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Journal of Science & Technology 135 (2019) 048-051 Polyamorphism of Amorphous SiO2 under Compression Based on Two-State Model Luyen Thi San*, Nguyen Van Hong HaNoi University of Science and Technonoly – No. 1, Dai Co Viet Str., Hai Ba Trung, Ha Noi, Viet Nam Received: December 05, 2017; Accepted: June 24, 2019 Abstract Microstructure and polyamorphism of amorphous SiO2 at 500 K and 0÷20 GPa were investigated by molecular dynamics simulation. The results indicate that in the studied pressure range, the network structure of amorphous SiO2 includes SiOx structure units (x = 4, 5, 6) and OSiy (y = 2, 3). The two-state model (high density and low density) is used to describe the network structure of the amorphous SiO2. High-density phase is formed by SiO5 and SiO6 linked via OSi3, low-density phase is formed by SiO4 linked via OSi2. The proportion of high density phase and low density phase depend on pressure. Keywords: simulations, molecular dynamics, polyamorphism 1. Introduction* strutural transition in amorphous SiO2 under pressure. In addition, we also diccuss further the relationship between structural and mechanical properties published by the other authors. The polyamorphism is the coexistence of many amorphous state (glass or liquid), which have the same composition but different local structure and density [1]. Microstructure and polyamorphism in amorphous SiO2 are investigated by both simulations [2, 3] and experiments [4, 5]. The results show that the structure of amorphous SiO2 is mainly the mixture of SiOx polyhedra (x = 4, 5, 6) under compression. Hight pressure X-ray diffraction experiment on amorphous SiO2 have insighted into the structure. Sato et al. have just observed the three-dimension network structure, comprising of coner-shared SiO4 tetrahedra up to 8÷10 GPa [4]. This was confirmed by using molecular dynamics (MD) simulation [3]. At higher pressure, the present of 5-fold coordination number (SiO5) and 6-fold coordination number (SiO6) correspond to the tranformation from tetrahedral network to octahedral network [5]. To clarify the changing structural process, two-state model has been developed [6]. Basing on this model, the structure of some amorphous material such as SiO2, H2O, GeO2, P, Si, etc. can be considered comprising two phases: low density phase and high density phase. The coexistence of these phases will lead to many states which have the same chemical composition and the different densities. However, the structural details are still a matter of debate. Our previous study, we used MD simulations and visulaziation to study polyamorphism and structural transition in liquid SiO2 under pressure, the structural characteristic of low and high density phases. In this study, we continue to use the same tool to investigate the 2. Caculation method The SiO2 models comprising 666 silicon and 1332 oxygen particles have been generated by MD simulations with BKS (Van Beest-Kramer-Van Santen) potential and periodic boundary condition [7]. It can be described as: = ( + (1) Where uij is the interatomic potential; qi or qj is an effective charge of the ith atom; e is the electronic unit charge; rij is the interaction distance between atoms i and j; aij, bij and cij are the interaction parameters (table 1). The Verlet algorithm is used to integrate the equation of motion, with the time step is 0.47 fs. Table 1. Parameters of BKS potential used to model amorphous SiO2 [8]. Aij (eV) Bij (Å-1 ) Cij (eV Å6) O-O 1388.773 2.760 175.000 Si-O 18003.757 4.873 33.538 Si-Si 0.0 0.0 0.0 Charge (e) qO = 1.2 qSi = + 2.4 The SiO2 models are contructed at 500 K and in the 0÷20 GPa pressure ranges. Initial configuration is generated by placing all particles in simulation box. * Corresponding author: Tel.: (+84) 989.856.138 Email: san.luyenthi@hust.edu.vn 48 Journal of Science & Technology 135 (2019) 048-051 This configuration is heated to 5000 K and then cooled to 500 K. After that, the sample at 500 K and ambient pressure has been done in NPT ensemble (the constant pressure and temperature) until reaching equilibration. From this sample, we contructed samples at 500 K and different pressure. The obtained samples are relaxed in NVE ensemple (the constant volume and energy) for about 106 MD time steps. The coordination number and pair radial distribution function are caculated by averaging over 1000 last configurations seperated by 10 MD time steps. x=4, 5, 6 and OSiy with y=2, 3. Fig. 1a and 1b show how the fraction of structure units depend on pressure. At ambient pressure, the fraction of SiO4 units and SiO5 units are 96% and 4%, respectively; the fraction of SiO6 units is very small (fig. 1a). As increased pressure, the fraction of SiO4 units reduces to approximately 1% at 20 GPa, while the fraction of SiO6 units tends to an increase, approximately 95% at 20 GPa. The fraction of SiO5 units rises to maximum value in 10÷15 GPa range before tending a decrease when pressure increases. 3. Results and disscution Fig. 1b shows that the fraction of OSiy dependens on pressure. As increased pressure, the fraction of OSi2 units reduces from 96% at ambient pressure to 1% at 20 GPa. At 8÷10 GPa, the fraction of OSi2 and OSi3 units approximately equal. Fig. 1a also shows that at threshold pressure, the fraction of SiO4 units and the total fraction of SiO5 and SiO6 units have the same value. Therefore, as pressure increase, the decreasing fraction of SiO4 units occurs simultaneouly with the decreasing fraction of OSi2 and the increasing total fraction of SiO5 and SiO6 units occurs simultaneouly with the increasing fraction of OSi3 units. At ambient pressure, the first peak of the Si-Si, Si-O and O-O pair radial distribution functions (PRDF) are 3.12, 1.60 and 2.60 Å, respectively. This result is in agreement with experiment in the position and height of first PRDF peaks [9]. SiO4 SiO5 100 SiO6 SiOx(x=5, 6) Fraction (%) 80 60 To clarify the geometry structure of structure units as pressure changes, we investigated the angle distribution and distance distribution in the SiOx and OSiy units at 0, 5 and 15 GPa (fig. 2 and 3). The results show that with each type of SiOx structure units, the O-Si-O angle distribution and Si-O bonding distance distribution are independent on pressure. Thus, the network structure of amorphous SiO2 only changes in the fraction of structure units without the geometry structure of each type of units under pressure. 40 20 0 a) 0 5 10 15 20 Pressure (GPa) OSi2 OSi3 100 80 The network structure of amorphous SiO2 comprises of SiOx units that relate to short range order and OSiy units that relate to intermediate range order. The structure units consist of a centre atom that surrounded by neighbor atoms at the cut off distance. The cut off distance used equal 2.38Å. In the 0÷20 range pressure, most of structure units are SiOx with We visualized the SiO2 network structure at 5 and 15 GPa (fig. 4). The yellow domain is formed by SiO4 linked through OSi2. The distribution of this domain is not uniform. The yellow domain dominates at low pressure (or low density) and called low density phase. The black domain is cluster of SiO5 and SiO6 linked together through OSi3. At high Fraction (%) Fig.1. The fraction of SiOx (A) và OSiy (B) in amorphous SiO2 under pressure. Next, we investigated how SiOx structure units linked together. At atmosphere pressure, the most linkages between SiOx structure units via one bridging oxygen atom, the kind of linkage is called the corner-sharing linkage. As pressure increase, the number of OSi3 increase, which leads to increase in the number of edge-sharing linkages (linkage between SiOx structure units via two bridging oxygen atom or face-sharing linkages (linkage between SiOx structure units via three bridging oxygen atom), see table 2. This result show that the amorphous SiO2 structure becomes more tightly packed. 60 40 20 0 b) 0 5 10 15 20 Pressure (GPa) 49 Journal of Science & Technology 135 (2019) 048-051 pressure, this domain expands and dominates. So, the structure of amorphous SiO2 at high pressure (or high density) is mainly formed by the black domain, that called high density phase. The result indicates that the the structure of amorphous SiO2 seem to be similar to the structure of liquid SiO2 [10]. It was also shown in 25 SiO4 SiO6 5 GPa 10 GPa 15 GPa SiO5 15 10 SiO6 5 GPa 10 GPa 15 GPa 15 Fraction (%) 20 Fraction (%) 20 SiO5 SiO4 previous experiments [11]. The compression mechanism in amorphous SiO2 may be closely related to those in liquid SiO2. There is also transition from the low density phase to high density phase corresponding to the transition from OSi2 to OSi3 linkages, under pressure. 10 5 5 0 0 a) 100 150 200 50 50 b) 100 150 200 50 100 150 200 1.5 2.0 O-Si-O (Degree) 1.5 2.0 1.5 2.0 Distance O-Si (Å) Fig. 2. The angle distribution O-Si-O (a) and the bonding distance distribution O-Si (b) of SiOx. 20 15 OSi2 5 GPa 10 GPa 15 GPa Fraction (%) Fraction (%) 15 10 5 5 GPa 10 GPa 15 GPa a) 100 150 50 100 10 5 0 0 50 OSi3 OSi2 OSi3 b) 1.5 150 2.0 2.5 1.5 2.0 2.5 Distance O-Si (Å) Si-O-Si (Degree) Fig. 3. The angle distribution Si-O-Si (a) and the bonding distance distribution O-Si (b) of OSiy. 5 15 GPa Fig. 4. The distribution of SiOx and OSix at 5 and 15 GPa.The yellow domain is cluster of SiO4 linked together through OSi2. The black domain is cluster of SiO5 and SiO6 linked together through OSi3. 50 Journal of Science & Technology 135 (2019) 048-051 density phase dominates above 8÷10 GPa. The structural transition is the structural origins which is responsible for the enhanced ductility in amorphous SiO2 under pressure. Table 2. The number of OSi3, Ne and Nf in amorphous SiO2. Ne is the number of edge-sharing linkages, Nf is the number of face-sharing linkages. P(GPa) OSi3 Ne Nf 0 64 21 1 5 1007 560 17 10 1772 1054 69 15 2034 1229 72 Acknowledgments This research is funded by HaNoi University of Science and Technology (HUST) under grant number T2017-PC-130. Some studies using MD simulation showed that the relationship between structural and mechanical properties [12-14]. The strain at fracture increases from 10.5% to 24.1% when pressure increases from 0 to 15 GPa [12]. Other studies also indicated the transition from elastic to plastic behavior at 8÷10 GPa [13, 14]. Under pressure, the samples display more plastic before fracture. The apprearance of 5-fold coordination during compression have been shown to be responsible for the enhanced dutility in amorphous SiO2 [12, 14]. 5-fold Si atoms tend to stay closer together and the clusters of 5-fold Si atoms are not uniformly distributed throughout the sample. While, Davila et al. showed that the transition between elastic and plastic behavior is correlated to changes in the ring size distribution, which characterizes the intermediate range order of these amorphous materials [13]. References [1] [2] [3] [4] [5] [6] In this study, 5-fold coordination plays an intermediate role in the convertion from 4-fold coordination into 6-fold coordination (fig. 1b). The changing of intermediate range order leads to more and more tightly packed structure at high pressure. At 8÷10 GPa is an important pressure threshold. At this value, we observe the change in the correlation between the proportion of structure units. This leads to the domination of low density phase at below the pressure threshold and the domination of hight density phase at above the pressure threshold. So, the structural origins of enhanced ductility and the transition between elastic and plastic behavior in amorphous SiO2 can be attributed to the change of proportion of low density phase and high density phase in this material under compression. [7] [8] [9] [10] [11] 4. Conclusion Using MD simulation, we show that the network structure of amorphous SiO2 is formed by five structure units, SiOx units (with x=4, 5, 6) and OSiy units (with y=2, 3). The network structure divides into two phases: low density phase and high density phase. The low density phase consists of SiO4 linked through OSi2, high density phase consisting of SiO5 and SiO6 linked through OSi3. As pressure increases, there is a structure transition from the low density phase to the high density phase. The low density phase dominates at below 8÷10 GPa, and the high [12] [13] [14] 51 D.Machon, F.Meersman, M.Wilding, M.Wilson, and P.McMillan, Pressure-induced amorphization and polyamorphism: Inorganic and biochemical systems, Prog. Mater. Sci. 61 (2014) 216-282. D.J.Lacks, First-order amorphous-amorphous transformation in silica, Phys Rev Lett. 84 (2000) 4629–4632. T. Sato and N. Funamori, Sixfold-Coordinated Amorphous Polymorph of SiO2 under High Pressure, Phys.Rev.Lett. 101 (2008) 255502. M. Wu, Y. Liang, J.Z. Jiang and S.T. John, Structure and properties of dense silica glass. Sci. Rep. 2 (2012) 1-5. Y. Liang, C. R. Miranda and S. Scandolo, Mechanical strength and coordination defects in compressed silica glass: Molecular dynamics simulations. Phys. 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Huang, Brittle to ductile transition in densified silica glass. Sci. Rep. 4(2014) 5035. L. P. Davila et al, Transformations in the MediumRange Order of Fused Silica under High Pressure. Phys. Rev. Lett. 91 (2003) 205501. Y. Liang, C. R. Miranda and S. Scandolo, Mechanical strength and coordination defects in compressed silica glass: Molecular dynamics simulations. Phys. Rev. B 75(2007) 024205. Journal of Science & Technology 135 (2019) 048-051 52