Kinetic equations for concurrent size and shape coarsening by the ledge mechanism
- PDF / 1,560,076 Bytes
- 10 Pages / 597 x 774 pts Page_size
- 43 Downloads / 220 Views
I.
INTRODUCTION
KNOWLEDGE of the microstructural instability of a material is important, since such instabilities can often lead to reductions in the properties of the material. The ability to predict accurately microstructural changes with time is required in order to assess reliably the performance limits of a material in a given application. Precipitate coarsening or Ostwald ripening is a common instability observed in materials which have a dispersion of particles within a matrix, such as in precipitationstrengthened alloys. At elevated temperatures, an increase in the average particle size is observed with time. The most rigorous and commonly used theory to describe this process is due to Lifshitz and Slyosov tl~ and Wagner t21and is generally referred to as the LSW theory of coarsening. This theory predicts the development of a time-independent particle size distribution and a kinetic time law of 1/3 or 1/2 depending on whether the process is volume diffusion-controlled (VDC) or interface reaction-limited (IRL), respectively. In the development of the LSW theory, several assumptions are made. Unfortunately, most of these assumptions are never realized, particularly when both phases involved are solids. First, the theory assumes there to be a negligible volume fraction of particles coarsening in a fluid matrix. In reality, this is not true, and many important alloy systems which are subject to coarsening R.M. AIKIN, Jr., formerly Graduate Student, Michigan Technological University, is Scientist with Martin Marietta Laboratories, Baltimore, MD 21227. S. ELANGOVAN, formerly Graduate Student, University of Utah, is Scientist with Ceramatec, Inc., Salt Lake City, LIT 84119. T.G. ZOCCO, formerly Graduate Student, University of Utah, Salt Lake City, UT, is Staff Member with Los Alamos National Laboratory, Los Alamos, NM 87545. M.R. PLICHTA, Professor, is with the Department of Metallurgical and Materials Engineering, Michigan Technological University, Houghton, MI 49931. This paper is based on a presentation made in the symposium "The Role of Ledges in Phase Transformations" presented as part of the 1989 Fall Meeting of TMS-MSD, October 1-5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL. METALLURGICAL TRANSACTIONS A
have significant precipitate volume fractions. Recently, there has been much work [3-~sl devoted toward understanding and accounting for the effect of high precipitate volume fractions on coarsening kinetics. Second, and probably most important, the LSW theory assumes the particles to be spheres. The inference can be made, therefore, that the boundary energy and atomic processes at the interface, such as attachment or detachment, are isotropic. Furthermore, these spherical particles are naturally at their equilibrium shape, and hence, only the evolution of particle size need be considered during the coarsening process. However, this is not the situation for many precipitate: matrix systems. Because of the speci
Data Loading...
