2015/09/06 by Kai Jiang, Jiajun Tong, Pingwen Zhang
Materials Science · Physics and Astronomy · #Energy minimization #Microstructure and mechanical properties #Minification #Phase (matter) #Projection (relational algebra) #Projection method #Quasicrystal #Quasicrystal Structures and Properties #Quasiperiodic function #Solidification and crystal growth phenomena #Stability (learning theory) #cond-mat.soft
paper · pdf · doi:10.4208/cicp.181014.130715a
26 pages, 13 figures; accepted by Communications in Computational Physics
arxiv created 2015/09/06 · openalex publication_date 2016/01/01 · arxiv updated 2016/04/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms. Classic two-mode approximation method and direct numerical minimization are applied to the model. In the latter approach, we apply the projection method to deal with the potentially quasiperiodic ground states. A variable cell method of optimizing the shape and size of higher-dimensional periodic cell is developed to minimize the free energy with respect to the order parameters. Based on the developed numerical methods, we rediscover decagonal and dodecagonal quasicrystalline phases, and find diverse periodic phases and complex modulated phases. Furthermore, phase diagrams are obtained in various phase spaces by comparing the free energies of different candidate structures. It does show not only the important roles of system parameters, but also the effect of optimizing computational domain. In particular, the optimization of computational cell allows us to capture the ground states and phase behavior with higher fidelity. We also make some discussions on our results and show the potential of applying our numerical methods to a larger class of mean-field free energy functionals.