The effective long-range long-term tracer diffusivity, Deff, for interstitial H migration through heterogeneous systems was studied theoretically for model systems which consisted of isolated grains of one material which were embedded in a matrix of another material. Differing H solubilities in the 2 materials, as well as differing diffusivities, were allowed for. Modified diffusion barriers at the phase boundaries were included in the model, and the effects of various sizes, arrangements and forms of the grains were considered. The value of Deff was determined by performing Monte Carlo simulations for simple lattice models of the system. An equilibrium distribution of H atoms among the 2 constituent materials was assumed, and attention was focussed upon how Deff was related to mesoscopic or macroscopic parameters which characterized the heterogeneous system and its constituents. Such parameters included the volume fractions of the 2 materials, the fraction of lattice sites in the immediate vicinity of the phase boundary, the H concentrations in the grains and matrix, and the corresponding H diffusivities. In order to obtain good estimates for these relationships, in terms of analytical formulae, an attempt was made to model an heterogeneous system as a network of diffusion elements which were connected in series and in parallel. The properties of basic parallel and series connections were studied for layered structures, where analytical expressions for Deff could be derived. Network formulae for various grain-matrix systems were tested by comparison with results of Monte Carlo simulations. In general, the network formulae described the corresponding Monte Carlo results for Deff fairly well. It was found that differences in the H solubilities in the 2 phases, as well as modified energy barriers at the phase boundaries, could have a marked effect upon Deff.

Diffusion of Hydrogen in Heterogeneous Systems. A.Herrmann, L.Schimmele, J.Mössinger, M.Hirscher, H.Kronmüller: Applied Physics A, 2001, 72[2], 197-208