WIAS Preprint No. 885, (2003)

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



Authors

  • Dreyer, Wolfgang
  • Wagner, Barbara

2010 Mathematics Subject Classification

  • 74D10 74F05 74F10 77N25

Keywords

  • Matched asymptotics, boundary integral method, numerics

Abstract

We consider the problem of phase separation in eutectic alloy such e.g. SnPb. For this we derive a phase field model from a 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.

Appeared in

  • Interfaces Free Boundaries 7 (2005), pp. 199--227.

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