Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems

Abstract

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. PACS: 61.44.Br, 64.75.Yz, 64.70.Km,

An Adaptive Block Bregman Proximal Gradient Method for Computing Stationary States of Multicomponent Phase-Field Crystal Model

“…There are several multicomponent PFC models to describe the phase behaviors of alloys and soft-matters [2,3,19,24,26,28,36,38,38,39,48]. In this work, we consider the coupledmode Swift-Hohenberg (CMSH) model of multicomponent systems, which extends the classical Swift-Hohenberg model from one length scale to multiple length scales [26,28,47]. The CMSH model allows the study of the formation and relative stability of periodic crystals and quasicrystals.…”

“…The parameters in (2.2) are given in Table 2. The initial configuration of order parameters is chosen as references [27,28] suggest. The stationary quasicrystals, including physical space morphology and Fourier spectra, are given in Fig.…”

Stability of three-dimensional icosahedral quasicrystals in multi-component systems

“…Since the discovery of quasicrystals, a large number of theoretical studies have been carried out to investigate their symmetry, structure characterization physical properties and thermodynamic stability. Current theoretical results demonstrate that the formation and stability of the quasicrystalline phases may be characterized by two or more length-scales interaction potential 18,19,21,[23][24][25][26] .…”

Multiple-scale structures: from Faraday waves to soft-matter quasicrystals

“…Owing to its simplicity and clarity in explaining the stability of the decagonal (10-fold) and dodecagonal (12-fold) quasicrystals that it exhibits, as well as the ease with which one can numerically simulate the dynamical equation that it generates via simple relaxation @ t = ÀF LP =, the LP model has been studied in depth since its original publication and extended in a number of different ways (Wu et al, 2010;Mkhonta et al, 2013;Achim et al, 2014;Jiang & Zhang, 2014;Jiang et al, 2015Jiang et al, , 2016Jiang et al, , 2017Subramanian et al, 2016).…”

“…3 (ii) The generalization to two (or more) interacting densities or order-parameter fields. The use of two coupled fields or two coupled Swift-Hohenberg equations, where each field carries one of the length scales, was considered very early on (Mermin & Troian, 1985;Sachdev & Nelson, 1985;Narasimhan & Ho, 1988;Mu ¨ller, 1994) and has been resumed recently in the context of binary and ternary soft-matter systems (Dotera, 2007;Barkan, 2015;Jiang et al, 2016), with new insight gained from results of the LP and BDL models.…”