Grain growth diffusion-controlled solution

Another assumption concerns the rate controlling species. In the LSW theory, the species that controls the grain growth is the solute in the matrix. For compounds, however, the controlling species may vary. Maintenance of the correct chemical composition of the grains also requires a flux coupling of the species in the matrix. This composition constraint can be met by an effective diffusion coefficient as in the case of the diffusion in an ionic compound (see Section 13.1). 

Lifshitz and Slezov deduced that in a dispersion of spherical particles in which grain growth is occurring by diffusion-controlled solution precipitation a time-independent size-distribution function is approached asymptot-... 

Figure 4 shows this plot for the transformation when the ferrous and ferric hydroxides were precipitated separately by the quick addition of the sum of 2E ammonia and mixed together subsequently. The plot consists of two straight lines of slopes 1 and 2.5. When 2E ammonia was added to the mixture of ferrous and ferric solutions quickly the slopes were 1 followed by 1.85 when added slowly, the slopes were 1 and 1.82. Slope 1 indicates grain boundary nucleation after saturation. Slopes between 1.5 and 2.5 are indicative of diffusion controlled growth from small dimensions (Hi). Note that the curve for 2E Q seems to begin with a larger slope. 

Fig. 14 Grain boundary precipitate growth showing solute transport path during precipitate growth according to the collector-plate mechanism. Solute B is transported to the a-a grain boundary and then along the boundary to form the P precipitate. Diffusion-controlled precipitate growth results in solute depletion from the a phase along the homophase boundary due to fast boundary transport [44].

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