Part X – October 1969 - Papers - Calculations of Two-Phase Diffusion in Metallic Systems Including the Interfacial Reactions

Recent experimental evidence has shown that it is often incorrect to neglect the reactions occurring at an interface with respect to the diffusion reactions. By introducing reaction-rate constants and k for the transfer of components 1 and 2 between the a and b phases, a phenomenological description has been devised for the coupled processes of diffusion and in-terfacial reaction. An illustrative example has been analyzed with the aid of a suitable computer program. The results indicate that for kab values on the order of 10'1 cm per sec and Ð values of about 10¯10 sq cm per sec, the interfacial reactions are significant during the first 10 2 to l0 6 sec of a diffusion experiment. Among the observable effects of the interfacial reactions in this case appear to be the burying Kirkendall markers and an anomaly in the initial shifting of these markers. THE study of diffusion between two phases is especially important because of its direct connection to phase transformations. For example, the transformation of austenite to ferrite involves diffusion in the a and ý phases and also an interfacial reaction (trans formation) at the a/? interface. If ferrite and aus-tenite are the two members in a diffusion couple, the same two reactions occur during the diffusion process. The numerical values obtained for the diffusion coefficients and interfacial-reaction constants from diffusion experiments can then be employed to predict phase-transformation behavior. Refinement of the calculations of phase transformation is also suggested by the present method for treating two-phase diffusion. In the recent paper by Nolfi et al.' only the solute com ponent is considered in the interfacial reaction accompanying a phase transformation. The present analysis demonstrates that both components must be considered. It is generally recognized that reactions of some kind must occur at the interface in a two-phase diffusion couple, but usually it is assumed that the interface reaction occurs so rapidly that its effect on the overall process is unobservable because the slower diffusion process determines the kinetics of the process. However, Seith and Heumann 2 pointed out that effects of the interfacial reaction should always occur in the early stages of diffusion, and recently Eifert et al. 3 have shown that interfacial reactions influence the composition and motion of the interface in a/ß Al-Cu diffusion couples during the entire course of prolonged, high-temperature treatments. A general procedure for handling the combined processes of interfacial reaction and diffusion in a binary, two-phase system is to introduce kinetic coefficients for the interface reactions and to develop the system of equations governing the interlinked processes of diffusion and interface reaction. The resulting equations, although not amenable to solution in closed form, can be usefully manipulated by a digital computer. INTERFACIAL REACTIONS IN TWO-PHASE DIFFUSION Consider the general case of diffusion between two solid solutions, a and ß, which are adjacent phases in a binary system, Fig. 1. Two semiinfinite bars having compositions c1 and c0ß are jointed at x = 0. If concentrations are expressed in volume fraction,4