The solvent-fixed coordinate system applied to two-phase diffusion coatings resulting from a constant surface flux of solute

The explicit finite difference form of the diffusion equation has been used to describe a two-phase binary diffusion problem which includes a constant surface flux boundary condition, a concentration-dependent diffusion coefficient, and dimensional change due to both additions of material and nonideal solution behavior. The ξ_γ coordinate system, containing an equal number of mols of the substrate component per increment, has been employed to simplify the mathematical form of the diffusion equation. At the two-phase interface a Lagrangian extrapolation has been employed in conjunction with the finite difference equations to determine solute concentration and flux as well as interface movement. Results of sample calculations for the α and β phases formed when a constant flux of aluminum is admitted to a copper surface at 850°C are presented graphically. Results include concentration profiles, surface concentration as a function of time, and movement of theα-β interface for a flat plate and for a cylinder. This treatment is applicable to any two-phase binary system wherein the arrival rate of solute atoms at the solvent surface, either by ionic transport in high-temperature electrodiffusion cells or from the vapor phase, is equal to the diffusion rate into the surface.