Exploring atomic mechanisms of microstructure evolutions in crystals under vacancy super- or undersaturation states by a kinetic amplitude-expanded phase-field-crystal approach

Abstract

Exploring atomic mechanism of microstructure evolutions at long time still remains a great challenge at present. Amplitude-expanded phase field crystal (APFC) model derived from the classical density functional theory is a promising candidate to access this issue. However, it fails to describe dislocation evolutions in systems under super- or undersaturation states because of the lack of necessary rare events, which hampers its applications in the related realms, such as quick quenching, impacting, irradiating and so on. In this work, we find that the necessary rare events in solids are attributed to the kinetic disturbances due to the motion of local lattice elements instead of the traditional Gaussian noise. The kinetic disturbance is evaluated by the long-time-averaged motions of the local lattice elements as well as a general energy variation principle with respect to the virtual variation of the reciprocal lattice vector. The results by these two approaches are mutually verified. It is demonstrated that the APFC model with the kinetic disturbance converges to the mechanical-equilibrium-condition coupled APFC models at the long time limit and reduces to the original one when the high-energy events are forbidden. Further, the kinetic model is rationalized through theoretical analysis combined with numerical testing on the vacancy-mediated dislocation climb. As a practical application of the kinetic model, we explore the long-time annealing behaviors of dislocation loops in irradiated BCC crystals with different vacancy supersaturations. It is the first time that the vacancy-mediated shrinking, 1-D diffusive motion as well as changing habit plane of interstitial dislocation loops, known in experiments, are correctly predicted at atom scale.