Influence of initial conditions on trap-controlled hydrogen diffusion with calculations of effective diffusion coefficients

An effective diffusion coefficient for trap-controlled diffusion such as hydrogen in solid materials is generally determined considering the characteristics of trapping sites. However, it is possible that the initial conditions (initial hydrogen concentrations at normal and trapping sites) also influence the diffusion phenomena. To investigate the influence, we derive a two-dimensional analytic solution of a diffusion equation with an arbitrary number of trapping terms, and verify the model by comparing with the, experiments of hydrogen evolution from cylindrical specimens at two different initial conditions. The comparison shows that the experimental results can be explained fairly well using the present solution. We next calculate effective diffusion coefficients by varying initial conditions for the transient evolution from a cylindrical specimen, and show that the coefficients are much influenced by the initial conditions, which cannot be explained using the local equilibrium assumption. The effective diffusion coefficient determined with the local equilibrium assumption is shown to be a kind of average value of those calculated in the present study.