Ab Initio Investigation of the High Pressure Elasticity of Mg 2 SiO 4 Forsterite and Ringwoodite
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relatively complex structures that are important for understanding the earth's mantle for the first time [4]. I discuss theoretical results for two major materials of the earth's mantle with identical composition, but very different elastic properties. Mg 2 SiO4 forsterite is the most abundant mineral in the earth's upper mantle (100-410 km depth, 3-13 GPa). Mg 2 SiO 4 ringwoodite is a high pressure polymorph of forsterite and is believed to be the most abundant mineral in the earth's transition zone (410-660 km depth, 13-24 GPa). The focus is on their elastic properties at high pressure, including their anisotropy, and how these can be understood at the microscopic level in terms of their structure and bonding. METHODS An essential property of the theoretical methods discussed here is that they are parameter-free and completely independent of experiment. These methods of modem electronic theory provide the ideal complement to the experimental approach, and a unique standard of comparison. Our results are based on density functional theory, in principle an exact theory of the ground state [5]. In practice, exact solutions of the Kohn-Sham equations are not currently possible, because the form of the exchange-correlation functional, that accounts for the many-body electron-electron interactions, is unknown. We approximate this term with the widely studied local density approximation [6]. The only other essential approximation in the method is the pseudopotential approximation which treats the nuclear-electron interaction. The basic idea is that the interaction between valence electrons and nuclei is largely screened by the core electrons. The structure of these core electrons is essentially invariant over the range of structures, pressure, and strains that are of interest in geophysics. The full coulomb potential of the nucleus is replaced with a pseudopotential that varies much more smoothly in real space. This is an important advantage because it means that slowly varying and numerically convenient basis functions such as plane waves can be used to represent the charge density and the potential. In these calculations, we use Troullier-Martins [7] norm-conserving pseudopotentials. While pseudopotential based density functional calculations have been performed for some time, their widespread application to relatively complex materials, such as silicates, has been relatively recent. The number of structural variables in earth materials can be quite large: forsterite has an orthorhombic 28-atom unit cell with I internal degrees of freedom. The primary reason that such complex structures can now be treated is the development of ab initio molecular dynamics techniques that allow the ground state of a structure to be found efficiently [4,8]. The method of Wentzcovitch, used here, employs a pseudo-Lagrangian to efficiently minimize the Hellman-Feynman forces and stresses [9] acting on the atomic positions and lattice parameters respectively. To find the equilibrium structure of forsterite at a given pressure typically re
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