On the use of recombination rate coefficients in hydrogen transport calculations

The commonly accepted picture for the uptake of hydrogen isotopes (HIs) from the gas phase across the surface into a metal with an endothermic heat of solution for HIs is that of dissociation followed by thermalisation in a chemisorbed surface state and finally overcoming a surface barrier to enter the metal bulk where the HIs occupy interstitial solute sites. To leave the metal bulk the HIs first transition to the chemisorbed surface state from which they then enter gas phase by recombining into a diatomic molecule. This model is generally attributed to the work of Pick and Sonnenberg from 1985. They clearly distinguish surface states and subsurface solute sites where the recombination flux is proportional to the square of the concentration of chemisorbed atoms due the diatomic nature of this Langmuir-Hinshelwood process. In an effort to compare their extended model with an earlier surface model by Waelbroeck, which uses an expression for the recombination flux proportional to the square of the sub-surface interstitial solute concentration, they derive an effective recombination coefficient. However, also with the so-derived Pick and Sonnenberg recombination coefficient, the Waelbroeck model is only applicable under certain conditions. But, due to its simplicity, it is often used in boundary conditions of diffusion trapping type calculations, generally ignoring whether or not these conditions are met. This paper will use the full Pick and Sonnenberg model implemented in the TESSIM-X code and in simplified algebraic approximations, to show the limits of applicability of the Waelbroeck-Ansatz in modelling hydrogen transport in metals foreseen for the first wall of magnetic confinement fusion devices.