An analytic model of the shear modulus at all densities and temperatures

TL;DR

This paper introduces an analytic model for the shear modulus valid across all densities and temperatures up to melting, based on experimental and theoretical data, with parameters derived from zero-pressure measurements.

Contribution

It presents a new analytic model for the shear modulus applicable at all densities and temperatures, with parameters determined from zero-pressure data and validated against experiments and calculations.

Findings

Model agrees with argon experimental data within 1%.

Parameters derived from zero-pressure data for 11 elements.

Model matches theoretical calculations for aluminum, copper, and gold.

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.