Unified analytic model of the Grüneisen parameter, melting temperature, and shear modulus
Abstract
A unified analytic model of the Grüneisen parameter, melting temperature, and shear modulus is presented. It is based on three essential components. First is a relation between the melting temperature and the shear modulus at melt obtained from the dislocation-mediated melting model, second is a relation between the Grüneisen gamma and the density derivative of the zero-temperature shear modulus, and third is a linear approximation for the temperature dependence of the shear modulus at a given density. We model the density dependence of the Grüneisen parameter as γ (ρ )=1/2+γ 1/ρ 1/3}+γ2 /ρ {q, where γ 1, γ 2, and q>1 are constants. This form accurately represents the experimentally determined low-pressure behavior of gamma, and its high-compression limit follows from a generalization of the Slater, Dugdale-MacDonald, and Vashchenko-Zubarev forms. We calculate melting curves for a number of substances of geophysical and general interest and compare them to available experimental melt data.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2004
- Bibcode:
- 2004AGUFMMR11A0893B
- Keywords:
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- 8124 Earth's interior: composition and state (old 8105);
- 3909 Elasticity and anelasticity;
- 3919 Equations of state;
- 3924 High-pressure behavior