Influence of bulk and surface phenomena on the hydrogen permeation through metals

Abstract

We discuss the permeation of hydrogen through metals and alloys such as iron, nicket, steels and Inconel wherein H dissolves endothermically from an H$_{2}$ gas. We assume first that trapping centers, surface contaminatian layers, the saturation of the H surface coverage and the irrplantation profile when energetic Ions drive the permeation can be neglected, that a quasi-equilibrium exists between the H atom concentration $\gamma$ in the adsorbed layer and c in the near surface layers and that the H solubility and diffusivity are homogeneous in the membrane. We evaluate thereafter separately the influence of these various effects and identify the parameter domains where appreciable corrections result. The permeation phenomenon is complex even when these simplifications are male : the Penetration rate is proportional to the flux of thermal molecules, atoms or energetic ions - depending upon the rase - which strike the surface; the diffusion in the metal is proportional to the gradient of c ; the release rate depends an c$^{2}$; the time-dependent diffusion equation includes a double spatial derivative of c. Permeation can only be fully described when computer codes such as PERI described elsewhere is used. Simple analytical relations are however obtained in several limiting cases. They are the object of this report. Same of them had already been derived by other authors but they were not shown to be part of a single, seif consistent permeation model. A comparison of predicted and experimental results shows that the simplified model describes surprisingly accurately the hydrogen exchange between gas and metal solutions. Two extreme regimes exist where either the surface reactions or the bulk diffusion titelt the flow. The first arises usually when c is small and the second when c is large. A broad, continuous domain separates them, where both surface and volume effects are important. A permeation number W is introduced ; it allows to identify the flow regime which corresponds to a given experimental situation. With molecular hydrogen upstream, the steady state flux is proportional to the driving pressure P when the permeation number W, i. e. P, is small and to $\sqrt{p}$ when W>>1. Its variation is evaluated analytically in the intermediate domain. An universal function is obtained which involves twa material constants - the permeability and the rate constant of the recombination steil - when the surfaces of the membrane are identical ("symmetrical membrane"). The transient flux variation which follows a change of the driving pressure is described by analytical equations in both extreme cases : the equation of Daynes and Barmer applies when tel whereas the build-up of the permeation flow and the outgassing of hydrogen from metal samples obey other simple equations when W << 1. The equations valid for asymmetric membranes (with differing up- and downstream surfaces) are derived. [...