Abstract
A theory for crystal nucleation and growth with the recalescence front is developed. The theory is based on the saddle-point technique for evaluating a Laplace-type integral as well as the small parameter method for solving the moving boundary heat transfer problem. The theory developed shows the U-shaped behavior of the growth velocity–melt undercooling curve. The ordinary upward branch of this curve is caused by the growth dictated by heat transport and the predominant crystal growth, while the unusual downward branch demonstrates the anomalous behavior caused by the predominant nucleation and attachment kinetics of the growing crystals to the phase interface. Such a U-shaped behavior of the growth velocity–melt undercooling curve is consistent with experimental data carried out on the ground, under reduced gravity during parabolic flights, and in the microgravity conditions onboard the International Space Station [M. Reinartz et al., JOM 74, 2420 (2022); P.K. Galenko et al., Acta Mater. 241, 118384 (2022)].
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