Pressure-induced structural changes in liquid MgSiO3

Abstract. The micro-structure of liquid MgSiO3 is studied using molecular dynamics simulation (MD) with Born-Mayer potential. Models consisting of 5000 atoms are constructed at 3500 K over a large pressure range (0 - 25 GPa). The local structure as well as network topology of liquid MgSiO3 is clarified through analyses based on molecular dynamics simulation data. The change of network structure and the expansion of polymerization under compression are discussed in detail. Two adjacent units TOx (T is Mg or Si) are linked to each other through common oxygen atoms and form continuous random network of basic structural units TOx. The size of TO4-structural phase regions decreases and the size of TO6- structural phase regions increases as pressure increases. Inversely, the size of TO5-structural phase regions increases to a maximum value and then decreases as pressure increases.

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JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2015-0033 Mathematical and Physical Sci., 2015, Vol. 60, No. 7, pp. 62-67 This paper is available online at PRESSURE-INDUCED STRUCTURAL CHANGES IN LIQUID MgSiO3 Luyen Thi San and Nguyen Van Hong School of Engineering Physics, Hanoi University of Science and Technology Abstract. The micro-structure of liquid MgSiO3 is studied using molecular dynamics simulation (MD) with Born-Mayer potential. Models consisting of 5000 atoms are constructed at 3500 K over a large pressure range (0 - 25 GPa). The local structure as well as network topology of liquid MgSiO3 is clarified through analyses based on molecular dynamics simulation data. The change of network structure and the expansion of polymerization under compression are discussed in detail. Two adjacent units TOx (T is Mg or Si) are linked to each other through common oxygen atoms and form continuous random network of basic structural units TOx. The size of TO4-structural phase regions decreases and the size of TO6- structural phase regions increases as pressure increases. Inversely, the size of TO5-structural phase regions increases to a maximum value and then decreases as pressure increases. Keywords: Oxides, molecular dynamics, microstructure, magnesium-silicate. 1. Introduction The magnesium silicate system (MgSiO3) is an important material in many high technology applications as refractory brick, porous ceramic membranes for catalytic reactors and dental materials. Therefore, knowledge of the microstructure of glass and liquid MgSiO3 is essential for an understanding of its physical and chemical properties. This knowledge is also important for the geosciences because the MgSiO3 system is the simplest (two-component oxide) approximation to the composition of the Earth’s mantle, and ultramafic and mafic liquids. So, the structural properties (local structure, medium-range structure, network structure) of glass and liquid MgSiO3 have been investigated extensively using both experiments and simulation. The most common techniques used in an experimental investigation of the molecular structure of glasses are X-ray diffraction, nuclear magnetic resonance (NMR), Raman spectroscopy, X-ray absorption techniques (EXAFS and XANES) and vibrational spectroscopy. Of these techniques, vibrational spectroscopy is especially useful for in situ investigation at high pressures and temperatures. Meanwhile, NMR and Raman spectroscopy are techniques that are especially sensitive to the state of polymerization of glass silicate. X-ray diffraction data show that in MgSiO3, Mg has six-fold coordination and forming distorted octahedral structures [1] (4 O neighbors at 2.08 A˚ and 2 O neighbors at 2.50 A˚) or four-fold coordination forming tetrahedral structure with a mean distance dMg-O = 2.04 A˚ [2]. By using NMR, the authors in [3, 4] reveal Received January 21, 2015. Accepted October 12, 2015. Contact Luyen Thi San, e-mail address: san.luyenthi@hust.edu.vn 62 Pressure-induced structural changes in liquid MgSiO3 that Mg coordination that is both five- fold and six-fold and six-fold is dominant. By coupling x-ray and neutron diffraction with a reverse Monte Carlo (RMC) simulation, experiment values have recently been obtained with an average coordination number of Mg in MgSiO3 at about 4.5 [2-11]. However, a similar study gives a higher coordination of 5.1 [8]. Base on the diffraction data, it can be interpreted that the structure of MgSiO3 glass is the mixture of MgO4 and MgO5 polyhedra, which are connected to the silicate network by corner sharing with SiO4 tetrahedra. Besides experimental methods, simulation is also a useful tool to investigate the local environment and network structure of glass and liquid silicate, especially in the case of high temperature and pressure. An investigation by molecular dynamics simulation indicated a tetrahedral coordination with a Mg-O distance of 1.90 - 1.96 A˚. However, Kubicki and Lasaga [9] predicted that Mg resides in a distorted site, with 4.3 O atom neighbors at a distance of about 2 A˚ and two more at a distance of 2.2 A˚, in agreement with a recent molecular dynamic simulation that indicated distorted MgO6 octahedra with an average Mg-O distance of 2.07 A˚ and average coordination number of 5.7. Despite having been investigated for a long time both experimentally and theoretically, the local structure (short and medium-range order) and network structure of MgSiO3 systems are still not clear. In this paper, we used MD simulation to clarify the local structure and network structure as a structural transition of liquid MgSiO3 under compression. 2. Content 2.1. Calculation method Molecular dynamics simulations are carried out on MgSiO3 models consisting of 5000 atoms (1000 Si, 3000 O and 1000Mg atoms). The Born-Mayer potential and the periodic boundary conditions are used to construct the models. uij = ZiZje 2 r +Aij exp (−Bijr)− Cij r6 where e is the electron charge and is equal to 1.602 × 10(−19) C; Zi,Zj are the charges of ions i and j, respectively. To integrate the equation of motion, the Verlet algorithm is used with a time step of 0.47 fs. The initial configuration is generated by placing all atoms randomly in a simulation box and heating it up to 6000 K to remove possible memory effects. After that the sample is cooled down to 5000, 4000, and finally to 3500 K. Next, a long relaxation was done in isothermal-isobaric ensemble NPT (constant temperature and pressure) to produce a model at 3500 K upon ambient pressure. Hereafter, the obtained model is called M0. Next we produce seven different models of liquid MgSiO3 by compressing the models to different pressures. The structural data of considered models is determined by averaging more than 1000 configurations during the last 104 MD steps. Table 1. Born-Mayer potential parameter used in this study i, j Zi(e) Aij(eV) Bij(A˚−1) Cij(eV.A˚6) Mg-O 1.2 1042.37635 3.25918353 0 Si-O 2.4 1137.9639 3.4373187 0 O-O -1.2 2024.686563 3.739716 3.3052647 63 Luyen Thi San and Nguyen Van Hong 2.2. Results and discussions The notation ABn is used where n is the number of B atoms that are nearest neighbor to the central A atom. The first Si-O peaks are sharp and symmetric at about 1.66 ± 0.02 A˚ whereas the first Mg-O peaks are broad and skew toward the higher r of about 1.98 ± 0.02 A˚ at ambient pressure. This result is in good agreement with the experimental results [11]. Figure 1. Distribution of coordination number Si (a) and Mg (b) as a function of pressure The distribution of coordination units SiOx andMgOx at different pressures were calculated to clarify the local structure of amorphous MgSiO3 under compression (Figure 1). At ambient pressure, it is dominated by four-fold Si (around 75%) and rapidly decreases as pressure increases (Figure 1a). The amount of coordination unit SiO4 is dominant at ambient pressure, indicating a tetrahedral network structure. The five-fold Si increases and reaches a maximum of 55% at 10 GPa. The fraction of six-fold Si increases monotonically and attains 50% at 30 GPa. In Figure 1b, at ambient pressure, the four-fold Mg is around 40%, approximately 30% is five-fold Mg the proportion of six-fold Mg is about 10% and the seven-fold Mg is around 0%. However, the 6-fold and 7-fold Mg dominate at high pressure which indicates a structural change tendency to higher coordination states at higher pressure. In addition, a recent MD study of glass MgSiO3 reported a dominance of 6-fold coordinated Mg [4, 5]. Figure 2. The bond angle distribution in coordination units SiOx (x = 4, 5, 6) 64 Pressure-induced structural changes in liquid MgSiO3 To elucidate the characteristics of short range order, we analyzed the topology of SiOx through the bond length of Si-O and bond angle of O-Si-O at different pressures (Figures 2, 3). The distributions of the bond length of Si-O and the bond angle of O-Si-O in the units are independent of pressure which reveals that the structure of SiOx units remains unchanged and the topology of units SiOx at different pressures is identical as pressure changes. In order to characterize IRO mediated via Si-O-Si binding, it is useful to examine the coordination statistic of Si and Mg around central O atoms (OTx), which relates to the linkage among TOy. Because the valence of Si is 4 and Mg is 2, the network structure must be different when Si atoms are replaced by Mg atoms. Figure 3. Distribution of coordination units OTy as a function of pressure (T is Mg, Si; y = 3, 4, 5, 6) At ambient pressure, the fraction of coordination units of OT3 is about 47%, with OT4 at about 30% and OT5 approximately 5% (Figure 4). As pressure increases, that of OT3 decreases slightly and attains about 0% at 30 GPa while the fraction of coordination units OT5 increases and attains about 45% at 30 GPa. In contrast, the fraction of coordination units OT4 increases and reaches a maximum of about 47% at 5 GPa, then decreasing monotonically and reaching 30% at 30 GPa. Figure 4. The distribution of all types of tri-cluster OT3, tetra-cluster OT4 and penta-cluster OT5 65 Luyen Thi San and Nguyen Van Hong We also have calculated the distribution of all types of OT3, OT4 and OT5 (Figure 5). Most coodination units of OT3 are Si2-O-Mg1 with the number of Si-O-Mg2 decreasing monotonically from about 50% at 0 GPa to about 20% at 30 GPa. In structure units of tetra-cluster OT4 and penta-cluster OT5, coordination units Si2-O-Mg2 or Si2-O-Mg3 oscilate slightly in the range of 40 - 50%. As pressure increases, the decreasing oxygen having one nearest neighbor Si atom (Si-O-Mg2, Si-O-Mg3, Si-O-Mg4) is in good agreement with the experimental results presented by Lee et al [8]. However, the concentration of bridging oxygen that have two nearest neighbor Si atoms increases slightly (Si2-O-Mg1, Si2-O-Mg2, Si2-O-Mg3). That is in good agreement with results published [6, 7] and shows the extent of polymerization as pressure increases. The formation of oxygen having three nearest Si neighbors (ex Si3-O, Si3-O-Mg, Si3-O-Mg2) shows an increasing abundance of these structural units as pressure increases from about 5% at 0 GPa to about 20% at 30 GPa which initiates the appearance of smaller member rings. This is in good agreement with the results of the experiment of Lee et al. for glass MgSiO3 [8] although they could not quantify the magnitude of the effect. Oxygen having three nearest Si neighbors (a tri-cluster) is known to be one of the dominant factors affecting the liquid’s properties at high pressure, a potential explanation for the anomalous pressure-induced changes in viscosity and oxygen diffusivity. They also suggested that the formation of five-fold and six-fold Si atoms (SiO5, SiO6) is probably associated with the formation of the tri-cluster. However, experimental evidence for its formation in the glass and liquid silicate at high pressure is lacking. Non-network oxygen atoms, that is oxygen with no nearest neighbor Si atom (O-Mg3, O-Mg4 or O-Mg5), make up approximately 8% of the non-network oxygen at 0 GPa and this decreases as pressure increases (Figure 6). These non-network oxygen atoms in MgSiO3 predicted that provide connectivity to the MgOx polyhedron via Mg–O–Mg bridges and form the Mg-rich region. In addition, the number of non-network oxygen atoms increases when Mg increases in amount from 4.5% in MgSiO3 to 16% in Mg2SiO4 [2]. Figure 5. The distribution of Qn The structural and chemical local order within the silicate network can be characterized by the concentration of various types of Si environments, typically denoted as Qn species, where Q is the SiOx and n is the number of bridging oxygen. A change in Qn species from predominantly Qx (x = 2, 3, 4) at low pressure to Qy (y = 4, 5, 6) at high pressure. This tendency is consistent 66 Pressure-induced structural changes in liquid MgSiO3 with the progressive polymerization of the silicate network with increasing pressure. As increase pressure, it is also indicate that the form of Si-rich region. 3. Conclusion Structure of magnesium silicate consists of basic structural units SiOx (x = 4, 5, 6) and MgOy (y = 4, 5, 6, 7, 8). The SiOx connected to each other through common O atoms forms a network of SiOx units that is similar to a pure silica network. Mg2+ incorporates into the silicate network and breaks the silicate network down into a sub-network. The topology structure of SiOx is independent of pressure and the structural transformation of glass under pressure concluded that transforms rom a four-fold to a six-fold coordinated structure at high pressure. This study reports a slight change under pressure. 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