K. Toh et H. Ozoe, DOPANT CONCENTRATION PROFILE IN A CZOCHRALSKI FLOW OF LIQUID-METAL INA VERTICAL OR A HORIZONTAL MAGNETIC-FIELD, Journal of crystal growth, 130(3-4), 1993, pp. 645-656
Dopant concentration profiles are obtained for a Czochralski flow of l
iquid metal in a static crucible under either an axisymmetric vertical
magnetic field or a horizontal uniform magnetic field. The latter mag
netic field inevitably requires fully three-dimensional cylindrical co
ordinate model equations, which are successfully solved for the repres
entative parameters Gr = 10(7), Pr = 0.01, Re = 1620 and Ha less-than-
or-equal-to 1000. Asymmetric concentration profiles are obtained. The
average heat flux decreased with the Hartmann number. The circumferent
ial rotational direction was found to be reversed in a lower regime ag
ainst that of a top rotating crystal rod in a strong lateral magnetic
field. In a vertical magnetic field, the concentration profile approac
hed the pure diffusion state.