The mixed P, T derivatives of elastic moduli and implications on extrapolating throughout Earth's mantle

Details The mixed P, T derivatives of elastic moduli and implications on extrapolating throughout Earth's mantle The mixed P, T derivatives of elastic moduli and implications on extrapolating throughout Earth's mantle

Oct 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993pepi...80...37i&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 80, Issue 1-2, p. 37-48.

Physics

15

Scientific paper

Compositional profiles of Earth's mantle require accurate extrapolation of elasticity to simultaneous high pressure P and temperature T, using the first P and T derivatives of elasticity measured near ambient conditions. We present thermodynamic relations that elucidate ∂2KT/∂P∂T for minerals for which data on the volume dependence of (∂T/∂P)S are available (KT is the isothermal bulk modulus and S indicates constant entropy). We find that ∂2KT/∂P∂T is positive for almost all solids and has values of (0.39 +/- 0.10, 0.33 +/- 0.09) × 10-3K-1 for MgO and olivine, respectively. We suggest that neglect of ∂2KT/∂P∂T could cause the olivine content of the upper mantle to be overestimated by 3% at most, if second-order pressure effects are not considered. This result is based on a comparison of the longitudinal velocities of the α and β phases of olivine at 400 km P, T conditions. We show that the isothermal ∂2KT/∂P∂T decreases with increasing P. Ab initio model calculations on MgO are consistent with the results from thermodynamics. We show for MgO the theoretical values of (∂KT/∂P)T and (∂G/∂P)T, where G is the isotropic shear modulus, along a geotherm.
Also at Azusa Pacific University, Department of Math and Physics, 901 E. Alosta Ave., Azusa, CA, USA.

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