An innovative concept for interstitial diffusion in stressed crystals

Existing concepts for diffusion of interstitial atoms in stressed bodies mostly assume that the mechanical driving force stems from the gradient of the hydrostatic stress component. However, both octahedral and tetrahedral interstitial positions in bcc lattice have tetragonal symmetry only. Therefore, deposition of an atom there causes an anisotropic distortion of the lattice. Considering occupation of octahedral positions, three types of them exist differing in misfit eigenstrain tensors and, consequently, in the interaction energies with any stress field. Thus, the state of the system must be described by three independent site fractions (internal variables) corresponding to the three types of octahedral positions. An according new diffusion equation and respective evolution equations for the three site fractions are derived. The concept is demonstrated on a simple example for diffusion of hydrogen in the stress field of a crack in an elastic body loaded by a uniaxial stress. The current new concept is also directly applicable to the occupation of tetrahedral positions.