A Phase-Field Model for the Diffusive Melting of Isolated Dendritic Fragments
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FOLLOWING the recent publication of a series of papers[1–3] relating to the cyclic melting of material as part of the Isothermal Dendrite Growth Experiment (IDGE) there has been a resurgence of interest in the melting of dendritic crystal fragments. Three IDGE experiments were flown[4–6] in the cargo bay of the space shuttle in order to study the dendritic solidification of the plastic crystals succinonitrile (SCN) and pivalic anhydride (PVA) in the very stable, low gravity environment provided by this platform. Therefore, unlike terrestrial melting experiments in which the fragments experience sedimentation due to the density difference between the solid and liquid phases, the dendritic fragments observed during the melting phase of the IDGE remained stationary within their parent melt. The consequent elimination of Stoke’s flow means that the heat transfer between the crystal and the melt can, to a very high degree of precision, be regarded as purely diffusive. During the IDGE experiments the SCN (IDGE-1 and 2) or PVA (IDGE-3) test substances were brought to a uniform undercooling at which they were held to within ±0.002 K (227.98 C) prior to the nucleation of crystallization. Following nucleation an array of dendritic crystals would propagate into the melt, the growth of which could be observed and photographically recorded through the transparent SCN or PVA melt. The results thus obtained have provided an invaluable data set against which theories of dendritic growth have been tested, including verification of the Ivantsov relationship[7] between undercooling and growth Peclet number[8] and that the radius selection eigenvalue, r*, is not constant but varies with undercooling.[9] Once the ANDREW M. MULLIS, Professor of Solidification Processing, is with the Institute for Materials Research, University of Leeds, Leeds LS2-9JT, U.K. Contact e-mail: [email protected] Manuscript submitted March 20, 2013. Article published online March 18, 2014 METALLURGICAL AND MATERIALS TRANSACTIONS A
growth phase was complete the temperature was raised in order to remelt the dendritic mush so that the cycle could be repeated. As the focus of the experiment was the solidification stage of the process, not the subsequent remelting, the remelting phase was much less carefully controlled and less well recorded. Despite this, during the final IDGE experiment video data of around 100 melting cycles in PVA was captured at 30 fps. It is the analysis[1–3] of these data that has stimulated the renewed interest in the melting of dendritic fragments. The quantitative analysis of the melting of dendritic fragments conducted by Glicksman and coworkers[1–3] was generally restricted to the later stages of the melting cycle, wherein the complex interpenetrating array of side-branches can be reduced to a series of isolated crystals. Moreover, the almost complete melting back of secondary and tertiary arms gives rise to fragments, each of which can be approximated closely as a figure of revolution with an elliptic cross-section. These ellipsoidal
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