Diffusion-limited coarsening

Figure 15.2 The mean-field approximation for diffusion-limited coarsening. Each...

Figure 15.5 Final steady-state normalized particle-size distribution for diffusion-limited coarsening.

Work by Voorhees and Glicksman concludes that the classical theory is correct in the limit of zero volume fraction of the coarsening phase and that both the kinetics and the size distributions are significantly dependent on the precipitate volume fraction,

volume fractions, but the rate constant Kp is a monotonically increasing function of , as in Fig. 15.8. 

Diffusion-limited coarsening therefore leads to an increase in the mean particle size with the cube root of time (f / ). 

Source-Limited Coarsening. During source-limited coarsening, the interfaces surrounding the particles behave as poor sources and sinks, and the coarsening rate then depends upon the rate at which the diffusion fluxes between the particles can be created or destroyed (accommodated) at the particle interfaces. In a simple model, the same assumptions can be made about the source action at the particles as those that led to Eq. 13.24. The rate of particle growth can then be written... 

If the coarsening process is limited by the rate at which atoms diffuse through the matrix from the source particles to the sink particles, it can be shown [13] that the mean particle size of the distribution will increase with time according to... 

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