Simulation of crystalline pattern formation by the MPFC method

Abstract

Abstract.The Phase Field Crystal model in hyperbolic formulation (modified PFC or MPFC), is investigated as one of the most promising techniques for modeling the formation of crystal patterns. MPFC is a convenient and fundamentally based description linking nano-and meso-scale processes in the evolution of crystal structures. The presented model is a powerful tool for mathematical modeling of the various operations in manufacturing. Among them is the definition of process conditions for the production of metal castings with predetermined properties, the prediction of defects in the crystal structure during casting, the evaluation of quality of special coatings, and others. Our paper presents the structure diagram which was calculated for the one-mode MPFC model and compared to the results of numerical simulation for the fast phase transitions. The diagram is verified by the numerical simulation and also strongly correlates to the previously calculated diagrams. The computations have been performed using software based on the effective parallel computational algorithm.

Correlated noise effect on the structure formation in the phase‐field crystal model

“…But the Langevin dynamics underlying the definition of particles which are described by the PFC density field may give extremely slow dynamics. 34 So the delta-correlated noise source was introduced into the PFC dynamical equation by many groups 2,12,36,37 justified by the fact that the random noise allows the system to jump over any "metastability barrier" in a finite time. 34,38 Another attempt of justification is a phenomenological approach when (⃗ r, t) regarded as a coarse-grained in time density.…”