When a Nb film on a Ti substrate was heated in vacuum, the Ti diffused very rapidly into the Nb film and the results could be described by:

D (cm2/s) = 5.6 x 102 exp[-52.4(kcal/mol)/RT]

This activation energy was equal to about 60% of that for Ti diffusion in bulk Nb. The driving force for rapid Ti diffusion in the Nb film was considered to be a reduction in the surface energy of the Nb film.

M.Yoshitake, K.Yoshihara: Journal of the Japan Institute of Metals, 1990, 54[9], 1013-7