Numerical analysis for migration of interface between liquid and solid phases during reactive diffusion in the binary Cu–Al system

The kinetics of reactive diffusion was experimentally examined for the binary Cu–Al system using Cu/Al diffusion couples initially consisting of pure Cu and Al in a previous study. The diffusion couple was isothermally annealed at temperatures of T = 973–1073 K. During annealing, compound layers of the β, γ and ɛ phases are formed between the Cu-rich solid (α) and Al-rich liquid (L) phases, and the L/ɛ interface migrates towards the ɛ phase. The migration rate of the L/ɛ interface is much greater than the overall growth rate of the compound layers, and there exists the parabolic relationship between the migration distance and the annealing time. This means that the interdiffusion in the solid phases is negligible and the migration of the interface is controlled by the interdiffusion in the L phase. The parabolic relationship may hold good only in a semi-infinite diffusion couple. Within the experimental annealing times, however, overlap of diffusion field occurs in the L phase, and thus the diffusion couple becomes finite. In order to account for the experimental result, the migration behavior of the L/ɛ interface in the finite Cu/Al diffusion couple was numerically analyzed using a mathematical model. The analysis yields that the parabolic relationship holds good within experimental uncertainty even in a finite diffusion couple on condition that volume diffusion is the rate-controlling process and overlap of diffusion field lightly takes place in each phase.