A nucleation algorithm for the coupled conserved–nonconserved phase field model

Abstract

This paper presents a refinement to the existing nucleation algorithm for a coupled conserved–nonconserved phase field model. In the new method, which offers greater ease of implementation as compared to the existing approach, only the nonconserved order parameter is modified to seed supercritical nuclei (thus termed order-parameter-only seeding). The order-parameter-only seeding method naturally satisfies the conservation law for the conserved order parameter. In addition, the implementation within a finite element framework is described. The evolution of a single nucleus is examined to ensure that the precipitate growth kinetics are not affected by the seeding method. We find that, after a brief initial transient period, order-parameter-only nucleation yields similar precipitate growth characteristics to that of the existing model. The kinetics of a phase transformation exhibiting concurrent nucleation and growth is analyzed in the form of the Avrami equation, and a statistical analysis is performed to determine if mesh and/or time adaptivity affects the simulation results. The statistical analysis indicates that the nucleation algorithm is amenable to adaptive meshing and adaptive time stepping.