Theory of layered-structure formation in peritectic systems
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INTRODUCTION
SIGNIFICANT theoretical and experimental studies have been carried out to determine the microstructure formation in single-phase alloy growth. The transitions from planar to cellular to dendritic microstructures at low velocities and the high-velocity transitions from dendritic to microcellular to planar interface have been examined in detail. For alloy compositions in which two phases form, most studies have concentrated on eutectic growth. In this case, the conditions for coupled growth and the variation in microstructural scales with growth rate have been established quantitatively. In contrast, the solidification of two-phase microstructures in peritectic systems has not received detailed quantitative examination. The aim of this article is to develop basic theoretical ideas that dictate the formation of two-phase microstructures in peritectic systems and to quantitatively establish the characteristic lengths of these microstructures. Figure 1 shows schematically the peritectic phase diagram. In order to capture the physics of microstructure formation in peritectic systems, we shall assume linear solidus and liquidus lines so that the problem can be examined analytically. The interesting feature in peritectic systems, which is also the feature that complicates microstructure formation, is the possibility of formation of metastable/3 phase above the peritectic temperature, Tp. This can lead to the formation of a layered structure in which the two phases form alternately parallel to the interface. [~-61 The formation of layered structures has been observed in several peritectic systems. Boettinger IJJ reported the formation of a layered growth in the Sn-Cd system, which was also verified later on by Brody and David. 121 Layered growth has also been observed in Sn-Sb, f3J Zn-Cu, t31 and Ag-Zn L41systems. Boettinger observed layered structure only for alloy compositions within the hypoperitectic region (two-phase range) at high G/V values R. TRIVEDI, Professor, Department of Materials Science and Engineering, and Senior Scientist, A m e s Laboratory of the United States Department of Energy, is with Iowa State University, A m e s , IA 50011. Manuscript submitted July 21, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS A
(G and V are the temperature gradient and interface velocity, respectively). In contrast, Fuh I6] observed layeredstructure formation over a wider composition region. No layered structure was observed in the Pb-Bi system by Brody and David, t21 and they found that initially a phase forms, which then transforms to a/3 phase. Barker and Hellawell tS] carried out several experiments in the Pb-Bi system, and they observed the formation of layered structures in two out of six samples. In contrast, experimental studies by Fuh L61in the Pb-Bi system found that the initial a phase is followed by a finite range of a layered structure, which subsequently transforms to a /3-phase microstructure. There is no clear quantitative understanding as to why these three different types of structures a
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