Ostwald Ripening and Relaxation in Dendritic Structures

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I.

INTRODUCTION

C A S T microstructures develop from a succession of disparate processes, such as primary nucleation, dendritic growth of the pro-eutectic phase, nucleation and cooperative growth of secondary and tertiary phases, and finally, processes such as precipitation and solid-state diffusion. An important phenomenon, often occurring in parallel with these processes and which has received only scant attention, is dendritic relaxation m also known as dendritic coarsening or ripening. Coarsening occurs typically during and immediately following dendritic growth, as for example within the equiaxed zone of a casting or within the mushy zone of directionally solidified melts, such as within the columnar zone of a casting. The chief requirement for the occurrence of dendritic coarsening is the presence of interdendritic liquid, which permits relatively rapid redistribution of matter within the two-phase mixture. Interdendritic liquid is copiously present when the cast alloy is at temperatures between the solidus and liquidus, although in general the last liquid to freeze interdendritically will actually persist below the liquidus temperature of the average alloy composition to the much lower eutectic, monotectic, or peritectic isotherm. It is now recognized that cast microstructures display microsegregation patterns which are distinctly different from that of nascent (growing) dendrites. Early observations of dendritic structure were carried out by Michael and Bever, ~ Bardes and Flemings, 2 and especially by Kattamis et al. ,3 who clearly established that secondary dendrite ann spacings are determined largely by coarsening processes which depend on the total time over which the solid and liquid coexisted during solidification. The purpose of this M. E. GLICKSMAN is Chairman, Materials Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12181. P. W. VOORHEES is with National Bureau of Standards, Metal Science and Standards Division, Mat. A-153, Gaithersburg, MD 20760. This paper is based on a presentation made at the symposium "Establishment of Microstructural Spacing during Dendritic and Cooperative Growth" held at the annual meeting of the AIME in Atlanta, Georgia on March 7, 1983 under the joint sponsorship of the ASM-MSD Phase Transformations Committee and the TMS-AIME Solidification Committee. METALLURGICALTRANSACTIONS A

paper is to review some of the fundamental aspects of dendrite formation, especially regarding factors that establish the size scale of their morphology, and their subsequent relaxation processes. The scaling laws which determine dendritic tip and branching dimensions are based on a series of investigations in which the kinetics and morphology were carefully measured in well characterized model systems? '5'6 In addition, a body of theory is accumulating which clarifies the roles of transport and morphological stability in setting the initial size scales of dendritic structures .7,8,9 The major mechanism of subsequent dendritic coarsening will be shown to be akin to Ostwald r

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