The self-energy of straight-line dislocation segments in pseudo-continuum theory

Expressions for the self-energy of straight-line dislocation segments are derived on the basis of the pseudo-continuum theory. Final results are given in simple form and are shown to be valid even for very short segments of the order of 10 interatomic distances. The dependence of the energy expressions on the assumptions introduced is discussed. Dispersive terms are also derived and their influence on the values of the energy is studied. The results are compared with those obtained on the basis of the classical theory of elasticity. The use of the pseudo-continuum model obviates the necessity of introducing an ill-defined core parameter, because in this model the singularity on the dislocation line does not exist. It is the presence of this singularity in classical elasticity which necessitates the introduction of the core parameter. Numerical data illustrate the results obtained as summarized in two tables.