It was noted that classical diffusion theory could not explain the temperature kink in the activation energy, or the anomalous isotopic effect, observed for H-atom migration in body-centred cubic metals. A theory was presented, based upon the equations of quantum statistical mechanics, that permitted a complete interpretation of both of these phenomena. Three possible mechanisms were considered for an elementary act of H diffusion in metals: over-barrier hopping, thermally activated tunnel transition and tunnelling due to the decay of a local deformation near to the H atom.

Three Regimes of Diffusion Migration of Hydrogen Atoms in Metals. Y.A.Kashlev: Theoretical and Mathematical Physics, 2005, 145[2], 1590-603