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

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 "rst order. The data reveal a PeH clet (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 o!ered, including residual convection, far-"eld chamber e!ects, 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 a!ect the transport process. The method of moving heat sources is used to describe the di!usive 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 modi"ed to better re#ect 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 signi"cantly to the thermal "eld at the tip. This suggests that the scatter in the IDGE data can be explained by stochastic variations in this in#uential 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 e!ects and dendrite self-interaction. Until now, these conclusions have not been completely supported by quantitative evidence. ( 1999 Elsevier Science B.V. All rights reserved. PACS: 68.70.#w; 68.35.Bs; 81.30.Fb; 61.50.Jr