Effects of anisotropy and regime of diffusion on the measurement of lattice diffusion coefficient of hydrogen in metals

Abstract

The lattice diffusion coefficient of hydrogen in metals is commonly measured by permeation tests. Such tests assume isotropic diffusivity with a set-up which measures permeation flux only along one direction. The measured values of the lattice diffusion coefficient are strongly influenced by the trapping of hydrogen at microstructural defects. These factors lead to highly inaccurate determination of the lattice diffusion coefficient, more so in an anisotropic medium. In this work, we present a three-dimensional (3D) diffusion equation in non-dimensional form for an anisotropic medium with source and sink terms which account for detrapping and trapping of hydrogen. The concentration of hydrogen at lattice and trap sites is assumed to be in a local equilibrium. An initial boundary value problem of the permeation test is formulated and the governing partial differential equation is implemented in a 3D finite-element code. The influence of anisotropic diffusivity on the measurement of lattice diffusion coefficient is shown by numerical simulations. Asymptotic analysis of the governing equation reveals that the lattice diffusion coefficient can only be measured in certain regimes when performing permeation tests at varying temperatures. The nonlinear behaviour of Arrhenius plots of diffusion coefficient versus inverse of temperature due to trapping is analytically and numerically predicted.