An hypothetical binary system composed of 1 intermetallic compound and 2 primary solid-solution phases was considered in order to examine the kinetics of reactive diffusion controlled by boundary and volume diffusion. If a semi-infinite diffusion couple which initially consisted of the 2 primary solid-solution phases with solubility compositions was isothermally annealed at a suitable temperature, the compound layer was always produced at the interface between the primary solid-solution phases. However, there was no diffusional flux in the primary solid-solution phases. Moreover, it was supposed that the compound layer was composed of a single layer of square-rectangular grains with identical dimensions. Here, the square basal-plane was parallel to the interface, and hence the height was equal to the thickness of the compound layer. Under such conditions, the growth behaviour of the compound layer was analyzed numerically. In order to simplify the analysis, it was assumed that there was no grain boundary segregation, and that volume and boundary diffusion took place along the direction perpendicular to the interface. When the size of the basal-plane remained constant regardless of the annealing time, the thickness of the compound layer was proportional to the square root of the annealing time. However, the growth of the compound layer took place in a complicated manner if the size of the basal plane increased in proportion to a power function of the annealing time. Nevertheless, at around a certain critical annealing time, the thickness of the compound layer could be approximately expressed as a power function of the annealing time. For each grain, the layer growth was associated with an increase in the height, and the grain growth was relevant to increases in the size of the basal-plane. The exponent for layer growth decreased almost linearly with increasing exponent for grain growth.

Numerical Analysis for Kinetics of Reactive Diffusion Controlled by Boundary and Volume Diffusion in a Hypothetical Binary System. A.Furuto, M.Kajihara: Materials Transactions, 2008, 49[2], 294-303