An analysis of reaction diffusion in metal-non-metal systems

The formation of a single M_xN_y intermediate phase in a metal-non-metal system is governed by two parabolic growth regions if the metal side of the couple is finite in extent and initially unsaturated with non-metal. The first parabolic region is described by semi-infinite conditions on the metal side of the couple, while the second is according to saturated conditions. The intermediate phase reaction layer grows non-parabolically when conditions are such that the concentration profile cannot be described by either semi-infinite or saturated conditions on the metal side of the couple. Expressions have been obtained relating the growth constants to diffusion coefficients and information from an equilibrium phase diagram. The mathematical formulation of the problem was tested by application to the titanium-carbon system. The diffusion coefficient of carbon in titanium carbide was found to be in close agreement with values reported elsewhere in the literature.