Multi-layer problems in time-lag measurements applied on metal–hydrogen systems

Abstract

Time-lag techniques are powerful tools to determine diffusion coefficients of hydrogen in metals. The quality and reliability of time-lag measurements depends strongly on an exact consideration of the experimentally established boundary conditions in the mathematical evaluation of the measured time-lag curves. This also means that a change of inner and/or outer boundary conditions can lead to another type of time-lag experiment with a different solution for the diffusion equation. In numerous cases the metal foil is coated by surface layers possessing hydrogen solubilities and diffusivities different from that of the enclosed metal. The surface layers determine the boundary conditions at the interface between the metal and the surface layer. In these cases solutions of the diffusion equation for multi-layer problems have to be found. Complete analytical solutions normally do not exist; however, numerical calculations allow to solve the problems reliably. We present results from those calculations for double (AB) and triple (ABA) layer systems for cases where A or B controls the time-lag, but also for the situations in between these two extreme cases. The simulation also describes the transition from one type of time-lag experiment to another one.