We derive a phase field method for computing rigorously the nucleation rate and the incubation time from the sole knowledge of the free energy of the system in the metastable regime. Our theoretical results are assessed against experimental data relative to demixing of an iron-chromium alloy. Our work clarifies the notions of nucleation rate and incubation time extensively used in classical nucleation theory (CNT) processes in solids. Our work thus emerges as an alternative to CNT but of more general applicability, and enables us to model the nucleation process across the whole range of condition encountered in first order phase transitions, an aspect in which CNT fails.

• Received 13 February 2023
• Revised 11 April 2023
• Accepted 16 August 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.117101