Implications of the interface shape on steady-state dendritic crystal growth

Abstract

Experimental results obtained as part of a series of experiments on dendritic growth in microgravity, the isothermal dendritic growth experiment (IDGE), indicate that Ivantsov's transport solution to the dendrite problem is valid to first order. The data reveal a Péclet (Pe) number vs. supercooling relationship that is both systematically lower than expected, and exhibits larger scatter than is accounted for by the uncertainties of the individual data points. A range of explanations have been offered, including residual convection, far-field chamber effects, and dendrite self-interaction. Although some of these explain certain features of the experimental data, quantitative evidence remains lacking concerning the cause of the two issues mentioned above. This investigation examines the dendritic growth data in the context of how the actual shape of the dendrite tip and its trailing side-branch structure may affect the transport process. The method of moving heat sources is used to describe the diffusive thermal transport processes around a crystalline body of revolution growing into its quiescent melt at a constant rate. Results indicate that when Ivantsov's assumed paraboloidal tip shape is modified to better reflect the actual observed tip shape, enhanced agreement can be obtained between the model and the experimental data. Additionally, these results support earlier work by Schaefer (J. Crystal Growth 43 (1978) 17) in predicting that under the conditions of the IDGE experiment, the side-branch region of a dendrite can contribute significantly to the thermal field at the tip. This suggests that the scatter in the IDGE data can be explained by stochastic variations in this influential side-branch structure. With these observations in hand, it is reasonable to claim that the basic transport solution describing dendritic growth is correct, provided adequate account has been taken of details such as container wall effects and dendrite self-interaction. Until now, these conclusions have not been completely supported by quantitative evidence.