Analytic model of the shear modulus at all temperatures and densities

Abstract

An analytic model of the shear modulus applicable at temperatures up to melt and at all densities is presented. It is based in part on a relation between the melting temperature and the shear modulus at melt. Experimental data on argon are shown to agree with this relation to within 1%. The model of the shear modulus involves seven parameters, all of which can be determined from zero-pressure experimental data. We obtain the values of these parameters for 11 elemental solids. Both the experimental data on the room-temperature shear modulus of argon to compressions of $\sim 2.5,$ and theoretical calculations of the zero-temperature shear modulus of aluminum to compressions of $\sim 3.5$ are in good agreement with the model. Electronic-structure calculations of the shear moduli of copper and gold to compressions of 2, performed by us, agree with the model to within uncertainties.