Ostwald Ripening in Two Phase Mixtures with Application to Rapid Solidification
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B.H.
Kear, B.C. Giessen,
and M. Cohen, editors
33
OSTWALD RIPENING IN TWO PHASE MIXTURES WITH APPLICATION TO RAPID SOLIDIFICATION P. W. VOORHEES AND M. E. GLICKSMAN Materials Engineering Department, Rensselaer Polytechnic Institute, Troy, New York, USA ABSTRACT Rapid solidification invariably results in fine-scale microstructures with concomitant fine-scale segregation. These microstructures, which are produced relatively far from equilibrium, have large. specific surface energies and tend to coarsen rapidly. Experiments were carried out on highly supercooled bulk specimens of elemental P4 in which the average temperature of rapidly solidified 2-phase mixtures was accurately monitored over time. A continuous rise in temperature toward the bulk melting point is always measured, independent of the volume fraction of solid produced at recalescence. New theoretical work outlined here shows that this temperature rise can be associated with the Ostwald ripening of the as-solidified solid-plusliquid mixture. The new theory permits calculation of coarsening rates after recalescence and the distribution of dendritic particle sizes as a function of time. Implications for establishing limiting dendritic particle sizes are discussed. INTRODUCTION Surface energy driven morphological changes are common phenomena in nature. Often termed "Ostwald ripening", or phase coarsening, such processes can, in general, occur in any multiphase mixture in which a large specific interfacial area is present. As a result, coarsening has been observed in many multiphase systems ranging from gas-liquid mixtures such as soap bubbles, to solid-solid mixtures such as fine second-phase particles in alloys. The Ostwald ripening processes occurring in all these systems are accompanied by a decrease in the total interfacial area, and a concomitant increase in the average size of the coarsening phase. Although the fundamental basis of Ostwald ripening is now well understood to be the decrease in total surface free energy, a realistic yet tractable theoretical description of such ripening processes is difficult to formulate. Furthermore, it is also difficult to make accurate, revealing, quantitative measurements on multiphase mixtures which are ripening. These two shortcomings in our present understanding of Ostwald ripening provide the impetus for this work. Of the many types of two-phase systems which undergo Ostwald ripening and deserve detailed investigation, solid-liquid mixtures produced as a result of rapid solidification have received little attention. This is particularly unfortunate because of the well known critical dependence of materials' properties on the as-solidified microstructure. Ostwald ripening undoubtedly occurs during and after rapid solidification because: 1) a large thermodynamic driving force is available for Ostwald ripening as a result of the extremely fine-scale microstructure which often accompanies rapid solidification, and 2) recent experimental evidence provides support for microstructural coarsening during dendritic so
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