Grain-boundary diffusion modeling in a microstructural material

The paper presents a two-dimensional model of grain-boundary diffusion with consideration for triple junctions. A diffusant is assumed to come from an amorphous film containing an active component. In heating, the diffusant is transferred from the film into the crystalline material, which is composed of the two phases: grain (volume) phase and grain-boundary phase. The material structure is specified explicitly, which allows an investigation of the influence of the phase size and triple junctions on diffusion dynamics. Boundary conditions suggest a perfect contact between the phases. Consideration is given to a temperature dependence of the diffusion coefficient. A variation in temperature with time is specified explicitly. The problem is solved numerically. We plot concentration-time dependences at points of the computational domain as well as the diffusant concentration distribution over the phases to illustrate the effect of grain size on diffusion. The diffusant is found to behave nonmonotonously, accumulating and consuming, at the triple junction during diffusion. The higher the diffusion coefficient ratio between the phases and the smaller the grain, the faster the concentration variation at the triple junction.