General analytical expressions for multiphase diffusion under non steady-state conditions, which treats the special degenerative case of steady-state diffusion, were developed. The validity of these solutions was examined by application to multiphase layer growth in the Zr-0 and Fe-N systems. The analytical solutions examined include closed-form error function solutions and steady-state approximations to the solutions developed by Wagner. The solutions were general and could accommodate solubility ranges in all phase layers as well as terminal solubilities in the end member phases of the diffusion couple. In diffusion couples where the end member phases have finite, terminal solubilities and where these terminal phases have diffusivities greater than in the intermediate phases (which was common in many metal-interstitial phases), closed-form error function solutions were particularly useful in determining chemical diffusivities from simple intermediate phase layer growth measurements.

Solutions to Multiphase Diffusion in Binary Metal Interstitial Systems. E.Metin, O.T.Inal, A.D.Romig: Metallurgical and Materials Transactions A, 2005, 36[6], 1407-15