The Voigt-Reuss-Hill Approximation and Elastic Moduli of Polycrystalline MgO, CaF2, β-ZnS, ZnSe, and CdTe

Abstract

The Voigt‐Reuss‐Hill (VRH) approximation, a useful scheme by which anisotropic single‐crystal elastic constants can be converted into isotropic polycrystalline elastic moduli, is shown to apply for moderately anisotropic cubic crystals like MgO, CaF₂, β‐ZnS, ZnSe, and CdTe. Experimental values of polycrystalline isotropic elastic moduli for these materials are presented here, and the validity of the VRH approximation is established. The VRH approximation is then discussed for these materials with respect to their elastic anisotropy of crystals. To provide further support to this work, a numerical confirmation on the VRH moduli is made with the use of a high‐speed computer by calculating the mean velocity of sound in crystals and comparing this result with the corresponding quantity calculated from the actual polycrystalline elastic moduli. The general agreement is observed.