Main Approximations of the LSW Approach

2) The mean-field approximation is applied, that is, the supersaturation of the parent phase A = (C — in the vicinity of any precipitate is taken as one and the same, common for the whole system without considering correlations between the size and local supersaturation. 

3) The steady state approximation is employed. This means that the Laplace equation V C S 0 is solved rather than the diffusion equation (second Pick s 

Here a for the case of precipitation of an almost pure element B from a diluted solution of B in A equals 

Taking into account the steady state and Gibbs-Thomson conditions, the growth (or dissolution) rate for a spherical precipitate is determined by the following balance equation at the moving spherical boimdary  

The critical radius increases with time (as supersaturation diminishes), catching up with the growing particles one by one, which then start dissolving (ultimately, the only one must remain in a finite system, yet this falls beyond the statistical theory). 

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