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A comparison of different approaches to enforce lattice symmetry in two‐dimensional crystals
Author(s) -
Backofen Rainer,
Sahlmann Lisa,
Willmann Anna,
Voigt Axel
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000192
Subject(s) - lattice (music) , affine transformation , rotational invariance , symmetry (geometry) , statistical physics , physics , scale invariance , crystal structure , condensed matter physics , mathematics , quantum mechanics , geometry , chemistry , acoustics , crystallography
The phase‐field crystal (PFC) model allows for the resolution of atomic‐scale structures on diffusive time scales. It is based on an approximation of the two‐particle direct correlation function in the free energy, which provides the symmetry of the lattice structure. Various approaches have been proposed to model common lattices. We here only focus on two‐dimensional crystals, review the different approaches and demonstrate that one, which is based on affine linear deformations, violates rotational invariance. The consequences of this physical inconsistency are shown numerically using a pseudospectral algorithm for the higher order equations.