Optimization of Intensities and Orientations of Magnets Controlling Melt Flow During Solidification

Abstract

When growing large single crystals from a melt, it is desirable to minimize thermally induced convection effects so that solidification is achieved predominantly by thermal conduction. It is expected that under such conditions any impurities that originate from the walls of the crucible will be less likely to migrate into the mushy region and consequently deposit in the crystal. It is also desirable to achieve a distribution of the dopant in the crystal that is as uniform as possible. A finite volume method and a least-squares spectral finite element method were used to develop accurate computer codes for prediction of solidification from a melt under the influence of externally applied magnetic fields. A hybrid constrained optimization algorithm and a semi-stochastic self-adapting response surface optimizer were then used with these solidification analysis codes to determine the distributions of the magnets that will minimize the convective flow throughout the melt or in desired regions of the melt only.

Acknowledgements

M.J.C. is grateful for the postdoctoral fellowship received from CNPq, a Brazilian council for scientific and technological development, and from University of Texas at Arlington. This work was supported in part by the NSF grant DMS-0073698.