Dendritic solidification: The role of heat conduction in the solid

Ivantsov’s equation of dendritic solidification under a given supercooling ΔT provides the product of the growth velocity V and the tip radius of curvature R, but not V and R separately. However, experimentally, it is observed that both V and R are uniquely determined by ΔT. Assumptions, such as maximum velocity criterion, marginal stability criterion and solvability criterion, have been proposed to deal with the paradox, but it has been repeatedly pointed out that another fundamental equation must be missing from the treatment, since Ivantsov’s single equation includes two unknowns. Here, such a first-principles equation is proposed based on the dissipation and heat transfer of interfacial energy within the solid. It is demonstrated that combining this previously unrecognized mechanism with the conventional heat transfer to the liquid, provides a dendrite growth selection law in harmony with experimental data.