The relationship between the adiabatic bulk modulus and enthalpy for mantle-related minerals

Abstract

It is found that the adiabatic bulk modulus, K_S, is linear with enthalpy over a wide temperature range: up to at least 1825 K, the present limit of the measurement of the bulk modulus. This correlation is shown to hold for Al₂O₃, MgO, and Mg₂SiO₄. Since the enthalpy is listed in thermodynamic tables up to 3000 K, one can reasonably safely extrapolate K_S up to lower mantle temperatures using this correlation. This correlation was anticipated in a theoretical 1966 paper, where the definition of the anharmonic parameter δ _S was made in terms of properties which vary with temperature, $\delta _s = - \left( {\frac{1}{{\alpha K_S }}} \right)\left( {\frac{{\delta K}}{{\delta T}}} \right)_{P'}$ where α is the volume coefficient of thermal expansion. The correlation was first confirmed for polycrystalline oxides in an experimental 1966 paper. Since the isotropic shear modulus, G, is linear with T, it is possible to estimate the sound velocities in the temperature regime just below the melting point.