Steady‐state hydrogen transport in a metal membrane exposed to hydrogen gas and/or a hydrogen ion beam: Reexamination of transport regime and synergistic effects

We reexamined the formalism to describe the steady‐state hydrogen transport in a metal membrane exposed to hydrogen gas or a hydrogen ion beam. On the basis of the formalism, we derived the relation between the material/injection parameters and the transport regimes, which were characterized by specific profiles of the hydrogen concentration in the membrane or specific rate‐limiting processes. The obtained relation was inconsistent with the previous one of Doyle and Brice (DB). Our derivation is directly based on the concentration profiles, and should therefore be correct as far as the concentration profile is concerned. We then extended the formalism to the ion‐driven transport in the presence of the simultaneous gas‐driven transport. Our formalism is different from DB’s in that the former treats the increment in the concentration and the flux density due to the ion injection whereas the latter treats the total concentration and flux density. As far as the total quantities are concerned, DB’s formalism will be preferable. However, our formalism may be more illuminating when the transport of the ion‐originating hydrogen is important.