Analytic model of the Grüneisen parameter all densities Original Research Article

We model the density dependence of the Grüneisen parameter as γ(ρ)=1/2+γ1/ρ1/3+γ2/ρq, where γ1,γ2, and q>1 are constants. This form is based on the assumption that γ is an analytic function of V1/3, and was designed to accurately represent the experimentally determined low-pressure behavior of γ. The numerical values of the constants are obtained for 20 elemental solids. Using the Lindemann criterion with our model for γ, we calculate melting curves for Al, Ar, Cu, Pd, and Pt and compare them to available experimental and theoretical melt data. We also determine the Z (atomic number) dependence of γ1.The high-compression limit of the model is shown to follow from a generalization of the Slater, Dugdale–MacDonald, and Vashchenko–Zubarevforms for the volume dependence of the Grüneisen parameter.