ǻ and 1.7 Ǻ corresponding to the SiO4, SiO5 and SiO6 structure units in the 0-20 GPa pressure range (Figure 5). This data agrees well with the results introdued in work [7] which showed that at 16 GPa and 300 K, Si-O bond lengths corresponding to SiOx (x = 4, 5, 6) structural units are 1.6 Ǻ, 1.68 Ǻ and 1.75 Ǻ. Figure 5 also shows that Si-O average bond lengths of all SiOx structural units decrease slightly under pressure of 20-100 GPa. From figure 5, it can be seen that the Si-O average bond length of SiO4 is the shortest and that of SiO6 is the longest at any pressure within the 0 - 100 GPa pressure range. Thus, it can be determined that the Si-O average bond length increases under compression in the 0-20 GPa pressure range and decreases at higher pressure. This rule is also observed from the moving of the first peak position of the Si-O PRDF under compression as describled in Figure 6. The change of intermediate range order in the model of amorphous silica under compression was also a topic of interest in this paper. As shown in the analyzed results above, at the low pressure, most of the structure units are SiO4 and the linkages are OSi2. In this case, we found that the Si-O-Si bond angle is appoximate 145 o which agrees with the results shown in [6] that the Si- Figure 2. Network structure of SiO6 at 15, 20, 40 and 100 GPacoressonding from left to right. The short and intermediat range orders in a model of amorphous silica under compression 173 O-Si bond angle is appoximately 146 o at zero pressure. The structural unit transition from SiO4 to SiO6 is accompanied by the change of linkage from OSi2 to OSi3 under compression. It can be seenin Figure 7 that at ambient pressure, there is a peak at appoximate 120 o and a shoulder at around 95 o in the Si-O-Si bond angle fraction ditribution of OSi3. This shoulder tends to grow with increased pressure forming a new peak at 20 GPa. Moreover, Figure 7 also shows that the positions of two peaks shift to two sides with increasing pressure. At about 20 GPa, the positions of the two peaks are appoximate 135 o and 90 o . This result agrees with the previous work [12] which found the change of peak position of the Si-O-Si bond angle ditribution from 147° to 135° under compression in 0-20 GPa pressure range in a silica model at 500 K. However, a formation of two peaks of Si-O-Si bond angle ditributions was not found with this work. We also observed that the position of the peaks is almost unchanged at pressures exceeding 20 GPa. 0 20 40 60 80 100 0 20 40 60 80 100 F ra c ti o n o f S iO x (% ) P(GPa) SiO4 SiO5 SiO6 0 20 40 60 80 100 0 20 40 60 80 100 F ra c ti o n o f O S i y ( % ) P (GPa) OSi2 OSi3 Figure 3. Distribution of fraction of SiOx as a function of pressure Figure 4.Distribution of fraction of OSiy linkage as a function of pressure 0 20 40 60 80 100 1.3 1.4 1.5 1.6 1.7 P(GPa) SiO 4 SiO 5 SiO 6 r S i- O (Å )) 1.4 1.5 1.6 1.7 1.8 1.9 2.0 0 5 10 15 20 25 g S i- O (r ) r(Å) 0GPa 5GPa 15GPa 20GPa 30GPa 50GPa 100GPa Figure 5.The Si-O average bond length of SiOx as a function of pressure Figure 6. The first peak of pair radial distribution function gSi-O (r) The formation of new peaks and a shifting of the peaks of the Si-Si PRDF describled in Figure 8. The positions of Si atoms replaced with the pressure increasing leads the distance change of Si-Si atom pairs. We found that at ambient pressure, there is only an initial peak of Si- Si PRDF at appoximate 3.14 Ǻ. Under compression to 5 GPa, this PRDF appears as a shoulder to the left of this peak. The shoulder grows with pressure and forms a new peak at a pressure of about 20 GPa when a new peak of Si-Si PRDF is formed. Specially, Figure 7 also shows that at a Nguyen Thi Thu Ha and Mai Thi Lan 174 pressure range of 0 - 20 GPa, the initial peak shifts to the right and the new peak shifts to the left. This shows that there are a pair of Si-Si atoms present corponding to the larger or smaller Si-O-Si bond angles under compression. It can be seen that the influence of pressure on the distance between the Si-Si pairs observed in Figure 8 agrees with the rule observed in Figure 7. These results show that the change of distance of the Si atom pairs is caused by the redistribution of Si- O-Si bond angles in process of structural unit transition under compression. We also confirmed that the positions of the two peaks of the Si-Si PRDF are at 2.62 Ǻ and 3.16 Ǻ at 20 GPa and these peaks tend to shift to the left under higher pressure. This indicates that the distance between the Si-Si pairs is shorter while the Si-O-Si bond angles are almost unchanged in the 20-100 GPa pressure range, and that most of the structural units are SiO6 units. This is due to the decrease of Si-O bond length as pressure increases in the 20 - 100 GPa pressure range. 80 100 120 140 160 180 0.00 0.05 0.10 0.15 0.20 0.25 0.30 OSi 3 0GPa 5GPa 15GPa 20GPa 30GPa 50GPa 100GPa F ra c ti o n Si-O-Si bond angle (deg) 2.2 2.4 2.6 2.8 3.0 3.2 3.4 0 1 2 3 4 5 6 7 8 0GPa 5GPa 15GPa 20GPa 30GPa 50GPa 100GPa g S i- S i( r) r(Å) Figure 7. Si-O-Si bond angle fraction distribution of OSi3 Figure 8. The first peak spliting of pair radial distribution function gSi-Si (r) The change of short and intermediate range orders under compression leads to increased density and this is the densification mechanism in silica. Figure 9 describles the molar volume dependence on pressure. It can be seen that the molar volume decreases with increasing pressure. Namely, the molar volume is appoximate 24 cm 3 /mol at ambient pressure, 14 cm 3 /mol at 20 GPa and 12 cm 3 /mol at 100 GPa. These results agree with the results reported in previous works [9, 13] which showed that the molar volume decreases from 25 cm 3 /mol to 16.5 cm 3 /mol [9] and from 20 cm 3 /mol to 16 cm 3 /mol [13] in the 0-20 GPa pressure range. Figure 9.The pressure dependence of silica molar volume. 0 20 40 60 80 100 10 12 14 16 18 20 22 24 SiO 2 (500 K) M o la r v o lu m e ( c m ^ 3 /m o l) P(GPa) The short and intermediat range orders in a model of amorphous silica under compression 175 3. Conclusion Using molecular dynamics simulation, the short and intermadiate range orders in silica model at 500 K under pressure of 0 - 100 GPa are clarified. Compression causes the coordination number of Si atoms to increase from 4 to 6. At pressure greater than 20 GPa, the number of SiO6 structural units in the model is over 94%. The Si-O average bond length of all SiOx is almost unchanged in the 0-20 GPapressure range and decreases slightly at higher pressure. Specially, we indicated that the Si-O average bond length of SiO4 is the shortest and that of SiO6 is the longest in the investigated pressure range. Moreover, we observed that at pressures greater than 20 GPa, the Si- Si, Si-O and O-O PRDFs have manysharp peaks which show crystalline formation. Obviously, amorphous silica tends to transform to a crystal structure under compression. The change in the structural units leads to the change in the linkages. Most of the OSi2 linkages are replaced by the OSi3 linkages when under apressure of less than 20 GPa. Additionally, we also confirmed that the first peak spliting the Si-Si PRDF is caused by the redistribution of Si-O-Si bond angles in the process of structural unit transition under compression. The change of intermediate order is the main densified mechanism of silica under compression. Acknowledgements. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number: 103.05-2017.306. REFERENCES [1] Liping Huang, Murat Durandurdu and Jonh Kieffer, 2006. Transformation pathways of silica under high pressure. Nature Materials 5, pp. 977 -981. [2] Przemyslaw Dera, John D, Lazarz, Vitali B, Prakapenk, Madison Barkley, Robert T. Downs, 2011. New insights into the high-pressure polymorphism of SiO2 cristobalite. Physics and Chemistry of Minerals 38 (7), pp. 517-529. [3] Hemley, R. J., et al., 1986. Raman Spectroscopy of SiO2 Glass at High Pressure. Physical Review Letters 57 (6), p. 747. [4] C. Meade, R. J. Hemley, and H. K. Mao, 1992. Raman Spectroscopy of SiO2 Glass at High Pressure. Phys. Rev. Lett. 69 (9), pp. 1387-1390. [5] Camille Sonneville, Thierry Deschamps, Christine Martinet, Dominique de Ligny, Alain Mermet, Bernard Champagnon, 2013. Polyamorphic transitions in silica glass. Journal of Non-Crystalline Solids, 382, pp. 133-136. [6] Neng Li, Ridw an Sakidja, Sitaram Arya l and Wai-Yim Ching, 2014. Densification of a continuous random network model of amorphous SiO2 glass. Chem. Chem. Phys. 16, pp. 1500-1514. [7] James Badro, David M. Teter, Robert T. Downs, Philippe Gillet, Russell J. Hemley, Jean-Louis Barrat, 1997. Theoretical study of a five-coordinated silica polymorph. Phys. Rev. B 56 (10), pp. 5787-5905. [8] Tahir Cagin, Ersan Demiralp, William A. Goddard, 1998. Pressure induced phase transformations in silica. Mat. Res. Soc. Symp. Proc. 492, pp. 287-292. [9] Madeleine M. Roberts, Reffrey R. Wienhoff, Kaye Grant, Daniel J. Lacks, 2001. Structural transformationsin silica glass under high pressure. J. Non-Cryst. Solids 281, pp. 205-212. [10] B. van Beest, G. Kramer, and R. van Santen, 1990. Force fields for Silicas and Aluminophotphates Based on Ab Initio Calculations. Phys. Rev. Lett., 64 (16), pp. 1955-1958. [11] Nguyen Viet Huy, Le The Vinh, Le Văn Vinh and Pham Khac Hung, 2012. Simulation microstructure of SiO2 liquid with three potentials: BKS, MS and BM. Jounal of science of hnue, 57 (7), pp. 134-141. [12] Liping Huang and John Kieffer, 2004. Amorphous-amorphous transitions in silica glass. I. Reversible transitions and thermomechanical anomalies. Phys. Rev. B 69, p. 224203. [13] Daniel J. Lacks, 1999. First-Order Amorphous-Amorphous Transformation in Silica. Phys. Rev. Lett. 84 (20), pp. 4629-4632.