Phase field study of precipitate growth: Effect of misfit strain and interface curvature

Abstract

We have studied diffusion controlled growth of an isolated, misfitting precipitate in a supersaturated matrix using a phase field model. Treating our simulations as computer experiments, we have critically compared our simulation results with those from Zener-Frank and Laraia-Johnson theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the ZF theory is very good for 1D systems. In 2D systems with interfacial curvature, we still get good agreement between simulations and both ZF and LJ theories, but only for large supersaturations. At small supersaturations, the growth coefficient from our simulations does converge towards that from theory, but a large gap does remain when the simulations end due to overlap of diffusion fields. An interesting finding from the simulations is the less complete realization of the Gibbs-Thomson effect during growth, particularly in more supersaturated alloys. Thus, even at the same precipitate size, the curvature effects are less severe in more supersaturated alloys.

Verifying Larché–Cahn elasticity, a milestone of 20th-century thermodynamics

“…By concatenating the fields of alloy thermochemistry and solid mechanics, the Larché–Cahn theory is one of the key advances in thermodynamics of the 20th century. The approach is embraced by many modern studies of phase transformations by theory and numerical modeling ( 3 – 9 ), and its predictions for the impact of stress on the chemical potential and, thereby, on the driving force for diffusion during lithium insertion are a current topic in the active field of battery research ( 10 – 12 ). The Larché–Cahn theory is also at the heart of an ongoing controversy about the extent of solute enrichment in Cottrell atmospheres and its consequences for stress shielding in dislocation plasticity ( 13 – 18 ).…”

Impact of Particle Arrays on Phase Separation Composition Patterns

“…The greater the quench depth (or χ i j ), smaller the λ sp . Elastic interactions can also affect the compositional history and coarsening kinetics of SDSD microstructure phases that can be simulated, for example, using microelastic classes of phase-field models [64,[86][87][88]. The mechanical behavior of the resulting patterns can be estimated using a finite element [89] or finite volume [90] based analysis of the representative microdomains.…”

Particle-Size-Grouping Model of Precipitation Kinetics in Microalloyed Steels

“…[46] However, these small-scale models are only suitable for fine particles, such as at the nucleation stage. Phase field methods are based on minimization of free energy and have been applied to calculate the interface dynamics and effects such as strain, interface curvature, and diffusivity on growth of an isolated preciptiate in a supersaturated matrix, [47,48] such as M 23 C 6 carbide in steel. [49] Recently, a commerical precpitation-kinetics software package, Matcalc, was developed based on thermodymamic extremum principles, and it was applied to simulate multiphase precipitation kinetics in multicomponent systems, including separate models within the matrix [50,51] and on grain boundaries.…”