Invariant functions and homogeneous bases of irreducible representations of the crystal point groups, with applications to thermodynamic properties of crystals under strain

Abstract

A general method is described for deriving the integrity bases of finite transformation groups. A generalization of an integrity basis which determines the homogeneous bases of irreducible representations of such groups is also given. It is shown that such bases can be expressed as linear combinations of a finite number of these bases with coefficients which are homogeneous polynomials that are invariant to the Coxeter group containing the group in question. Tables are given for the integrity bases for polynomial functions of a symmetric second-order tensor which are invariant to the crystal point groups. It is shown how these results may be applied to the finite strain tensor and hence to the thermodynamics of anisotropic crystals.