An analytic model of the Gruneisen parameter at all densities

TL;DR

This paper presents an analytic model for the density dependence of the Gruneisen parameter, fitting experimental data and predicting melting curves for various elements, with implications for high-pressure physics.

Contribution

It introduces a new analytic form for gamma(rho) based on the assumption of analyticity in V^{1/3} and applies it to multiple elements to predict melting behavior.

Findings

Model accurately fits experimental gamma data for 20 elements.

Predicts melting curves for Al, Ar, Ni, Pd, and Pt.

Derives Z-dependence of gamma_1 and high-pressure limits.

Abstract

We model the density dependence of the Gruneisen 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 is based on the assumption that gamma is an analytic function of V^{1/3}, and was designed to accurately represent the experimentally determined low-pressure behavior of gamma. The numerical values of the constants are obtained for 20 elemental solids. Using the Lindemann criterion with our model for gamma, we calculate the melting curves for Al, Ar, Ni, Pd, and Pt and compare them to available experimental melt data. We also determine the Z (atomic number) dependence of gamma_1. The high-compression limit of the model is shown to follow from a generalization of the Slater, Dugdale-MacDonald, and Vashchenko-Zubarev forms for the dependence of the Gruneisen parameter.