Diffusion-controlled dissolution of planar, cylindrical, and spherical precipitates

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Abstract
The results of a theoretical study of diffusion-controlled dissolution of planar, cylindrical, and spherical precipitates are presented. Graphical relationships between the precipitate size and the dissolution time are developed for a constant diffusion coefficient. The validity of various approximate solutions is considered and it is shown that the invariant-interface treatment provides the best approximation. In this development the composition profile is considered independent of the movement of the phase interface. For concentration-dependent diffusion coefficients, the same dissolution curves can be used, but the time axis must be multiplied by De, an effective diffusion coefficient taken from the plot of diffusion coefficient vs composition. All three precipitate shapes have De equal to the interface value of the diffusion coefficient at very high saturations. At low saturations De is equal to ?, the weighted mean coefficient for spherical precipitates, to ?, the first moment of the diffusion coefficient about the matrix composition for planar precipitates, and to (?+?)/2 for cylindrical precipitates. Procedures for determining De at other values of saturation are discussed.