Finding Critical Nucleus in Solid-State Transformations

Based on the phase-field total free energy functional and free-end nudged elastic band (NEB) algorithm, a new methodology is developed for finding the saddle-point nucleus in solid-state transformations. Using cubic fi tetragonal transformations in both two and three dimensions as examples, we show that the activation energy and critical nucleus configuration along the minimum energy path (MEP) can be determined accurately and efficiently using this new approach. When the elastic energy contribution is dominant, the nucleation process is found to be collective with the critical nucleus consisting of two twin-related variants. When the elastic energy contribution is relatively weak, the critical nucleus consists of a single variant, and the polytwinned structure develops during growth through a stress-induced autocatalytic process. A nontrivial two-variant critical nucleus configuration is observed at an intermediate level of the elastic energy contribution. This general method is applicable to any thermally activated process in anisotropic media, including nucleation of stacking faults and dislocation loops, voids and microcracks, and ferroelectric and ferromagnetic domains. It is able to treat nucleation events involving simultaneously displacive and diffusional components, and heterogeneous nucleation near pre-existing lattice defects.