Dendritic solidification. III - Some further refinements to the model for dendritic growth under an imposed thermal gradient

Some further refinements to a simple model for dendritic solidification in a binary alloy melt under an imposed positive thermal gradient are presented. Two new expressions for the dendrite tip undercooling have been obtained and shown to yield a limiting value of Delta T sub 0 and very small growth rates. Here Delta T sub 0 is the equilibrium solidification range of the alloy. At very large growth rates, all three tip undercooling expressions reach the same limiting value depending on the value of a dimensionless parameter lambda which is related to the effective diffusion distance ahead of the dendrite tip. The predicted tip undercoolings are, however, somewhat lower at intermediate growth rates. An improved calculation for the solute buildup at the dendrite tip due to curvature effects is also included.