Structure and properties of forsterite-MgSiO3 liquid interface: molecular dynamics study
© Noritake and Kawamura; licensee Springer. 2014
Received: 14 March 2014
Accepted: 25 May 2014
Published: 20 June 2014
The mechanical properties of partially molten rock, such as their permeabilities and viscosities, are important properties in geological processes. We performed molecular dynamics simulations in terms of structures and diffusivities in forsterite-MgSiO3 liquid interfaces to obtain the nanoscale dynamic properties and structure of the interface. The characteristic structure of the forsterite-MgSiO3 liquid interfaces was observed in the simulations. In the layered structure of the altered surfaces, Si-rich and Mg-rich layers exist alternately in the vicinity of the crystal-liquid interfaces. The layered structure might be formed by the strength difference between Si-O covalent bonds and Mg-O ionic bonds. The difference in the layered structure, indicated by the thickness of the MgSiO3 liquid film, might be caused by the difference in degrees of freedom of the configuration in the liquid film. The two-dimensional diffusivity of oxygen atoms parallel to the interface is controlled by two factors. One factor is the thickness of the liquid film, which decreases oxygen diffusivity with decreasing film thickness. The other is the composition of the sliced layer, where oxygen diffusivity increases with increasing Mg/Si ratio. The effect of the crystal-liquid interface found in this study is negligible in texturally equilibrated rocks. However, the interface can affect the melt flow in deformed samples because a grain boundary melt film with a thickness of several nanometers exists stably in deformed partially molten rock.
Knowledge on viscosity and permeability of partially molten rocks is important for understanding volcanism and the thermal history of the earth. To understand the results obtained by experiments and to estimate physical properties in extreme conditions that are difficult to reproduce in laboratory experiments, it is necessary to know the local structure and the properties of silicate crystal-liquid interfaces. In particular, knowledge on the nanoscale structure and properties of silicate crystal-liquid interfaces might be useful in estimating the properties of rocks containing a small degree of melting. Hiraga et al. ( 2002) reported the presence of nanoscale melt films using high-resolution electron microscopy and energy dispersive X-ray profiling in scanning transmission electron microscopy. The properties of melt in such thin regions are considered to be different from properties in a bulk melt because of the effect of crystal surfaces. For instance, the lateral self-diffusivity of water to a crystal surface is different from a bulk surface in the case of a water-brucite surface (Sakuma et al. 2003), a water-muscovite mica surface (Sakuma and Kawamura 2009), and others. The dynamic property anomalies on solid-liquid interfaces affect the properties of bulk rock, e.g., permeability (Ichikawa et al. 2001).
Molecular dynamics simulations are widely used to investigate the physical properties and structures of crystals, liquids, gasses, and interfaces. In these simulations, we set the initial positions and velocities of all atoms; then, the atoms are forced to move according to given force fields under a proper ensemble. Molecular dynamics simulations are useful methods for investigating the nanoscale structure and properties because they give us the trajectory of each atom. In this study, the structure and properties of the forsterite-MgSiO3 liquid interface are investigated by application of molecular dynamics simulations. It is essential to know the structure and physical properties of forsterite-MgSiO3 liquid interfaces because forsterite is the liquidus mineral of primordial magmas.
Inter-atomic potential parameters
Potential parameters and their values
c (kJ mol-1 Ǻ3)
D 1 (kJ mol-1)
β 1 (1/Ǻ)
D 2 (kJ mol-1)
β 2 (1/Ǻ)
f (kJ mol-1)
θ 0 (deg)
r m (Ǻ)
g r (1/Ǻ)
Comparison of lattice constants between MD simulations and experiments
Density (g cm-3)
K 0 (GPa)
Results and discussion
4-nm liquid film: the structuralized liquid film
16-nm liquid film
Effect of film thickness
The layered structure is also reported by Gurmani et al. ( 2011). They investigated forsterite-MgSiO3 liquid with a film thickness of up to 8 nm by the classical molecular dynamics method. However, the contrast of composition and decrease of self-diffusion coefficients by the interface was much smaller than in our study. The difference between Gurmani et al. ( 2011) and our studies is caused by the area of the surface cross section. Horbach et al. ( 1996) reported the finite-size effects in simulations of silicate glass. According to their study, the system should contain more than 8,000 atoms (4 to 5 nm for each side of the periodic cell) to avoid the size effects. Gurmani et al. ( 2011) simulated the same system with approximately 2-nm length sides for the cross section of the interface. The length of the cross section of our simulation is approximately 5 nm to avoid the size effects reported by Horbach et al. ( 1996).The structure of the altered crystal surface seems to be different because of the thickness of the liquid films. The concentration of magnesium in the altered crystal surface with the 4-nm liquid film is much higher than that with the 16-nm liquid film (Figures 4a and 8a). In addition, the orientation of Si-O-Si bridging in the altered crystal surface with the 16-nm liquid film is strongly perpendicular to the crystal surface compared with the surface with the 4-nm liquid film (Figures 5 and 9). These differences might be explained by the degree of freedom of the configuration of the liquid films. There might be no structural flexibility in the liquid domain to accept the excess magnesium atoms in altered crystal surfaces because there are only five layers in the 4-nm liquid film. In contrast, the concentration of magnesium in the altered crystal surface with the 16-nm liquid film is lower than that with the 4-nm liquid film because of the structural flexibility of the liquid film. The surface becomes well-ordered by acceptation of magnesium in liquid and disordered by existence of excess magnesium atoms.
The two-dimensional self-diffusion coefficients parallel to the crystal surface are dependent on their distance from the altered crystal surface. Those coefficients show larger values in Mg-rich layers and smaller values in Si-rich layers. The regional dependences are simply explained by the composition of the sliced layer. Self-diffusion coefficients of network-forming elements in binary silicate liquids depend on their SiO2 contents (Keller et al. 1982; Keller and Schwerdtfeger 1979). Self-diffusion coefficients of Si and O atoms decrease with increasing SiO2 contents in bulk silicate liquids because of the difference in bond strength between Si-O covalent bonds and ionic bonds. Consequently, the self-diffusion coefficients of oxygen atoms decrease in Si-rich layers and increase in Mg-rich layers. The two-dimensional self-diffusion coefficients of oxygen in the 4-nm liquid film are lower than those in the 16-nm liquid film by an order of magnitude (Figures 4b and 8b). The difference in the self-diffusion coefficients might be explained by the structural flexibility of liquid films. The variety of Mg/Si ratios in the 4-nm liquid film is larger than that in the 16-nm liquid film. The degree of freedom of the configuration in the 4-nm liquid film is lower than that in the 16-nm liquid film. The liquid film is strongly structured by the crystal surface in the case of thin liquid films. Consequently, the flexibility of motion of each atom in the 4-nm liquid film is lower than that in the 16-nm liquid film, and mobility is decreased by the lower flexibility.
where D is the self-diffusion coefficient, k is the Boltzmann constant, T is the temperature, r is the radius of diffusing particles, and η is the shear viscosity. This equation has been used with remarkable success in a variety of silicate liquids to relate diffusivity of network forming atoms and shear viscosity (e.g., Oishi et al. 1975; Dunn 1982; Shimizu and Kushiro 1984; Rubie et al. 1993; Lacks et al. 2007). Applying the Einstein-Stokes relation to the results of this study, the viscosity of thin film silicate liquid might be considered to have higher viscosity than bulk liquid by 1 order of magnitude (Figure 6c). In the 16-nm film liquid, the viscosity of the liquid is slightly lower than that of bulk liquid in the near surface region, the same as with bulk liquid in the Mg-rich layer, and oscillates with distance from the crystal surface (Figure 10c).
We showed the results of molecular dynamics simulations of forsterite-MgSiO3 liquid, which contribute to our understanding of the nanoscale structure of the interface and diffusivity of atoms in the interface. From these simulations, the characteristic structure of liquid films in forsterite-MgSiO3 liquid interface is observed. We also observe the layered structure of an altered crystal surface, an Si-rich layer, and an Mg-rich layer in the crystal-liquid interface. The layered structure is formed by the strength difference between Si-O covalent bonds and Mg-O ionic bonds. Si-O-Si bridging and free oxygen atoms are excessively formed in the near surface because Si-O bonding is much stronger than Mg-O bonding. The difference in the layered structure indicated by the thickness of MgSiO3 liquid films might be caused by the difference in degree of freedom of the configuration in liquid films. The two-dimensional diffusivity of oxygen is controlled by two factors. One factor is the thickness of the liquid films that decreases oxygen diffusivity with decreasing film thickness because of the decrease of degree of freedom of the configuration in the liquid films. The other factor is the composition of the sliced layer, where oxygen diffusivity increases with increasing Mg/Si ratio because Si-O bonding is much stronger than Mg-O bonding. The degree of Mg/Si layering strongly depends on film thickness and decreases with increasing film thickness. The effect of the crystal-liquid interface is negligible in texturally equilibrated rocks. However, the interface can affect the melt flow in deformed samples because the grain boundary melt film of several nanometer thickness exists stably in deformed partially molten rocks.
We thank the editor and three anonymous reviewers for the valuable comments. This work was supported by the Grant-in-Aid for JSPS fellows, 251856.
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