# American Institute of Mathematical Sciences

November  2006, 15(4): 1035-1047. doi: 10.3934/dcds.2006.15.1035

## Phase-field modelling of nonequilibrium partitioning during rapid solidification in a non-dilute binary alloy

 1 Karlsruhe University of Applied Sciences, Department of Computer Science, Moltkestrasse 30, D-76133 Karlsruhe, Germany, Germany

Received  June 2005 Revised  January 2006 Published  May 2006

Rapid solidification of a non-dilute binary alloy is studied using a phase-field model with a general formulation for different diffusion coefficients of the two alloy components. For high solidification velocities, we observe the effect of solute trapping in our simulations leading to the incorporation of solute into the growing solid at a composition significantly different from the predicted equilibrium value according to the phase diagram. The partition coefficient tends to unity and the concentration change across the interface progressively reduces as the solidification rate increases. For non-dilute binary alloys with a value of the partition coefficient close to unity, analytical solutions of the phase-field and of the concentration profiles are found in terms of power series expansions taking into account different diffusion coefficients of the alloy components. A new relation for the velocity dependence of the nonequilibrium partition coefficient $k(V)$ is derived and compared with predictions of continuous growth model by Aziz and Kaplan [1]. As a major result for applications, we obtain a steeper profile of the nonequilibrium partition coefficient in the rapid solidification regime for $V/V_D>1$ than previous sharp and diffuse interface models which is in better accordance with experimental measurements (e.g. [2]).
Citation: Denis Danilov, Britta Nestler. Phase-field modelling of nonequilibrium partitioning during rapid solidification in a non-dilute binary alloy. Discrete & Continuous Dynamical Systems - A, 2006, 15 (4) : 1035-1047. doi: 10.3934/dcds.2006.15.1035
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