Phase field calculations of pattern formation in solidification of binary alloys

Wolfram Miller

Institute for Crystal Growth, Group Numerical Modelling, Berlin, Germany

The cellular growth of NiCu and GeSi has been studied. While in the first case we used typical conditions for solidification of metals leading to sturcture of some micrometer in the second case growth velocities and temperature gradients are much smaller. Therefore, structures are much larger (up to mm) and we have to use a modified phase-field model in order make calculations feasable with real material and process parameters. Varying the temperature gradient and the diffusion coeffient for Si in the melt the resulting depth and wave length of the cells have been measured. The variation of the diffusion coeffient was within the limits of values observed experimentally and by computed by MD calculations. We found a linear dependence of the cell depth on the inverse temperature gradient up to a critical concentration difference between top and bottom of the cells.
The influence of a shear flow has been investigated both for NiCu and GeSi. In the latter case, the cells are not only tilted by the flow but the structures (wave length and amplitude) become significantly smaller. They now are of the order as those observed in experiments using Czochralski growth technique, where melt convection is caused by buoyancy forces and crystal plus crucible rotation.

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