# Anelasticity and stress-induced ordering of point defects in crystals

## Abstract

Point defects may exist in a crystal on a set of crystallographically equivalent orientations or sites. The response of a crystal containing point defects to an externally applied stress takes the form of ‘stress-induced ordering’, or preferential alignment of the defects. Recent experiments have used optical and spin resonance techniques to observe this stress-induced ordering directly. This same process also gives rise to anelasticity, e.g. to an internal friction peak. In describing such behaviour, the concept of a point defect as an ‘elastic dipole’, introduced by Kröner and others, is very useful. The elastic dipole is here defined as a second-rank tensor, the ‘λ-tensor’, equal to the average strain per mole fraction of defects all aligned in a particular orientation. This definition is then used to develop a thermodynamic theory of stress-induced ordering, which includes the interaction among defects and the possibility of a ‘reaction’ or interconversion between two species of defects. Applications of the theory are made to defects of various point symmetries in cubic crystals, and a number of specific examples are discussed to illustrate each type of defect symmetry. The usefulness of the theory is that it enables one to calculate the values of the components of the λ-tensor from experimental information and the defect symmetry. Typical values of these λ-parameters range from 10-2 unity. © 1963 Taylor & Francis Group, LLC.