Extended thermodynamical analysis of a motion of the solid-liquid interface in a rapidly solidifying alloy

On the basis of extended irreversible thermodynamics [D. Jou, J. Casas-Vazquez, and G. Lebon, Rep. Prog. Phys. 51, 1005 (1988); 62, 1035 (1999)] an analysis of the solid-liquid interface motion is presented. In addition to the formalism of the classic irreversible thermodynamics of Onsager and Prigogine, a space of independent thermodynamic variables is extended by introducing the solute diffusion flux in consistency with the extended thermodynamic approach to local nonequilibrium processes. Considering the rapid solidification front motion, when the crystal growth velocity is of the order or even greater than the speed for solute diffusion, a local nonequilibrium at the solid-liquid interface and inside bulk liquid is adopted by the model. Taking into account the solute diffusive speed at the phase interface and the finite speed of solute diffusive propagation in bulk system, the equations for thermodynamical fluxes, conjugated driving forces, the Gibbs free energy change on solidification, and liquidus line slope are derived. A discussion of the outcomes predicted by the present model and a comparative analysis of the model predictions with experimental data are made.