It was recalled that the hydrogenation of metals could lead to the production of high vacancy concentrations in a solid when equilibrium was reached. The achievement of equilibrium in this up-quenching process depended upon the migration of vacancies from the surface and into the interior of the solid. Because individual vacancy jump frequencies could depend upon the position within the vacancy density gradient, especially when the solid was under an applied stress, solutions of Fick's second law were not appropriate. A finite-difference method was developed in order to treat such vacancy diffusion problems.

A Finite-Difference Calculation of Vacancy Migration under Non Steady-State Conditions. D.Zang, R.B.McLellan: Acta Materialia, 1999, 47[5], 1671-83