Some Effects of Strain on Diffusion in Crystalline Solids.

We examine the effects on diffusion of both externally applied strains and internal strains generated by large particles embedded in a coherent crystal. Constant-strain and constant-stress ensembles are constructed in order to study non-hydrostatically deformed crystals via computer simulation, and various stress and strain tensors are identified. The Monte Carlo and molecular dynamics simulation methods are used to characterize the elastic properties of a Lennard -Jones-like crystal and a hard-sphere crystal, and to simulate the diffusion of interstitials in a binary hard-sphere crystal. The simulation results are interpreted by using a multiclass master equation and by using some predictions about the coupling of strain and diffusion in coherent crystals obtained from linear response theory. We examine quantitatively the dependence of the diffusivity of a tagged interstitial particle, known as a tracer diffusivity, migrating through a crystal on the crystal's state of strain and on the size of the interstitials. The tracer diffusivity, associated with the decay of long wavelength, single-particle interstitial density fluctuations, is found to be independent of crystallographic orientation, as expected. The collective diffusivity, calculated from the decay of total interstitial density fluctuations, is found to depend on crystallographic orientation for large interstitials in accordance with a prediction due to Cahn. This behavior is attributed to the existence of long-range interparticle correlations which arise because of the deformability of the crystalline medium. The distinction between tracer diffusion and collective diffusion in crystals is then discussed in detail. The diffusion response functions E(vec k) and E_{c}(vec k), which describe the decay of density fluctuations in time in reciprocal space, for tracer diffusion and collective diffusion, respectively, are compared and contrasted. The implications of a collective diffusion response which depends on crystallographic orientation in reciprocal space for the formulation of a non-local diffusion equation in real space in coherent crystals are considered. The strictly local Fickian diffusion law is found to be inadequate for the description of diffusion of sufficiently large particles in a coherent crystal.