A molecular dynamics study of grain boundary diffusion in MgO
Introduction
Grain boundaries are interfacial regions connecting a network of regular crystal lattices, where the crystal lattices are of the same phase (Lejček, 2010). The grain boundary regions generally have chemical and transport properties that are very different from the interior of the crystals. For this reason, grain boundaries can significantly alter the properties of polycrystalline materials, including melting temperature and characteristics (de Kloe et al., 2000), their bulk electrical conductivity and chemical diffusivity, (Tschöpe et al., 2001, Dohmen and Milke, 2010) and their creep viscosity (Frost and Ashby, 1982).
Diffusion of atoms along grain boundaries is in general several orders of magnitude faster than diffusion within crystal lattices (Joesten, 1991). This rapid transport along grain boundaries can enable chemical transfer between physically separated mineral pairs (Eiler et al., 1992, Dohmen and Milke, 2010), and potentially enable large-scale transport between major geochemical reservoirs such as the core and mantle (Van Orman et al., 2003, Hayden and Watson, 2007). Grain boundary diffusion also plays a key role in many geophysical processes. It can control mantle viscosity under some conditions (Hirth and Kohlstedt, 1995), is an important mechanism in the attenuation of seismic waves (Karato and Spetzler, 1990), and contributes to the temperature dependence of seismic velocities (Karato and Wu, 1993).
Periclase (MgO, with FeO in solid solution) is thought to be the second most abundant phase in the lower mantle, and may be the most abundant phase in some regions, including in the thin, ultra-low velocity zones just above the core (Wicks et al., 2010). Periclase has lower creep strength than the other major minerals of the lower mantle (Lin et al., 2009, Reali et al., 2019), and hence may have an important influence on mantle viscosity. Studies of periclase suggest that grain boundary diffusion may govern viscous creep under some mantle conditions (Frost and Ashby, 1982, Van Orman et al., 2003), as well as viscoelastic and anaelastic deformation (Webb and Jackson, 2003, Barnhoorn et al., 2016). Because of its simple crystal structure and lack of phase transitions below 450 GPa (Karki et al., 1997), periclase is also a useful model material for studying diffusion over a wide range of conditions.
Grain boundary diffusion in periclase has been studied experimentally (Wuensch and Vasilos, 1964, McKenzie et al., 1971, Osenbach and Stubican, 1983, Van Orman et al., 2003, Hayden and Watson, 2007) but many uncertainties remain on the fundamental processes that are involved in grain boundary transport, and how the rates vary with temperature and pressure. Grain boundary diffusion is typically modelled as a thin, highly diffusing region of width , with diffusion coefficient and, for impurity atoms, a segregation coefficient, s, which represents the equilibrium fraction of impurity in the grain boundary. In systems where volume and grain boundary diffusion both occur, experiments typically cannot disentangle the triple product (Joesten, 1991). More recently, methods have been developed to obtain these separate quantities experimentally (Marquardt et al., 2011a, Marquardt et al., 2011b), but these methods have not yet been applied to MgO.
Further insight on grain boundary diffusion can be obtained from molecular simulations. Ab initio simulations based on density functional theory (DFT) have been performed on MgO systems with grain boundaries (Verma and Karki, 2010, Karki et al., 2015). These calculations provide important insight on grain boundary structure, and on the migration enthalpies for specific atomic transitions within the grain boundary. However, DFT calculation of all of the thermally available grain boundary conformations is computationally expensive, and at present it is not possible with these techniques to fully account for the entropic effects involved in grain boundary diffusion. Kinetic monte carlo (KMC) simulations have also been used to study grain boundary diffusion (Harding and Harris, 2001), but these simulations require a specific grain structure to be assumed, and also require knowledge a priori of the attempt frequencies for each mode of migration.
In this paper, we use classical molecular dynamics, which enables large scale simulations for long simulation times (25 nanoseconds per day on a supercomputer using 80 Intel Xeon E5-2680 cores), without supposing a predetermined grain boundary lattice from which atoms transition. Molecular dynamics simulations of grain boundary diffusion are computationally intensive, even using simple pairwise atomic interactions. To simulate a polycrystalline material requires large systems containing many atoms, and long run times are necessary to study the migration of atoms in the diffusive regime. Here, simulations are performed on a polycrystalline MgO system to determine Mg and O grain boundary diffusion coefficients over a range of pressures and temperatures corresponding to conditions within Earth’s mantle. We show that the dynamics of grain boundary diffusion are related to grain boundary structure, and at low pressures are analogous to the behavior of liquids near the glass transition temperature.
Section snippets
Methods
In molecular dynamics simulations of polycrystalline MgO, the key considerations are how to: (a) define and construct the polycrystalline system; (b) model the atomic interactions; (c) simulate the system dynamics and equilibration; and (d) analyze the results to obtain meaningful physical insight. We describe below our approaches in these regards.
Results
Molecular dynamics simulations were carried out for the polycrystalline MgO system at pressures between zero and 135 GPa, and temperatures between 1200 and 3500 °C. We identify relationships between grain boundary structure and diffusion, and how these properties change with temperature and pressure.
Comparison with experimental data
It is difficult to estimate grain boundary diffusion coefficients from experiments, and only a few studies have investigated grain boundary diffusion in MgO. Each of these studies has involved a polycrystalline MgO sample coupled to an environment enriched in isotopic magnesium and/or oxygen, or another cation such as Ni or Cr. After heating to a high temperature for a period of time, the distribution isotopes or cation dopant in the polycrystalline MgO sample is determined, and fit to a model
Conclusions
The grain boundary diffusion coefficients and activation volumes obtained here from molecular dynamics simulations are in reasonable agreement with experimental values, and provide additional insight on how diffusivity varies with pressure and temperature. For both Mg and O, the apparent activation energy for grain boundary diffusion is larger than the migration energy for volume diffusion in MgO. This strong temperature dependence is connected to a gradual shift to more ordered structures with
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The calculations of this work were carried out using resources of the Ohio Supercomputing Center and the high performance computing center at Case Western Reserve University. This work was supported by the National Science Foundation under Grant No. EAR-1250331. We thank the reviewers for their helpful comments in improving the manuscript.
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