On defective crystallography

Abstract

Suppose that a solid crystal derives from a perfect (Bravais) lattice of atoms, so that the set of rearrangements of the points of this lattice provides symmetries of the crystal. In the elasticity theory appropriate to such a crystal, it is traditional to assert that the corresponding strain energy density function has invariance properties related to a (proper) subset of these symmetries. Here I discuss similar issues in the context of the continuum mechanics of smoothly defective crystals, focusing on planar distributions of defects.