Bulk Diffusion-Controlled Thermal Desorption Spectroscopy with Examples for Hydrogen in Iron

Bulk diffusion-controlled thermal desorption spectroscopy (TDS) is studied by solving the corresponding transport equations numerically as well as analytically with appropriate approximations. The two solutions are compared in order to validate the derived equations including the Kissinger equation. Besides the diffusion of the desorbed species through the sample, trapping of the species at special lattice sites within the sample is included in the numerical and approximate analytical solutions. Trapping energies are mono-energetic, multi-energetic, or are described by a box-type distribution. TDS-peaks were simulated for different heating rates, sample thicknesses, trap concentrations, and initial degrees of trap saturation. It is shown that for the case of mono-energetic traps, Kissinger’s equation is obeyed for both numerical and analytical results. This widely used equation for reaction rate-controlled studies is derived in an explicit form for diffusion-controlled processes. Together with a newly derived relation between maximum desorption rate and temperature, TDS-spectra yield information about diffusion coefficient, trap energies, and trap concentration as well as trap saturation. This is exemplified using data of two experimental studies. Although the numerical and analytical treatment is in general applicable to all diffusion species, hydrogen in iron alloys is used as a model system because of its technological importance and the increasing number of experimental work with this material.