Image forces on edge dislocations: a revisit of the fundamental concept with special regard to nanocrystals

Abstract

Two conditions under which image forces become significant are when a dislocation is close to a surface (or interface) or when the dislocation is in a nanocrystal. This investigation pertains to the calculation of image forces under these circumstances. A simple edge dislocation is simulated using finite element method (FEM) by feeding-in the appropriate stress-free strains in idealised domains, corresponding to the introduction of an extra half-plane of atoms. Following basic validation of the new model, the energy of the system as a function of the position of the simulated dislocation is plotted and the gradient of the curve gives the image force. The reduction in energy of the system arises from two aspects: firstly, due to the position of the dislocation in the domain and, secondly, due to deformations to the domain (/surfaces). The second aspect becomes important when the dislocation is positioned near a free-surface or in nanocrystals and can be calculated using the current methodology without constructing fictitious images. It is to be noted that domain deformations have been ignored in the standard theories for the calculation of image forces and, hence, they give erroneous results (magnitude and/or direction) whenever image forces play an important role. An important point to be noted is that, under certain circumstances, where domain deformations occur in the presence of an edge dislocation, the ‘image' can be negative (attractive), zero or even positive (repulsive). The current model is extended to calculate image forces based on the usual concept of an ‘image dislocation’.