Magnetic Damping of Axisymmetric Thermocapillary Convection in Float Zones in Microgravity

Introduction I N the  oating-zone process, surface tension holds a small body of liquid between a melting polycrystalline feed rod and a coaxial growing crystal. On Earth, the size of the single crystal is limited by the balance between the hydrostatic pressure and surface tension of the melt, whereas, in space, the size of the crystals that can be grown is much larger. With the residual acceleration as low as 10– 10 g, buoyant convection is negligible, and thermocapillary convection is dominant and causes two cells of circulation with  ow along the free surface from the hotter middle circumference of the free surface to the colder circumferences at the feed rod and crystal. Numerical simulations of thermocapillary convection in the  oating-zone process were performed by Chang and Wilcox, who reported unsteady thermocapillary convections in their calculations for small temperature differences along the free surface. In commercial applications, temperature differences along the free surface are large and cause unsteady conditions in the melt that produce undesirable dopant striations in the single crystal. Robertson et al. and Croll et al. grew nearly striation-free crystals using a strong, uniform, axial magnetic Ž eld in their  oat zone experiments. Muller and Rupp presented numerical simulations that veriŽ ed these experimental Ž ndings, and they attributed the improved crystal quality to the magnetic suppression of the unsteady thermocapillary convection. Series and Hurle reviewed the beneŽ ts of magnetic Ž elds in semiconductor crystal growth. We present numerical and asymptotic solutions of the thermocapillary convection in  oating zones with a strong axial magnetic Ž eld under axisymmetric conditions. Comparisons of the numerical and asymptotic solutions are made and asymptotic behaviors are discussed.