Some aspects of the elastic energies of dislocations.

The standard methods which may be employed to determine the elastic energy associated with a dislocation loop in an infinite, isotropic medium are reviewed in Chapter 1. The equations which are used to obtain the energy are presented in simplified forms, and a correction term which must be included is given. In Chapter 2, an expression for the self-energy of a symmetrical loop having n sides and arbitrary Burgers vector is derived, and errors in the energies given by previous workers are discussed. The energy of a parallelogram-shaped loop with arbitrary Burgers vector is determined in Chapter 3. This is used to study the variation of energy with orientation for a loop on a {111} glide prism in f. c. c. metals, and a similar analysis is presented for a loop on a square glide prism. In Chapter 4, a determination of the variation of energy with orientation for a loop on a circular glide cylinder is described, and the variation of energy with shape for elliptical loops having equal area is also studied. Comparisons are made throughout with the reported observations of circular and elliptical loops. In Chapter 5, the elastic energy associated with a jog which is perpendicular to an infinite straight dislocation line is determined. Errors in the analyses of earlier workers, and the limitations of the present, more rigorous treatment, are considered. The relative merits of the methods for determining elastic energies are outlined in Chapter 6. The approximations employed here, and their possible effects on the results of preceding chapters, are discussed in detail. A preliminary study on the elastic energy associated with double-faulted dislocation loops is also described. Finally, crystallographic angles have been computed for the metals mercury, bismuth, antimony and arsenic. The work is outlined in an appendix, and a volume of angles is also submitted