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The solid-liquid interface shape during growth from the melt has been determined for pure materials in the vicinity of external and internal surfaces; both the cases of isotropy and anisotropy of solid-liquid interfacial energy have been considered. From these considerations it is possible to determine some effects associated with interface and external surface anisotropy. For example, a preferred direction of growth, a surface layer phenomenon and stray-crystal formation during seeding and normal crystal growth may arise as a result of the solid-liquid interface configuration.

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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.''