Investigation of microstructural coarsening in Sn-Pb alloys
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I. INTRODUCTION A. Particle Coarsening
PHASE coarsening is the structural change wherein the average size of the particles in a microstructure increases with time. The phenomenon, in general, is also commonly referred to as Ostwald ripening. The reduction in the total interfacial energy of a two-phase system was shown by Ostwald[1] to provide the driving force for coarsening. The process results in an increase in the distance of separation between neighboring particles and in a decrease in the number of particles in the system. The rate of coarsening usually increases rapidly with temperature and is of concern to the design of stable alloys for high-temperature applications. The study of phase-coarsening phenomena is critical to a variety of industrial applications involving two-phase systems, where the dispersed phase controls the behavior of the alloy. For instance, the ripening of second-phase particles in precipitation-hardened alloys results in the loss of strengthening from the precipitates. Liquid-phase sintering, casting, semisolid processing, and spray deposition are just a few examples of processes where the ripening process has important technological implications. The thermodynamic basis of coarsening in alloys is the Thomson–Freundlich solubility relationship.[2] According to this relation, the solute concentration in the matrix adjacent to a particle will increase as the radius of curvature decreases. Thus, the solubility in the matrix in contact with a b particle increases as the radius of the b particle decreases. Hence, concentration gradients will develop in the matrix, which cause the solute to diffuse in the direction of the largest particles and away from the smallest particles. Consequently, SRIDHAR K. KAILASAM, Graduate Student, and ME. GLICKSMAN, John Tod Horton Professor, are with the Materials Science and Chemical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180. S.S. MANI, formerly Senior Engineer with Northrop Grumman Corporation, Pittsburgh, PA 15235, is Senior Staff Member with Sandia National Laboratories, Albuquerque, NM 87185. V.E. FRADKOV is Research Professor, Stamford, CT 06802. Manuscript submitted December 9, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
phase coarsening causes small particles to shrink and large particles to grow. As the flow of solute proceeds, the small particles dissolve to compensate for the decrease in concentration at the their interface. Likewise, the solute migrating toward the larger particles will precipitate at the particles and remove the excess solute arriving as the diffusion flux. This competitive growth and dissolution process will continue, in principle, until the system is finally phase separated. There have been numerous experimental and theoretical attempts over the last few decades to understand the kinetics of coarsening in multiphase systems. However, the complexity arising in real systems often precludes general conclusions. The theoretical models have to incorporate a number of factors such as the volume fraction of t
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