Diffusion with multiple kinds of trapping sites

Since diffusion in solid is influenced by trapping sites which have different binding energies, analytic solutions to describe diffusion with multiple kinds of trapping sites have been derived for dilute systems without using the assumption of local equilibrium. Numerical comparisons with the local equilibrium treatment show that the transport of free atoms evaluated by the present solutions is faster at short times than that of the local equilibrium treatment. As time passes, the difference becomes small. The present solutions also show that the transport of free atoms is influenced by the initial concentrations at trapping sites, and that the apparent transport is accelerated in some cases. Using the present solutions, systematic investigations of diffusion phenomena with many kinds of trapping sites become possible.