A complete list of invariants for defective crystals

Abstract

The classical theory of continuous distributions of dislocations has traditionally focused on the Burgers’ vectors and the dislocation density tensor as descriptions of defectiveness. We prove that, generally, there is an infinite number of tensor densities with similarly descriptive properties, and that there is a functional basis for this list which strictly includes the Burgers’ vectors and dislocation density. Moreover the changes of state which preserve these densities turn out to represent slip in certain surfaces associated with crystal geometry, so that the basic mechanism of plasticity emerges naturally from abstract ideas which neither anticipate nor involve the kinematics of particular types of crystal defects.