Role of entropy of solution in
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REFERENCES 1. R. Willnecker, D.M. Herlach, and B. Feuerbacher: Appl. Phys. Len., 1990, vol. 56, pp. 324-26. 2. M. Suzuki, T.J. Piccone, M.C. Flemings, and H.D. Brody: Metall. Trans. A, 1991, vol. 22A, pp. 2761-68.
Role of Entropy of Solution in Controlling Eutectic Microstructures P. RAMACHANDRARAO and K.S. DUBEY Variations in the microstructure of eutectic alloys have earlier been explained empirically on the basis of the magnitudes of entropies of solution of the constituent phases and their volume fractions. We demonstrate that these parameters can be thermodynamically related to each other through the equations for the slopes of the liquidus lines on either side of the eutectic and that models for predicting microstructures on the basis of the volume fraction and entropy of solution of a given phase do not have thermodynamic support. It is argued that any observed correlation between microstructure and these parameters should be a consequence of kinetic aspects of the eutectic reaction. Many attempts have been made to predict the microstructures of eutectic alloys and to classify the vast variety of microstructures encountered in these alloys) 1 6] Such studies do not always consider the kinetic aspects of eutectic growth and are often found to be inadequate. Among the many investigations to date, the classification of Taylor et al. TM based on the roughness parameter and its development by Croker e t a / . 16] to include entropy of solution of solid eutectic phases in the liquid, volume fraction of phases, and growth rate has found P. RAMACHANDRARAO, Professor, School of Materials Science and Technology, and K.S. DUBEY, Lecturer, Department of Applied Physics, are with the Banaras Hindu University, Varanasi-221 005, India. Manuscript submitted June 21, 1991.
METALLURGICAL TRANSACTIONS A
s o m e f a v o r . [71 In the analysis of Croker et al.,[61 eutectic microstructures are broadly divided into normal and anomalous groups. The phase ( a ) with a higher entropy of solution (AS H ) is expected to control the microstructure, and when the absolute value of this entropy is less than 23 J mo1-1 K -l, normal microstructures (lamellar and rod-like) are found to result while anomalous eutectics with broken lamellar, irregular, quasi-regular, and other complex microstructures obtain at higher values of entropy of solution. At any given rate of growth, R, the volume fraction, ~b, of the phase with the higher entropy of solution enables one to determine the particular microstructure that will arise in either of the groups. Each type of microstructure occupies a characteristic region in the 4, (percent) vs A S ~L plots. Superficially, the parameters AS ~L and 4, do not appear to be related to each other and Croker et al. 161had to justify their use as factors of significance by considering the micromechanisms of growth and the nature of the solid-liquid interface. In this article, we seek to establish a thermodynamic relationship between these parameters and to discuss the implications of the same with respect to eutec
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