On the growth of dendritic needles from a supercooled melt

A model of dendrite growth in deeply undercooled pure substances is developed. The dendrite growth velocities and the tip radii are determined theoretically using the analytical solution of the heat diffusion equation, the recently developed theory of the thermally activated phase transition processes, based on the classical Turnbull equation, and the maximal growth velocity principle. The application of the model developed here to a concrete pure substance provides a correct description of the experimental evidence.