Eutectic Growth in Three Dimensions
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Eutectic Growth in Three Dimensions H. WALKER, SHAN LIU, J.H. LEE, and R. TRIVEDI Critical experimental studies have been carried out to examine the stability of eutectic morphology in three-dimensional (3-D) samples under diffusive growth conditions. By directionally solidifying capillary samples of the well-characterized Al-Cu eutectic alloy, it is shown that the observed minimum spacing agrees with the value predicted by the Jackson and Hunt (JH) model, but the range of stable spacing is reduced significantly in three dimensions. The ratio of the maximum to minimum eutectic spacing in three dimensions is found to be only 1.2 compared to the predicted value of 2.0 in two dimensions. The narrow range of stable spacing is shown to be due to the instabilities in the third dimension that forms when the local spacing becomes larger than some critical spacing value, which corresponds to the maximum stable spacing. A new mechanism of lamellar creation in the third dimension is observed in which lamella with a local spacing larger than the critical value becomes unstable and forms a sidewise perturbation that becomes enlarged at the leading front and then propagates parallel to the lamella to create a new lamella. Alternately, an array of sidewise perturbations form, which then coalesce at their leading fronts and then become detached from the parent lamella to form a new lamella. I. INTRODUCTION
EUTECTIC microstructure has been studied extensively for both scientific and technological reasons. It is a classic example of the spontaneous two-phase pattern formation in nature, and has important applications as in-situ grown composite materials. Over the years, the status of eutectic growth has been reviewed by several authors.[1,2,3] The theoretical model of coupled growth was first proposed by Hillert[4] for an alloy of eutectoid composition, and a more general model for eutectic growth was developed by Jackson and Hunt (JH)[5] for eutectic growth in eutectic as well as off-eutectic alloy compositions. The results of these models were examined to obtain relationships between eutectic spacing, interface undercooling and growth rate. However, for directional solidification, the diffusion-capillarity model gives a continuous spectrum of solutions for given growth conditions, with interface undercooling exhibiting a minimum with respect to eutectic spacing. The key question that has still remained unsolved is the selection of a band of stable spacing from these infinite solutions. On a suggestion by Cahn, JH considered that all spacing below that corresponding to the minimum undercooling (l , lm) would be unstable with respect to lamella elimination. Subsequently, Langer[6] quantitatively established this lower stability limit under the assumption that the lamellae grow normal to the interface. Karma and Sarkissian[3] relaxed H. WALKER, formerly Graduate Student, Department of Materials Science and Engineering, is Engineer, Bodycote Testing, Inc., Houston, TX 77040-3244. SHAN LIU, Scientist, is with the Division of Materials and E
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