Third-Order Elastic Coefficients of Crystals

Abstract

It is well known that the number of independent second-order elastic coefficients required to describe the behaviour of cubic crystals is three, irrespective of the class to which they belong, whereas the corresponding number for isotropic bodies is two. That a crystal of the cubic system differs from an isotropic body in another important respect, namely, its photo-elastic behaviour, was discovered by Pockels. Pockels, however, as in the case of elasticity, made no distinction between the five classes of crystals coming under the cubic system, but assigned three coefficients only for all of them. Contrary to this, one of us¹ showed, by a different method based on group theory, that the T and T_h classes of the cubic system require four coefficients for the description of their photo-elastic behaviour, whereas the other three classes T_d, O and O_h require only three. This prediction has been verified by us experimentally by working with crystals of potassium alum².