Phase-field simulation of three-dimensional dendrites: is microscopic solvability theory correct?

Abstract

Dendritic growth theory and experiment are critically examined in the light of recent three-dimensional phase-field simulations of the crystallization of a pure undercooled melt. These simulations make use of a new thin-interface limit of phase-field equations that makes it possible to perform efficient computations in three dimensions with negligible interface kinetics. These computations are applied to perform a quantitative test of microscopic solvability theory, which is reviewed here, and to make contact with low undercooling experiments by exploiting the scaling property of the dendrite growth problem. A good overall agreement is found between the steady-state operating state of the dendrite tip selected dynamically in the simulations and the one predicted by solvability theory over a wide range of crystalline anisotropy. Quantitative differences between solvability predictions and simulations are present at larger anisotropy but reflect the limitation of the axisymmetric approximation presently used to carry out these predictions rather than a conceptual breakdown of this theory. Phase-field simulation results yield an improved agreement with experiment for succinonitrile. A poor agreement however is still obtained for pivalic acid. Possible origins of this disagreement are discussed.