On the dendritic growth of pure materials

Abstract

The following three theoretical treatments of unconstrained dentritic growth are discussed: (i) The Ivantsov analysis, which assumes the existence of an isothermal liquid-solid interface and concludes that this dendrite body shape must be a paraboloid of revolution; (ii) and (iii) the non-isothermal treatments of both Bolling and Tiller, and Temkin. These latter two works take account of the variation in both curvature and interface attachment kinetics over the entire surface of the dendrite. They also enable one to calculate the velocity and curvature of the dendrite tip by assuming that the tip region can effectively be described as a paraboloid of revolution. It is proposed that Temkin's analysis is sensitive enough to determine the excess solid-liquid surface free energy, λ, and the linear kinetic coefficient for molecular attachment, μ o. Using the best available data for the ice-water system, the Temkin treatment yields 20 ± 2 erg/cm 2 and 16 ± 0.5 cm/sec °C for λ and μ o, respectively. These values are in remarkably good agreement with other experiments and theory.