Pressure-dependent structural heterogeneity in calcium silicate glass

Abstract. This work presents a molecular dynamics simulation (MDS) of CaSiO3 glass using Born–Mayer–Huggins potentials. The structural organization and structural phase transition under compression as well as network structure of CaSiO3 are clarified through analysis and visualization of molecular dynamics simulation data. The short-range order structure, intermediate-range order structure are investigated in detail through analysis the pair of radial distribution function, the coordination number distribution in TOn polyedra and OTm linkages (n = 4 ÷ 11; m = 2 ÷ 5; T = Si, Ca). Topology structure of TOn and OTm is also clarified by investigating bond angle and bond length distribution in TOn polyhedra and OTm linkages.

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JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2016-0046 Mathematical and Physical Sci., 2016, Vol. 61, No. 7, pp. 165-175 This paper is available online at PRESSURE-DEPENDENT STRUCTURAL HETEROGENEITY IN CALCIUM SILICATE GLASS Mai Thi Lan1, Nguyen Thi Thanh Ha1, Tran Thuy Duong1, Nguyen Thi Thao2 and Nguyen Van Hong1 1School of Engineering Physics, Hanoi University of Science and Technology 2Hanoi University of Education Abstract. This work presents a molecular dynamics simulation (MDS) of CaSiO3 glass using Born–Mayer–Huggins potentials. The structural organization and structural phase transition under compression as well as network structure of CaSiO3 are clarified through analysis and visualization of molecular dynamics simulation data. The short-range order structure, intermediate-range order structure are investigated in detail through analysis the pair of radial distribution function, the coordination number distribution in TOn polyedra and OTm linkages (n = 4÷ 11; m = 2÷ 5; T = Si, Ca). Topology structure of TOn and OTm is also clarified by investigating bond angle and bond length distribution in TOn polyhedra and OTm linkages. Keywords: Structure, phase transition, polymerization, molecular dynamics simulation, CaSiO3. 1. Introduction Calcium silicate (CaSiO3) is one of the members of Pyroxene, which is the main component of Basalt. The CaSiO3 is one of main components of the Earth’s lower mantle. It is the important component in the glass and ceramic materials [1-4]. Knowledge of structure of CaSiO3 system in both glass and liquid states under high pressure is necessary for understanding about volcanic activity, the physicochemical and thermal change of the Earth, as well as controlling and completing the process of new material fabrication technology. CaSiO3 system has widely been studied for a long time by both theoretical and experimental methods [1, 5-9]. However, experiment is usually difficult to do at high temperature and pressure due to the high melting temperature of CaSiO3 [5]. Available experimental data are mainly measured at the ambient condition [10-13]. The density functional theory-based molecular dynamics simulation of Silicate liquids [1] showed that the liquid CaSiO3 structure changes significantly under compression. At ambient pressure, the Ca-O coordination number is mainly 5, 6 and 7; Si-O coordination number is 4. However, at high pressure (120 GPa) the Ca-O coordination number increases to 8, 9, 10; Si-O coordination number increases to 6. The Ab-initio molecular dynamics calculation for CaSiO3 perovskite at high pressure and temperature [6] showed the existence of three stable structural Received October 2, 2016. Accepted October 28, 2016. Contact Mai Thi Lan, e-mail address: lan.maithi@hust.edu.vn 165 Mai Thi Lan, Nguyen Thi Thanh Ha, Tran Thuy Duong, Nguyen Thi Thao and Nguyen Van Hong phases: orthorhombic, tetragonal and cubic. The MDS results about local structure of CaSiO3 in [5] are in agreement with experimental Raman spectra. The Si-O mean coordination number is 4. It builds up the stable SiO4 tetrahedra in CaSiO3. Although it has been studied extensively for a long time but topology structure of Si-O network as well as the local environment of Ca2+, Si4+, O2+ ions and their change under compression are still in debate and it need to be studied more. This is also the motivation of our study in this work. 2. Content 2.1. Calculation method The Born-Mayer-Huggins interatomic potential for CaSiO3 glass Table 1. The potential parameters for CaSiO3 glass MDS Aij (eV) Bij (A˚−1) Cij (eVA˚) Si-Si 5006070.785 12.5 0.00 Si-O 7363.700 5.2632 0.00 O-O 1621.734 3.3333 30.22 Si-Ca 39991599.000 10.8696 0.00 Ca-O 29353.157 4.7619 0.00 Ca-Ca 200790000.000 9.6154 0.00 The atomic interaction potential is employed in MDS significantly affect to calculation results. The pair interaction potential has still widely been used because of its simplicity as building atomic model. Up to now, there have some evaluated potentials to study structure and dynamical properties of oxide silicate systems with high reliability [7, 14-18]. All of these used two-body Born-Mayer-Huggins form that is given by: Uij (r) = ( qiqj rij ) + ( Aije −Bij∗rij − Cij r6ij ) . Where U(ij) (r) is the potential that consists of the long-range Coulomb part and the short-range repulsion part; qi, qj is the effective charge of the atom i, j respectively. Aij, Bij, Cij are potential parameters. These parameters for CaSiO3 glass MDS are displayed in table 1 [14]; rij is distance between atom i and j. The MD model building for CaSiO3 glass The molecular dynamic (MD) initial configuration of the CaSiO3 sample is built by randomly placing N atoms in a cubic box with periodic boundary condition (N = 5000 atoms consist of 1000 Si, 1000 Ca, 3000 O atoms). Then, the sample is heated up to 6000K to remove the effect of remembering initial configuration and reaches to the equilibrium after 106 MD steps. Next, the sample is cooled down to the temperature of 600K at ambient pressure with the cooling rate of about 2.5K/ps after 2.105 MD steps to obtain the best equilibrium state (M1 model). We continue construct the M2, M3, M4, M5, M6 models by compressing model M1 to different pressures (corresponding to from 5 to 35 GPa) and then relaxed for a long time to reach equilibrium. After that, the structural characteristic such as radial distribution function, coordination number, bond-angle and bond-length distributions. . . are determined by mean over 2000 configurations in the last 103 MD steps. 166 Pressure-dependent structural heterogeneity in calcium silicate glass 2.2. Results of structural properties of CaSiO3 glass In this section, the structural properties of CaSiO3 glass in the short-range order (SRO) and intermediate-range order (IRO) will be investigated in detail. The pair radial distribution functions (RDFs) in CaSiO3 glass at different pressures are showed in Figure 1. The results present the height of first peak decrease and the wide becomes broader with compression. Moreover, the next peak height rapidly decrease and finally approaching unity at larger distances. These features demonstrate that the degree of structural order decrease with increasing pressure. In particular, the RDF of Si-O pair is much shaper peak and deeper minimum than Ca-O pair. The position of the first peak increase as increasing pressure. It means that the average Ca-O and Si-O bond length increase with compression. Figure 1. The pair radial distribution functions in CaSiO3 glass at different pressures. Figure 2. The coordination number distribution in SiOx (x = 4 ÷ 6) and CaOy (y = 5 ÷ 11) polyhedra at different pressures. 167 Mai Thi Lan, Nguyen Thi Thanh Ha, Tran Thuy Duong, Nguyen Thi Thao and Nguyen Van Hong Figure 3. The O-Si-O bond angle and Si-O bond length distribution in SiOx polyhedra at different pressures Conversely, for the RDF of Si-Si, Si-Ca, Ca-Ca and O-O pairs, the position of the first peak decreases with pressure. So the mean bond distance of Si-Si, Si-Ca, Ca-Ca and O-O pairs decrease as the pressure increases. In particular, the Si-O and Ca-O bond length that relates to SRO increases from 1.61, 2.36 A˚ to 1.64 A˚, 2.38 A˚, respectively. Whereas, the bond length of Si-Si, Si-Ca, Ca-Ca and O-O pairs which relate to IRO decreases from 3.12, 3.54, 3.64 A˚ to 2.60, 3.12, 3.28 and 2.46 A˚, respectively. This result is in good agreement with the works in [1, 9, 12]. Figure 2 shows the coordination number distribution in SiOx and CaOy polyhedra (x = 4 ÷ 6; y = 5 ÷ 11) under compression. This result is also in good agreement with the work [1]. The results show that, at ambient pressure, most of Si atoms (97.7%) have four coordinated oxygen atoms forming the SiO4 polyhedra. Most of Ca atoms have from five to seven coordinated oxygen atoms forming CaO5, CaO6 and CaO7 polyhedra. As increasing pressure, the percentage of SiO4 polyhedra decreases meanwhile the percentage of SiO5 and SiO6 polyhedra increases. At high pressure (35GPa), the percentage of SiO5 (43.52%) and SiO6 (53.38%) is mainly. This clearly illustrates that under compression, there is transformation from SiO4- to SiO6-network through SiO5 polyhedra. Similarly, as increasing pressure, the percentage of CaO5, CaO6 polyhedra strongly decreases, the percentage of CaO9, CaO10, CaO11 polyhedra strongly increases, meanwhile the percentage of CaO7, CaO8 increase and reach a maximum value 38.43%, 39.48% at 5, 10 GPa, respectively, 168 Pressure-dependent structural heterogeneity in calcium silicate glass then rapidly decreases. At 35 GPa, the percentage of CaO9, CaO10, CaO11 is dominant. It means that under compression, most of CaOy polyhedra are CaO5, CaO6 and CaO7 at low pressure and CaO9, CaO10 CaO11 at high pressure. Figure 4. The O-Ca-O bond angle O-Ca-O and Ca-O bond length distribution in CaOy polyhedra (y = 5, 6, 7) at different pressures The T-O coordination number increasing leads to T-O-T and O-T-Omean bond angle as well as the T-T and O-O mean bond length decrease (T = Si, Ca). This make the Coulomb repulsion between cation and cation (Ca2+ - Ca2+, Si4+ - Si4+, Si4+-Ca2+), anion and anion (O2− - O2−) increases lead to elongation of the T-O bond length. Thus we can summary that network structure of CaSiO3 glass is built up SiOx polyhedra (x = 4 ÷ 6) and CaOy polyhedra (y = 5 ÷ 11) with the percentage of SiO4, CaO5, CaO6 and CaO7 is mainly at low pressure and the percentage of SiO5, SiO6, CaO9, CaO10, CaO11 is dominant at high pressure. To clarify the SRO in CaSiO3 glass, we continue to study the topology structure of TOn polyhedra. Figure 3 presents the O-Si-O bond angle and Si-O bond length distribution in SiOx polyhedra (x = 4 ÷ 6) at different pressures. It shows that, these distributions are not dependent on pressure. It means that the size and shape of SiOx polyhedra are identical and not rely on pressure. The Coulomb repulsive force between O2− and O2− in SiO5 and SiO6 polyhedra is stronger than the one in SiO4, so the Si-O bond length in SiO5 and SiO6 increase. Specially, the Si-O bond length distribution in SiO4, SiO5 and SiO6 has a peak at 1.6, 1.66 and 1.72 A˚, respectively. 169 Mai Thi Lan, Nguyen Thi Thanh Ha, Tran Thuy Duong, Nguyen Thi Thao and Nguyen Van Hong Figure 5. The O-Ca-O bond angle and Ca-O bond length distribution CaOy polyhedra (y = 8, 9, 10, 11) at different pressures. Similarly, Figures 4 and 5 display O-Ca-O bond angle and Ca-O bond length in CaOy (y = 5 ÷ 11). The result shows that the bond angle distribution in CaO5, CaO6, CaO7, CaO8 undergoes a slightly change as increasing pressure in the 0 ÷ 15 GPa pressure range because of the significant change of percentage of CaO5, CaO6, CaO7, CaO8 in the 0 ÷ 15 GPa. At upper 15 GPa, the O-Ca-O bond angle distribution in CaO5, CaO6, CaO7, CaO8 are almost not rely on pressure. The O-Ca-O bond angle distribution in CaO9, CaO10, CaO11 are almost unchanged in a whole considered pressure. So the shape and size of CaO5, CaO6, CaO7, CaO8 is only slightly distorted in about under 15GPa, meanwhile the shape and size of CaO9, CaO10, CaO11 are almost 170 Pressure-dependent structural heterogeneity in calcium silicate glass not change and not depend on the range of considered pressure. These mean that SRO structure of CaSiO3 glass is almost unchanged and not dependent on compression. Figure 6. The distribution of OTm (m = 2 ÷ 6) linkages at different pressures. Now, we focus on clarify IRO structure that regard to the linkage among the TOn polyhedra in network structure of CaSiO3 glass. The distribution of OTm linkages (m = 2 ÷ 6) under compression are showed in Figure 6. At low pressure (0 GPa), the percentage of OT2, OT3 and OT4 linkages is 9.7%, 52.63% and 35.23%, respectively. Meanwhile the percentage of OT5 and OT6 is almost zero. When the pressure increases, the percentage of OT2, OT3 linkages decrease, in contrast the percentage of OT5 and OT6 linkages increase. At high pressure (35 GPa), the percentage of OT4, OT5 and OT6 is 30%, 46.6% and 26,6% respectively. Note that, the percentage of OTm(m = 2 ÷ 6) is k%, it means k% oxygen atoms link between m TOn polyhedra. Figures 7 and 8 displays the T-O-T bond angle (it can be Si-O-Si, Ca-O-Ca or Si-O-Ca bond angle) and O-T bond length (O-Si or O-Ca bond length) in OTm. The results show that, for OT2 linkages with T is mainly Si atoms, number of Ca atoms is small so exists one peak at 145◦ corresponding to T-O-T bond angle distribution and at 1.7 A˚ corresponding to O-T bond length distribution. The appearance two peaks in bond angle, bond length distribution of OT3, OT4, OT5 and OT6 linkages due to T consist of both Si and Ca. For example, OT3 is not only OSi3 or OCa3 but also Si2-O-Ca or Si-O-Ca2 meanwhile Si2-O-Ca and Si-O-Ca2 is dominant. Besides, the T-O-T bond angle distribution in OT2 and OT3 linkages has change under compression. In contrast, the T-O-T bond angle distribution in OT4, OT5 and OT6 linkages is almost unchanged under compression so the shape and size is unchanged and not dependent on pressure. Thus, IRO structure in CaSiO3 glass changes due to the change of OT2 and OT3 linkages. 171 Mai Thi Lan, Nguyen Thi Thanh Ha, Tran Thuy Duong, Nguyen Thi Thao and Nguyen Van Hong Figure 7. The T-O-T bond angle and O-T bond length distribution in OT2, OT3 linkages at different pressures. The existence of OTm linkages in CaSiO3 glass as well as a significant percentage of O atoms that only link among SiOx polyhedra (forming OSin linkages) or only link among CaOy polyhedra (forming OCan linkages) (n = 2, 3, 4) is origin of structural heterogeneity and micro phase separation. By visualizing, we show that OSin and OCan linkages (n = 2, 3, 4) tend to building up cluster to forming Si-rich regions (SiOx phase) and Ca-rich (CaOy phase) regions in network structure of CaSiO3 glass, see Figure 9. This is origin of structural heterogeneity and micro phase separation. Moreover, we see that SiOx polyhedra link together forming Si-O network in whole model, see Figure 10. It is the reason lead to polymerization on CaSiO3 glass. 172 Pressure-dependent structural heterogeneity in calcium silicate glass Figure 8. The T-O-T bond angle and O-T bond length distribution in OT4, OT5, OT6 linkages at different pressures. Figure 9. Spatial distribution of OSin and OCan (n = 2, 3, 4, 5) at 0 and 30 GPa. 173 Mai Thi Lan, Nguyen Thi Thanh Ha, Tran Thuy Duong, Nguyen Thi Thao and Nguyen Van Hong Figure 10. Network structure of CaSiO3 system and Si-O network that is extracted from CaSiO3 system at ambient pressure 3. Conclusion We have simulated CaSiO3 glass using MDS method to investigate their structure in the range of pressure from 0 to 35 GPa. Our results are in agreement with Neutron diffraction experiment and simulated works [1,9,12]. The network structure of CaSiO3 glass is built up the SiOx polyhedra (x = 4 ÷ 6) and CaOy polyhedra (y = 5 ÷ 11). At ambient pressure, SiOx and CaOy polyhedra are mainly SiO4 and CaO5, CaO6, CaO7, respectively. At high pressure, SiO5, SiO6 and CaO9, CaO10, CaO11 polyhedra are dominant. The O-T-O bond angle and T-O bond length distribution (T is Si or Ca) are almost not dependent on the change of pressure. 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