Effects of self-induced stress on the steady concentration distribution of hydrogen in fcc metallic membranes during hydrogen diffusion

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Abstract
Based on the thermodynamics involving the lattice expansion due to hydrogen insertion, the interaction between hydrogen atoms and the blocking effect in hydrogen diffusion, we discuss the profiles of hydrogen concentration and self-induced stress, and their interaction in the steady state during hydrogen diffusion across elastic membranes of fcc metals or alloys. Contrary to the conventional viewpoint, it is found that the self-induced stress suppresses the departure of the concentration distribution from the linearity. The residual stress profile depends on the phase of metal-hydrogen system. However, the diffusion flux is independent of the existence and magnitude of self-stress; this conclusion means that the conventional steady-state method for measurement of the diffusion coefficient can be applied experimentally even while the self-stress effect is significant. Finally, although these results are obtained from the fcc metal-hydrogen system, our conclusions can be extended to the diffusion problem of other interstitials in solid samples.