Rapid solidification under local nonequilibrium conditions

Abstract

The effects of local nonequilibrium solute diffusion on a solute concentration field, solute partitioning, interface temperature, and absolute stability limit have been considered. The model incorporates two diffusive speeds, V Db , the bulk-liquid diffusive speed, and V Di , the interface diffusive speed, as the most important parameters governing the solute concentration in the liquid phase and solute partitioning. The analysis of the model predicts a transition from diffusion-controlled solidification to purely thermally controlled regimes, which occurs abruptly when the interface velocity V equals the bulk liquid diffusive speed V Db . The abrupt change in the solidification mechanism is described by the velocity-dependent effective diffusion coefficient D*ϭD(1ϪV 2 /V Db 2 ) and the generalized partition coefficient K*. If VϾV Db , then D*ϭ0 and K*ϭ1. This implies an undistributed diffusion field in the liquid ͑diffusionless solidification͒ and complete solute trapping at VϾV Db . ͓S1063-651X͑97͒08504-8͔

Modeling constrained dendrite growth in rapidly directional solidification

“…an infinite vale. The reason is that for constrained dendrite growth, V max \ V A \\V D holds, implying that the local non-equilibrium effect in the bulk liquid is not so important as that in free dendrite growth [30,31,37,38]. In summary, only local non-equilibrium effect at the interface plays an important role in the constrained dendrite growth.…”

“…(3) and Eq. (7) are respectively the solute trapping model of Sobolev [28][29][30] and Aziz [22] with curvature correction [27]. If V D ?…”

“…The physical parameters are available in Table 1. The temperature dependent C s eq and C l eq are obtained by a polynomial fitting to the phase diagram assessed by Murray [46] and V D is determined following the proposal of Sobolev [30], i.e., V D = 2V DI . The evolution of V CS versus R and V A versus R are also shown in Fig.…”

“…Second, local non-equilibrium effect should be considered both at the interface and in the bulk liquid. The diffusion velocity in the bulk liquid V D should be a finite value but not an infinite one as in the classical diffusion theory [28][29][30][31].…”

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]. .…”