Energy of Dislocations

The atoms in a crystal containing a dislocation are displaced from their perfect lattice sites, and the resulting distortion produces a stress field in the crystal around the dislocation. The dislocation is, therefore, a source of internal stress in the crystal. For example, consider the edge dislocation in Fig. 1.18(b). The region above the slip plane contains the extra half-plane forced between the normal lattice planes and is in compression: the region below is in tension. The stresses and strains in the bulk of the crystal are sufficiently small for conventional elasticity theory to be applied to obtain them. This approach only ceases to be vaUd at
positions very close to the centre of the dislocation. Although most crystaUine sohds are elastically anisotropic, i.e. their elastic properties are different in different crystallographic directions, it is much simpler to use isotropic elasticity theory. This still results in a good approximation in most cases. From a knowledge of the elastic field, the energy of the dislocation, the force it exerts on other dislocations, its energy of interaction with point defects, and other important characteristics can be obtained. The elastic field produced by a dislocation is not affected by the application of stress from external sources: the total stress on an
element within the body is the superposition of the internal and externalstresses[1].

References
1- D Hull and DJ Bacon, Introduction to dislocations, Fourth Edition 2011.