Solutions to multiphase diffusion in binary metal interstitial systems

Abstract

General analytical expressions for multiphase diffusion under nonsteady-state conditions, which treats the special degenerative case of steady-state diffusion, are developed. The validity of these solutions is 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 are general and can 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 is common in many metal-interstitial phases), closed-form error function solutions are particularly useful in determining chemical diffusivities from simple intermediate phase layer growth measurements.