In the Burton, Prim and Slichter’s BPS formula, the effective segregation coefficient k_eff  is a function the stagnant film thickness δ.  During the past decades, the shortcomings of the BPS model have been recognized and several new models film-thickness based models have been proposed.  

The film-thickness models are revisited. A new effective segregation coefficient, were Nusselt numbers are used to quantify convection, is presented.  This combined-convection coefficient is presented in dimensionless form, k_CC (Nu_FC , Nu_NC , Pe), where Nu_FC and Nu_NC are Nusselt numbers for forced and natural convection and Pe is Peclet number for convection due to freezing.   In contrast to BPS, the “combined-convection” segregation coefficient k_CC  accounts for both forced and buoyancy-induced convection.  The proposed segregation coefficient is used to recalculate the diffusivity values of impurities in Si.  The presently accepted values have been calculated using the BPS formula (which ignores buoyancy-induced convection), and thus are inflated.

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