Interfaces and Free Boundaries


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Volume 7, Issue 2, 2005, pp. 199–227
DOI: 10.4171/IFB/121

Published online: 2005-06-30

Sharp-interface model for eutectic alloys. Part I: Concentration dependent surface tension

Wolfgang Dreyer[1] and Barbara A. Wagner[2]

(1) Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
(2) Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

We consider the problem of phase separation in eutectic alloy such as e.g. $SnPb$. For this we derive a phase field model from an atomistic point of view. We find the surface energy to be anisotropic, having in general a nonlinear dependence on concentration. We use matched asymptotic analysis to obtain a corresponding sharp interface model. The resulting expression for the surface tension agrees with that found on the basis of classical thermodynamics for jump conditions at singular interfaces. A boundary integral formulation of the sharp-interface model enables us to numerically describe the motion and deformation of the binary alloy.

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Dreyer Wolfgang, Wagner Barbara: Sharp-interface model for eutectic alloys. Part I: Concentration dependent surface tension. Interfaces Free Bound. 7 (2005), 199-227. doi: 10.4171/IFB/121