Phase field crystal simulation of the structure evolution between the hexagonal and square phases at elevated pressures

Abstract

Based on the two-mode phase field crystal (PFC) model and the principle of the common tangent, a two-dimensional PFC phase diagram is established. According to the phase diagram, the parameters for a steady growth of the hexagonal and the square phase are found. Moreover, the nucleation and growth characteristics of the square phase from hexagonal phase under different pressures are simulated by using these parameters. The movements of dislocation core under pressure at different transformation stages are revealed and compared with each other. Finally, by changing the grain orientation, the formation and disappearance of grain boundaries at different angles are simulated and analyzed.

Implementation of the coupled two‐mode phase field crystal model with Cahn–Hilliard for phase‐separation in battery electrode particles

“…As time evolves the square phase grows at the expense of the hexagonal phase as seen in Figure 2(C) at time 600. This phenomenon was previously observed by Shuai et al 38 during their study on hexagonal‐to‐square phase transitions. Finally at time 1200, we see a polycrystalline structure composed only of square lattices with different orientations.…”

“…Such schemes have been already developed to study one‐mode phase field crystal 34,35 with body‐centered cubic (BCC) crystal structure. Work presenting simulations on 2MPFC 36‐38 all use spectral methods to solve the system. In this article, we propose a mixed finite element formulation to solve the 2MPFC system, which is a 10th order parabolic equation, to model face‐centered cubic (FCC) crystals.…”

Three-dimensional phase field simulation for rafting of multiparticle precipitate in elastic inhomogeneous alloy under external stress

“…3, it is seen that the number of precipitated particles has passed through two stages: the number of particles firstly increases steeply from 0 to the maximum in the first stage, and then the number of particles decreases in the second stage but with a slower rate than the first stage. These two stages of rafting phenomenon have been experimentally observed in Al-Cu alloys by Eto et al [29][30]. The authors found that the effects of stress on precipitation direction originated from nucleation stage by two-stage aging process.…”

A comprehensive analysis of three-dimensional normal grain growth of pure iron via multi-phase field simulation

“…For the evolution of complex microstructures, the unique definition of the grain boundary by the phase field equation makes it unnecessary to track the interface all the time, and can complete large-scale simulations while improving efficiency. The phase field method has been successfully applied in many fields such as dendrite growth, rafting process, and the second phase precipitation [10,11]. Zhu [12] has studied the  precipitate microstructure evolution in a nickel based high temperature alloy in 3D phase-field simulation with coupling CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry) database.…”