Growth from the Melt. III. Dendritic Growth

Abstract

A mathematical treatment of steady-state dendritic growth from pure and alloy liquids has been developed for isothermal and nonisothermal dendrites. The velocity of dendritic growth, dendrite size, dendrite direction, and the alloy content of the dendrite have been calculated as a function of the bath supercooling, the alloy content of the bulk liquid, and the atomic kinetics of the material. To specify the problem completely it was necessary to choose some ``optimization'' condition. We have chosen the condition of ``maximum velocity.'' Comparison of the theoretical predictions with experimental data for pure nickel, tin, and ice, and for KCl and acetic acid solutions have been made. Satisfactory agreement with experiment was found using the atomic mechanism of ``uniform interface advance.''