Effective dislocation lines in continuously dislocated crystals. II. Congruences of effective dislocations

TL;DR

This paper introduces the concept of congruences of effective dislocation lines with nonzero Burgers vectors, analyzing their geometry and energetic properties in continuously dislocated crystals.

Contribution

It defines and explores congruences of effective dislocation lines, especially principal Volterra-type lines, linking dislocation densities to crystal geometry and energy.

Findings

Effective dislocation lines have finite self-energy.

Dislocation densities relate to the geometry of dislocated crystals.

Principal Volterra-type lines are key to understanding crystal defect structures.

Abstract

The notion of a congruence of effective dislocation lines endowed with the nonvanishing local Burgers vector is introduced. Particularly, the class of congruences of principal Volterra-type effective dislocation lines associated with the dislocation densities (tensorial as well as scalar) is distinguished in order to investigate the geometry of continuized defective crystals in terms of these densities. It is shown that effective dislocation lines can be endowed with the dislocation line tension and with a finite self-energy.