We introduce a phase field crystal (PFC) model for particles with n-fold rotational symmetry in two dimensions. Our approach is based on a free energy functional that depends on the reduced one-particle density, the strength of the orientation, and the direction of the orientation, where all these order parameters depend on the position. The functional is constructed such that for particles with axial symmetry (i.e. n = 2) the PFC model for liquid crystals as introduced by Löwen (2010 J. Phys.: Condens. Matter 22 364105) is recovered. We discuss the stability of the functional and explore phases that occur for 1 ⩽ n ⩽ 6. In addition to isotropic, nematic, stripe, and triangular order, we also observe cluster crystals with square, rhombic, honeycomb, and even quasicrystalline symmetry. The n-fold symmetry of the particles corresponds to the one that can be realized for colloids with symmetrically arranged patches. We explain how both, repulsive as well as attractive patches, are described in our model.
Focus on Phase Field Crystal Modelling in Materials Science
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Amplitude phase field crystal simulations of a binary alloy. Top panels: A low angle grain boundary with the magnitude of density fluctuations (A) on the left and the corresponding concentration fluctuations on the right (Cottrell atmospheres). Bottom: Eutectic solidification with the reconstructed density on the left and A on the right.
Guest Editors
Ken Elder Oakland University, USANikolas Provatas McGill University, Canada
Zhi-Feng Huang Wayne State University, USA
Håkan Hallberg Lund University, Sweden
Scope
Phase field crystal (PFC) models have been used to study the physics of materials across multiple scales for almost two decades and have attracted significant interest across different disciplines of science and engineering. A great deal of research has gone into improving the complexity of PFC models far beyond the original model which covered only triangular or bcc crystal structures in single-component systems.
There are currently various PFC models for many crystalline symmetries and for multi-component alloys. There have also been attempts to improve the connection with both atomistic and traditional continuum descriptions of materials and to make the PFC methodology quantitative. Examples of such improvement include recent advances to reduce the small length-scale restriction of PFC through complex amplitude models (APFC) that are coarse grained from PFC models. In addition, various numerical methods have been developed to increase the computational efficiency. A large amount of current research efforts have focused on advancing the PFC to model and simulate solidification and phase transformations in a wide variety of solid and soft material systems.
The purpose of this issue is to highlight the numerous advances in the PFC field, as well as the challenges that remain.
How to submit
Log in to the Author page at https://mc04.manuscriptcentral.com/msmse-iop and start a new submission. In step 1 of the submission, select "Special Issue Article" as the article type, and then "Focus on Phase Field Crystal Modelling in Materials Science" as the special issue.
Important dates and deadlines
Submission deadline: 31st March 2022
Articles will be published in a regular journal issue on a rolling basis as they are accepted. Early submissions are encouraged and can be published early without delaying for other papers in the collection.