Interface kinetics and solidification of alloys: A discussion of some phenomenological models

Achieving realistic interface kinetics in phase-field models with a diffusional contrast

Phase-field models are powerful tools to tackle free-boundary problems. For phase transformations involving diffusion, the evolution of the nonconserved phase field is coupled to the evolution of the conserved diffusion field. Introducing the kinetic cross coupling between these two fields [E. A. Brener and G. Boussinot, Phys. Rev. E 86, 060601(R) (2012)], we solve the long-standing problem of a realistic description of interface kinetics when a diffusional contrast between the phases is taken into account. Using the case of the solidification of a pure substance, we show how to eliminate the temperature jump at the interface and to recover full equilibrium boundary conditions. We confirm our results by numerical simulations.

Relation between bulk and interface descriptions of alloy solidification

From a simple bulk model for the one-dimensional steady-state solidification of a dilute binary alloy we derive the corresponding interface description. Our derivation leads to exact expressions for the fluxes and forces at the interface and for the set of Onsager coefficients. The constitutive equations, connecting the crystallization and diffusion fluxes and forces, decouple in the low-velocity limit and there generate an occasionally negative, but nevertheless thermodynamically consistent friction coefficient. We, moreover, discover a continuous symmetry, which is independent of our model and allows to decouple the constitutive equations for the two components of the alloy for arbitrary growth velocities.

Kinetic cross coupling between nonconserved and conserved fields in phase field models

We present a phase field model for isothermal transformations of two-component alloys that includes Onsager kinetic cross coupling between the nonconserved phase field and the conserved concentration field ø C. We also provide the reduction of the phase field model to the corresponding macroscopic description of the free boundary problem. The reduction is given in a general form. Additionally we use an explicit example of a phase field model and check that the reduced macroscopic description, in the range of its applicability, is in excellent agreement with direct phase field simulations. The relevance of the newly introduced terms to solute trapping is also discussed.

Onsager approach to the one-dimensional solidification problem and its relation to the phase-field description

We give a general phenomenological description of the steady-state 1D front propagation problem in two cases: the solidification of a pure material and the isothermal solidification of two-component dilute alloys. The solidification of a pure material is controlled by the heat transport in the bulk and the interface kinetics. The isothermal solidification of two-component alloys is controlled by the diffusion in the bulk and the interface kinetics. We find that the condition of positive-definiteness of the symmetric Onsager matrix of interface kinetic coefficients still allows an arbitrary sign of the slope of the velocity-concentration line near the solidus in the alloy problem or of the velocity-temperature line in the case of solidification of a pure material. This result offers a very simple and elegant way to describe the interesting phenomenon of a possible non-single-value behavior of velocity versus concentration that has previously been discussed by different approaches. We also discuss the relation of this Onsager approach to the thin-interface limit of the phase-field description.