Effects of Shear Flow and Anisotropic Kinetics on Crystal Growth

Sam R. Coriell, Metallurgy Division
Bruce T. Murray, ACMD
Geoffrey B. McFadden, ACMD
Alex A. Chernov, USRA and Russian Academy of Sciences

During crystal growth or solidification of a binary alloy from a liquid phase, temperature and/or solute gradients are inherently present. In a gravitational field, these gradients can give rise to fluid flow in the melt. The interaction of fluid flow with the crystal-melt interface plays an important role in determining the properties of the solidified material. Convection in the melt and interface instability may both produce solute inhomogeneities. In the absence of fluid flow, the conditions for the onset of morphological instability are well established. However, the coupling between morphological instability and fluid flow can be complicated; interfacial instabilities depend on temperature and solute gradients which may be strongly influenced by the flow field. The flow field, in turn, may be influenced by the morphology of the interface.

There has been a very successful long-term collaboration between individuals in CAML and MSEL which has resulted in the development of predictive models for a variety of crystal growth techniques from the bulk liquid phase. These models consist of both analytic relations under restrictive simplified cases and relatively sophisticated numerical algorithms to treat the nonlinear behavior under more general conditions. The recent focus of this modeling research addresses the specific concerns associated with crystals that grow with faceted or stepped interfaces. This situation occurs for crystalline materials which have high anisotropy (preferred orientations) in either their surface energy or atomic attachment kinetics.

In the last three years, the effect of anisotropic interface kinetics on interfacial stability has been investigated for three crystal growth configurations and for materials of current practical interest. The dependence of the interface kinetic coefficient on crystallographic orientation is based on the motion and density of steps. As a result of the modeling work, it has been determined that anisotropic kinetics can provide a significant enhancement of interface stability. The growth conditions under which this stability enhancement can be obtained has been quantified as an outcome of this research effort.

[picture of stepped interface]

A recent phase of this research is to investigate more completely the interaction of fluid flow with a stepped crystal-melt interface. The above figure shows schematically a perturbed step bunch and the solute concentration field above the solid/liquid interface for growth from a supersaturated solution. Shear flows along the interface interact strongly with the step motion and cause decreased stability for a flow in the same direction as the step motion and enhanced stability for flows counter to step motion.

[graph of numerical data]

The above figure is a stability map given in terms of the spatial wavenumbers at which the system is neutrally stable as a function of growth velocity for an orientation slope of 0.01 and for shear rates of -0.1, 0.0, 0.0001, 0.001, 0.01, 0.1 and 0.5 for a linear Couette profile. The solid curves are numerical solutions of the complete linear stability equations while the dashed curves are from the analytic approximation which neglects the perturbed flow field. The two solutions are in excellent agreement except at small wavenumbers. The current objective is to quantify flow-interface interactions for a range of processing conditions for solution growth; the extension to more complex physical models and nonlinear interface morphologies will be part of the ongoing research.

Here is a list of recent publications related to this work:

A. A. Chernov, S.R. Coriell, and B.T. Murray, Morphological Stability of a Vicinal Face Induced by Step Flow, Journal of Crystal Growth 141, pp. 405-413, 1993.

S.R. Coriell, B.T. Murray, and A. A. Chernov, Kinetic Self-Stabilization of a Stepped Interface: Binary Alloy Solidification, Journal of Crystal Growth 141, pp. 219-233, 1994.

A. A. Chernov, S.R. Coriell, and B.T. Murray, Kinetic Self-Stabilization of a Stepped Interface: Growth into a Supercooled Melt, Journal of Crystal Growth 149, pp. 120-130, 1995.

S.R. Coriell, B.T. Murray, A. A. Chernov, and G.B. McFadden, Effects of Shear Flow and Anisotropic Kinetics on the Morphological Stability of a Binary Alloy, Met. Matls. Trans 27A, pp. 687-694, 1996.