MORPHOLOGICAL INSTABILITY IN A FLOAT ZONE

Morphological instability in a crystal sheet, float-zone geometry for which the width and thickness of the sheet are much larger than the height of the liquid zone is examined. The heat transfer across the boundaries of the system is assumed to be large so that the temperature profiles in the melt and solids are identical with the heater profile. A piecewise linear profile, applicable to systems with slow velocities of solidification and for which the thermal diffusivities are larger than the solutal diffusivities, is imposed. The height of the zone is calculated consistent with these assumptions. Linear and weakly nonlinear analyses in the limit of small segregation coefficient determine that for shorter zone configurations the system is less susceptible to long wavelength morphological instabilities. Solute redistribution leading to flatter axial concentration profiles is the proposed mechanism for the increased stability as compared to unidirectional solidification. A nonlinear evolution equation governing the dynamics of the solidification front and which includes surface free energy variation with interfacial concentration is also developed. Bifurcation analysis and numerical simulations of this equation predict transitions from planar to three-dimensional hexagonal node structures or two-dimensional band structures. © 1990.