Simple small polaron model for the hydrogen concentration dependence of hydrogen diffusion in Nb

This chapter generalizes simplified small polaron models for the tunneling of interstitials in solids to include interactions between the diffusing particles. It calculates the average hopping rate of hydrogen in niobium as a function of hydrogen concentration for small concentrations, i.e. for an H/Nb ratio (c) of .06 or less. It also examines the hopping of a single H under the influence of nearby, stationary H's, and finds that for cless than or equal to.06, the calculated increase in the hopping activation energy as a function of c was linear in c and comparable in magnitude with the experimental increase. The chapter shows that the strain interaction between H's in Nb is important for their diffusion and that this interaction needs to be included in whatever more elaborate diffusion models are developed