A model for nonclassical nucleation of solid-solid structural phase transformations

Abstract

A new model for homogeneous nucleation of structural phase transformations, which can span the range of nucleation from classical to nonclassical, is presented. This model is extended from the classical nucleation theory by introducing driving-force dependencies into the interfacial free energy, the misfit strain energy, and the nucleus chemical free-energy change in order to capture the nonclassical nucleation phenomena. The driving-force dependencies are determined by matching the asymptotic solutions of the new model for the nucleus size and the nucleation energy barrier to the corresponding asymptotic solutions of the Landau-Ginzburg model for nucleation of solid-state phase transformations in the vicinity of lattice instability. Thus, no additional material parameters other than those of the classical nucleation theory and the Landau-Ginzburg model are required, and nonclassical nucleation behavior can be easily predicted based on the well-developed analytical solutions of the classical nucleation model. A comparison of the new model to the Landau-Ginzburg model for homogeneous nucleation of a dilatational transformation is presented as a benchmark example. An application to homogeneous nucleation of a cubic-to-tetragonal transformation is presented to illustrate the capability of this model. The nonclassical homogeneous nucleation behavior of the experimentally studied fcc → bcc transformation in the Fe-Co system is examined by the new model, which predicts a 20 pct reduction in the critical driving force for homogeneous nucleation.

A micromechanical model of phase boundary movement during solid-solid phase transformations

“…Quantity c=R introduces a``length scale'', and is neglected in this study, since it is mostly of relevance only in the case of nucleation, see e.g [8,9]. Finally, one can formulate a relation…”

“…The question remains, which process is responsible for the generation of a nucleus with the radius R i or, in reality, the midrib of a plate or lens. We leave this question to the studies [8,9], which investigated the nucleation problem applying a Helmholtz free-energy function, supplemented by a strain-gradient term to bridge the gap to atomistic dimensions. Since the study dealt with a spherically symmetric con®guration, the accommodation of the transformation shear is not included in their approach.…”

Landau modeling of dynamical nucleation of martensite at grain boundaries under local stress

“…They denominated this type of nucleation as 'localized soft mode'. Later, the initial concept of heterogeneous dynamical nucleation was further consolidated with the efforts of Cao [40][41], Reid [36,[43][44][45], Chu [47], van Zyl [48][49] and Gröger [50] et al Based on the dynamical twinning [37], Reid et al [43] extensively analyzed the dynamical nucleation with a predefined local strain field (as an analog of heterogeneous nucleus) along with generalized boundary conditions. Their results demonstrated that the variation of morphology in MT, e.g.…”

Phase-Field Modeling of Nucleation in Solid-State Phase Transformations

“…Roy et al 18 examined the effect of spatially nonlocal interactions on the critical nucleus profile and nucleation rate employing the phase-field approach. Chu et al 19 developed a model to study the nonclassical nucleation behavior during structural transformations by introducing driving force dependencies into the interfacial energy, misfit strain energy, and nucleus chemical free energy change.…”