Use of microgravity to interpret dendritic growth kinetics at small supercoolings

The Isothermal Dendritic Growth Experiment (IDGE), first performed in low-earth orbit in March of 1994 showed variation in the growth data beyond that due to measurement uncertainties, and a significant deviation from predictions of diffusive transport theory with boundary conditions at infinity. Recently, two models described in the J. Crystal Growth suggested modifications from the Ivantsov model to describe the heat transfer of a dendrite growing into a supercooled melt. One model, by Sekerka et al. [J. Crystal Growth 154 (1995) 370], describes how convection resulting from the residual micro-accelerations present on orbit could enhance the heat transfer. Another, by Pines et al. [J. Crystal Growth 167 (1996) 383], describes the observed differences as a thermal boundary layer effect arising from the proximity of the growth chamber wall to the dendrite. Recent in-situ telemetry of dendrite images received during the second flight of the IDGE in March 1996 showed no correlation between the variations in the crystal growth velocities and the quasi-static microgravity environment. 1. I n t r o d u c t i o n Dendritic growth is commonly observed in casting and welding whenever metals and alloys solidify under small thermal or concentration gradients. The complex pattern that evolves from simple starting conditions can ultimately determine the microstructure and properties of the material. Even after completing solidification and further processing, the initial dendritic microstructure continues to influence a material 's physical properties. Thus, *Corresponding author. Fax: + 1 518 276 8554; e-mail: [email protected]. understanding and control of dendritic growth processes have great practical importance. The Isothermal Dendritic Growth Experiment ( IDGE) was designed to measure the kinetics and morphology of isolated dendrites growing from a pure supercooled melt under terrestrial and microgravity conditions [1]. The observation of dendrites growing from the melt during space flight permitted a fundamental test of theory by dramatically reducing gravity-driven convection and allowing kinetic observation of growing crystals. Results from the I D G E on the second United States Microgravity Payload (USMP-2) in March 1994, clearly showed an influence at low supercoolings not described by the standard Ivantsov conduction model [2, 3]. This paper discusses dendritic 0022-0248/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved PII S0022-0248(96)0 1 064-0 L.A. Tennenhouse et al. / Journal o f Cr).,stal Growth 174 (1997) 82 89 83 growth at low supercoolings in microgravity with regard to two recent models that purport to explain the deviations in microgravity from the transport model by Ivantsov. Additionally, initial data from USMP-3 are used to examine these models further. 2. Background and initial analysis Dendritic growth in a pure supercooled melt is controlled by the transport of latent heat away from the solid-melt interface into the cooler supercooled liquid phase. The heat transfer problem associated with dendritic growth was first solved by Ivantsov [4] for steady-state growth driven by thermal conduction. Ivantsovs solution can be expressed as the characteristic equation 0 = Pe exp (Pe)El(Pe), (1) where O is the Stefan number, or dimensionless supercooling, Pe is the growth P~clet number defined as VR/2~, ~ is the thermal diffusivity of the melt, V and R are the steady-state dendrite speed and dendritic tip radius, and E~(x) is the first exponential integral function. The lvantsov solution does not specify a unique dynamic operating state, only the allowable combinations of velocity and length scale that satisfy the steady-state energy equation, expressed here by the P+clet number. In practice, a given supercooling generates dendrites exhibiting a unique tip velocity and radius. According to theory [5], the velocity and tip radius scale according to a scaling relationship,