HR: 0800h
AN: MR11A-0893    [Abstracts]
TI: Unified analytic model of the Gr\"{u}neisen parameter, melting temperature, and shear modulus
AU: * Burakovsky, L
EM: burakov@lanl.gov
AF: Leonid Burakovsky, T-8, MS B221, Los Alamos National Laboratory, Los Alamos, NM 87545 United States
AU: Preston, D L
EM: dean@lanl.gov
AF: Dean L. Preston, P-22, MS D410, Los Alamos National Laboratory, Los Alamos, NM 87545 United States
AB: A unified analytic model of the Gr\"{u}neisen 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 Gr\"{u}neisen 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 Gr\"{u}neisen parameter as $\gamma(\rho)=1/2+\gamma_1/\rho^{1/3}+\gamma_2/\rho^{q}$, where $\gamma_1$, $\gamma_2$, 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.
DE: 8124 Earth's interior--composition and state (old 8105)
DE: 3909 Elasticity and anelasticity
DE: 3919 Equations of state
DE: 3924 High-pressure behavior
SC: Mineral and Rock Physics [MR]
MN: 2004 AGU Fall Meeting