A discrete model which described the influence of stress on interstitial diffusive processes in a simple cubic crystal was developed and analyzed. The model consisted of two parts: (i) elasticity equations governing the evolution of the displacements, and hence the stresses in the crystal, and (ii) an equation governing interstitial diffusion through the crystal. In a continuum limit, it was found that the displacements satisfy the usual partial differential equations for a simple cubic crystal. Two-dimensional equilibrium solutions to the discrete elasticity equations were constructed analytically, by introducing a discrete Airy stress function and calculating polynomial solutions to the fourth-order difference equation this function satisfies. Numerical solutions were also constructed, and all of the solutions obtained were used in the study of diffused profiles, the results largely being in conformity with intuitive expectations. The specific model problems that were investigated were intended to allow classes of qualitative behaviour of stress-effected diffusion to be catalogued.

Diffusion in a Strained Cubic Crystal. M.G.Meere, J.R.King: Journal of Engineering Mathematics, 2011, 69[1], 1-23