Analysis of nucleation and growth with the model for diffusion-controlled precipitation reactions based on the extended volume concept

Abstract

Recently (Starink, 2014) a new model for diffusion-controlled precipitation reactions based on the extended volume concept was derived. The model leads to an analytical equation describing the relation between the fraction transformed, α, the reaction time, t, and the reaction exponent, n, as:α={exp(-2(k1t)n)-1}/(2(k1t)n)+1 In the present work, new analysis methods are derived which allow determination of the reaction exponent n. The new methods are applied to analysis of nucleation and it is shown that generally during a reaction with growth in 3 dimensions there are only 2 modes: either the nucleation rate in the extended volume is constant or it is negligibly small. A new approach to the interaction of diffusion-controlled growth and nucleation is proposed to rationalise these findings. The exponential decay of the average solute content predicted by the new model is further analysed and compared with a range of experimental data and contrasted with other models. The new model is found to correspond excellently to these solute decay data.