2-DIMENSIONAL ANALYSIS ON SOLUTE SEGREGATION IN CRYSTAL-GROWTH FROM MELT .1. SOLUTION AT CRYSTAL MELT INTERFACE/

The classical one-dimensional solute segregation theory of BPS is exte nded to two dimensions, i.e., axial as well as radial dimensions. By s olving the two-dimensional boundary value problem at steady state, an analytical expression of solute concentration distribution near crysta l/melt interface is approximated. The new effective segregation coeffi cient is consequently derived as k(e) = k(eBPS) - (k(eBPS) - k(0))(r/R (c))(lambda beta), which decreases with the relative radial distance r /R(c) as compared to the constant k(eBPS) from the one-dimensional BPS theory. The rate of decrease depends on the power factor lambda/beta = lambda D(L)R(c)/U delta(2). Since it relates the solute segregation with the lateral flow strength U and the crystal radius R(c), the new model overcomes the weaknesses of the BPS model and gives explanations on both normal and lateral solute segregation phenomena.