Effect of volume fraction on particle coarsening: theoretical considerations. Topical report
The theory of diffusion-controlled particle coarsening developed by Lifshitz and Slyozov and Wagner (LSW) is modified to take into account the volume fraction, phi, of precipitate. The modification is based on the supposition that the diffusion of solute to a growing particle (or from a dissolving particle) will depend on a distance characteristic of the spatial distribution of the particles in the polydisperse assembly. The characteristic distance chosen for computational purposes is related to the mean free path between a particle and its nearest neighbor. While this is not the best choice, it serves to make the problem tractable analytically. Steady-state diffusion under conditions of spherical symmetry is also assumed. The modified LSW (MLSW) theory predicts that while the basic t/sup 1/3/ kinetics of the LSW theory are maintained, the coarsening rate increases with increasing volume fraction, even at very small values of phi. According to the MLSW theory, the theoretical distribution of particle sizes broadens rapidly at small values of phi. In the limit phi = 1 the theoretical particle size distribution becomes identical to that derived by Wagner for the case of interface controlled coarsening. All the results of the LSW theory are recovered from the MLSW theory in the limit of zero volume fraction. The results of the MLSW theory are in very good quantitative agreement with the available data on the coarsening rates of Co precipitates in Cu-Co alloys. The apparent absence of volume fraction effects on particle coarsening in a number of other alloys systems is discussed in light of the assumptions involved in both the LSW and MLSW theories.
- Research Organization:
- California Univ., Los Angeles (USA). School of Engineering and Applied Science
- DOE Contract Number:
- AT03-76ER70172
- OSTI ID:
- 6470001
- Report Number(s):
- UCLA-34P172-2; ON: DE81027376
- Country of Publication:
- United States
- Language:
- English
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