Solidification in syntectic and monotectic alloys

We study steady-state solidification along the liquid-liquid interface in a syntectic system by means of a boundary-integral technique. We study the case of small asymmetry of the pattern and extract from the results the scaling relations in terms of the undercooling and the asymmetry parameter. We also investigate monotectic solidification using the phase-field method.

Description

Among the rare materials which exhibit a syntectic point we mention P-Sn, which has relevance for lead-free solders, or U-Pb. In syntectic systems the three-phase equilibrium consists of two liquid phases and one solid phase, which is similar in this sense to the monotectic equilibrium. However, unlike the monotectic system, the syntectic one may exhibit a symmetric phase diagram which drastically simplifies the solidification problem. The physical processes involved below or above the syntectic temperature include diffusion of solutal elements, convection, and gravity effects. However, we are interested here in the solidification along the liquid-liquid interface in a general picture of three-phase equilibrium in binary alloys (eutectic, peritectic, eutectoid, etc.), and we restrict our study to solutal diffusion, which is assumed to take place only in the liquid phases.

*Fig. 1: Steady-state pattern during monotectic solidification, obtained with (a) boundary-integral equations and (b) a phase-field simulation.*

© Claas Hüter, Max-Planck-Institut für Eisenforschung GmbH

*Fig. 1: Steady-state pattern during monotectic solidification, obtained with (a) boundary-integral equations and (b) a phase-field simulation.*

© Claas Hüter, Max-Planck-Institut für Eisenforschung GmbH

Fig. 2: Close-up of the triple junction region for a typical dendritic front propagation in syntectic systems. The solid S grows with velocity v along the metastable liquid-liquid (L1/L2) interface. In the x direction, the triple junction is shifted by a distance a from the asymptotic position of the liquid-liquid interface. The latter adopts at the triple junction an angle with the velocity direction.

© Claas Hüter, Max-Planck-Institut für Eisenforschung GmbH

Fig. 2: Close-up of the triple junction region for a typical dendritic front propagation in syntectic systems. The solid S grows with velocity v along the metastable liquid-liquid (L1/L2) interface. In the x direction, the triple junction is shifted by a distance a from the asymptotic position of the liquid-liquid interface. The latter adopts at the triple junction an angle with the velocity direction.

© Claas Hüter, Max-Planck-Institut für Eisenforschung GmbH

We study the solidification problem in the syntectic system, which is initiated by the syntectic reaction at the liquid-liquid interface, the subsequent transformation occurring as growth of the solid zone along the liquid-liquid interface. Method of choice is the boundary-integral technique, using the framework developed earlier for the solidification of monotectics. This boundary-integral formulation is designed for the modeling of one liquid-liquid and two solid-liquid interfaces. The solidification takes place along the liquid-liquid boundary, and the solid phase appears as a finger-like shape.

In the syntectic system, the liquid-liquid mixture is the metastable state below the syntectic temperature for the whole range of concentrations of the syntectic plateau. This is different from the monotectic phase diagram, where below the monotectic temperature three possible metastable states exist. In this work, to complete the study of the phase transition in the monotectic system, we investigate patterns by the phase-field method which are obtained for the two remaining possible metastable states, i.e., a single liquid phase and a solid-liquid equilibrium.