A theory of defective crystals was outlined in which the microstructure was represented by fields of lattice vectors and their spatial derivatives. Since these fields were assumed to be smooth, it was very important to be precise about the sense in which such fields could represent defects. This was done by introducing elastic invariant integrals; the most elementary being the Burgers integrals and the dislocation density. It was found that the concept of slip had a natural place in the analysis of elastic invariant integrals. Moreover, the formulation naturally drew on results arising from Cartan’s theory of equivalence for vector fields, and from the theory of Lie groups. It was noted that it was remarkable that it was possible to identify material points, in a crystal that had a constant dislocation density tensor, with an appropriate Lie group. As a result, it was found that such crystals possessed a self-similarity which generalized the classical idea of generating a perfect crystal lattice by translating a given unit cell.

The 'Moving Frame', and Defects in Crystals. G.P.Parry: International Journal of Solids and Structures, 2001, 38, 1071-87