Numerical Analysis for Kinetics of Reactive Diffusion Controlled by Boundary and Volume Diffusion in a Hypothetical Binary System

Abstract

A hypothetical binary system composed of one intermetallic compound and two primary solid-solution phases has been considered in order to examine the kinetics of the reactive diffusion controlled by boundary and volume diffusion. If a semi-infinite diffusion couple initially consisting of the two primary solid-solution phases with solubility compositions is isothermally annealed at an appropriate temperature, the compound layer will be surely produced at the interface between the primary solid-solution phases. In the primary solid-solution phases, however, there is no diffusional flux. Furthermore, we suppose that the compound layer is composed of a single layer of square-rectangular grains with an identical dimension. Here, the square basal-plane is parallel to the interface, and hence the height is equal to the thickness of the compound layer. Under such conditions, the growth behavior of the compound layer has been analyzed numerically. In order to simplify the analysis, the following assumptions have been adopted for the compound layer: there is no grain boundary segregation; and volume and boundary diffusion takes place along the direction perpendicular to the interface. When the size of the basal-plane remains constant independently of the annealing time, the thickness of the compound layer is proportional to the square root of the annealing time. In contrast, the growth of the compound layer takes place in complicated manners, if the size of the basal-plane increases in proportion to a power function of the annealing time. Nevertheless, around a certain critical annealing time, the thickness of the compound layer is approximately expressed as a power function of the annealing time. For each grain, the layer growth is associated with increase in the height, and the grain growth is relevant to increase in the size of the basal-plane. The exponent for the layer growth almost linearly decreases with increasing exponent for the grain growth.