Dendrite growth at the limit of stability: tip radius and spacing

Abstract

In this paper, a general framework is proposed to relate tip radius, interface undercooling and primary arm spacing in alloy dendrite growth. All the growth morphologies (pox, cells, dendrites) developed between the limiting morphology at low and at high velocity: the plane front, are described to a first approximation, using an ellipsoid of revolution. In order to keep the model tractable and the solutions analytic, substantial simplifications are made. It seems nevertheless that this still permits a semi-quantitative prediction of the above-mentioned characteristics for alloy growth in a positive temperature gradient (as in the case of columnar growth or directional solidification).