A new model for diffusion-controlled precipitation reactions using the extended volume concept

In this work a new model for diffusion-controlled precipitation reactions is derived, analysed and tested against a wide range of data. The model incorporates elements of the extended volume concept and combines this with a new treatment of soft impingement of diffusion fields. The model derivation involves an integration over iso-concentration regions in the parent phase in the extended volume, which leads to a single analytical equation describing the relation the fraction transformed, a, and the extended volume fraction, alpha(ext), as: alpha = lexp(-2 alpha(ext)) -1}/(2 alpha(ext)) + 1. The model is compared to a range of new and old data on diffusion-controlled reactions including precipitation reactions and exsolution reactions, showing a very good performance, outperforming classical and recent models. The model allows new interpretation of existing data which, for the first time, show a consistent analysis, in which Avrami constants, n, equal values that are always consistent with transformation theory. (C) 2014 Elsevier B.V. All rights reserved.