Dielectric and anelastic relaxation of crystals containing point defects

Abstract

A theory is developed which describes the linear, reversible, time-dependent response of a crystal containing point defects to stress or electric fields, respectively known as anelastic and dielectric relaxation. Such relaxation occurs because of the redistribution of the defects among sites which are initially equivalent, but which becomes inequivalent in the presence of the external field. The macroscopic behaviour of such a crystal is found to be describable in terms of the symmetry which can be assigned to the defect. This defect symmetry determines whether or not the crystal will undergo dielectric or anelastic relaxation and, if relaxation can occur, which specific coefficients of elastic compliance or electric susceptibility show the relaxation effect. The latter information, called the ‘selection rules’ tells, in effect, which combination of stress or electric field components is capable of redistributing the defects. Tables are given for these selection rules for all possible defect symmetries in each of the 32 crystal classes. It is also shown that a hitherto unobserved phenomenon of piezoelectric relaxation may occur; the selection rules for this effect are also given. Aside from its symmetry, the defect can be described as an electric dipole in terms of a suitable dipole moment vector μ, and as an ‘elastic dipole’ in terms of a tensor λ. It is shown that the defect symmetry determines the number of independent components of μ and λ. Finally, a thermodynamic theory is developed which permits calculation of the relaxation strengths for those compliance, susceptibility, and piezoelectric coefficients which undergo relaxation, in terms of the independent components of μ and λ. Applications of the theory to specific cases are then reviewed.