High-Temperature Elasticity and Earth's Upper Mantle

The elastic properties of minerals are important constraints on modeling the chemistry of Earth's interior and in determining the olivine content of the upper mantle. Current efforts focus on requiring the olivine content of an assemblage to produce wave velocities which match the velocity discontinuities observed seismically at 400-km depth due to changes in elasticity and density associated with an alpha - to beta-olivine phase change. However since the elasticity of beta-olivine is not known for conditions at 400-km depth, it must be estimated, resulting in present models of the upper mantle with 40-70% olivine. The solution rests on knowing the temperature T dependence of the shear modulus G for beta -olivine. Here I introduce new experimental data and theoretical calculations to assess the likely behavior of |(partialG/ partialT)_{rm P}| in the alpha - to beta-olivine transition. High temperature elasticity data on oxides and silicates are used to investigate systematic relationships pertaining to |(partialG/ partialT)_{rm P}| in beta -olivine, and to examine equations used in extrapolating elasticity to high temperature. The theoretical calculations use the potential induced breathing model with quasiharmonic lattice dynamics. Changes in temperature derivatives of elastic moduli for a cubic oxide, CaO, are investigated across a pressure induced phase change. Uncertainties in elastic moduli at 400 km due to mixed pressure and temperature derivatives are examined. My results suggest a moderate increase in |(partialG/ partialT)_{rm P }| across the alpha - to beta-olivine transition. Nonlinear temperature dependence of elasticity is not significant. Mixed pressure and temperature effects introduce a larger uncertainty when extrapolating to 400-km conditions, but the mixed derivative decreases with pressure. I conclude that the mineral physics evidence supports an upper mantle with 50-60% olivine, in agreement with modal compositions found in kimberlite xenoliths, and requiring no special mineral physics data and seismic observations. New elasticity data were obtained by a resonance ultrasound technique and include the first measurements on several oxides and silicates at temperatures well above their Debye temperatures. Olivine data to 1500 K, far above previous temperatures reached for iron-bearing minerals, required new experimental configurations to control oxygen fugacity. The theoretical calculations represent an initial attempt to obtain a complete description of the thermodynamic elastic moduli for an oxide over wide pressure and temperature ranges using an ab initio model.