Macroscopic Interface Shape During Solidification

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Abstract
Steady-state heat transfer considerations have been used to determine the macroscopic solid-liquid interface shape in solidification processes such as floating zone melting and crystal pulling. It was found by means of computer solutions that the Biot number haR/k, is the prime determinant of the shape of the interface. As the Biot number increases, the interface becomes increasingly concave into the solid. A uniform heat input model was formulated which gives analytical results close to the computer results. A one-dimensional analysis showed that the fractional error in the position of the isotherms caused by ignoring the heat carried by the motion of the crystal is approximately Vρcp−R/8hak. The effect of various heat transfer parameters on the dislocation generation caused by thermal stresses was also predicted and found to compare fairly well with experimental results.

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