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

•New model for diffusion-controlled reactions using the extended volume concept.•α = {exp(−2αext) − 1}/(2αext) + 1, where αext = (kt)n, α is fraction transformed, t is the time.•Model fits well to extensive range of data, with reaction exponent n consistent with theory.

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, α, and the extended volume fraction, αext, as: α={exp(−2αext)−1}/(2αext)+1α={exp(−2αext)−1}/(2αext)+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.