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The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on diffusive timescales by focusing on continuous fields varying on length scales larger than the atomic spacing. Thus, it allows for the simulation of large systems still retaining details of the crystal lattice. Fostered by the applications of this approach, we present here an efficient numerical framework to solve its equations. In particular, we consider a real space approach exploiting the finite element method. An optimized preconditioner is developed in order to improve the convergence of the linear solver. Moreover, a mesh adaptivity criterion based on the local rotation of the polycrystal is used. This results in an unprecedented capability of simulating large, three-dimensional systems including the dynamical description of the microstructures in polycrystalline materials together with their dislocation networks.
Amplitude representations of a binary phase field crystal model are developed for a two dimensional triangular lattice and three dimensional BCC and FCC crystal structures. The relationship between these amplitude equations and the standard phase fie
This work develops a new open source API and software package called textit{SymPhas} for simulations of phase-field, phase-field crystal and reaction-diffusion models, supporting up to three dimensions and an arbitrary number of fields. textit{SymPha
Phase field methods have been widely used to study phase transitions and polarization switching in ferroelectric thin films. In this paper, we develop an efficient numerical scheme for the variational phase field model based on variational forms of t
Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free energy functions using
We address a three-dimensional, coarse-grained description of dislocation networks at grain boundaries between rotated crystals. The so-called amplitude expansion of the phase-field crystal model is exploited with the aid of finite element method cal