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

Abstract

On the basis of extended irreversible thermodynamics ͓D. Jou, J. Casas-Vazquez, and G. Lebon, Rep. Prog. Phys. 51, 1005 ͑1988͒; 62, 1035 ͑1999͔͒ 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.

Non-Equilibrium Solidification of Undercooled Metallic Melts

“…Under the conditions of rapid solidification, for the range of growth velocity V < V D (where V D is the atomic diffusive speed in the bulk liquid), the liquidus slope is described by [33]: (12) with k E the partition coefficient of the equilibrium phase diagram. The solute partitioning as a function of growth velocity is described by the non-equilibrium partition coefficient k(V), which becomes dependent on the growth velocity for the case of rapid solidification [34]:…”

Phase-field investigation on the non-equilibrium interface dynamics of rapid alloy solidification

“…To a certain extent, this is opposed to the interpretation of solute trapping phenomena by Aziz. It is similar to the solute drag, but the solute drag phenomena during solidification is not well analyzed or established yet [53,58,92,123,124,125,36,126,127,128,63,129]. .…”

Modeling of Ti-W Solidification Microstructures Under Additive Manufacturing Conditions

“…The driving free energy, G K , is proportional to an interfacial velocity V for the cell. The fundamental equations for these quantities are [87] …”