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Continuous chiral distances for two-dimensional lattices
Matthew J Bright1, Andrew I Cooper1, Vitaliy A Kurlin1
1Computer Science Department and Materials Innovation Factory, University of Liverpool, Liverpool, UK.
Abstract:
Chirality was traditionally considered a binary property of periodic lattices and crystals. However, the classes of two-dimensional lattices modulo rigid motion form a continuous space, which was recently parametrized by three geographic-style coordinates. The four non-oblique Bravais classes of two-dimensional lattices form low-dimensional singular subspaces in the full continuous space. Now, the deviations of a lattice from its higher symmetry neighbors can be continuously quantified by real-valued distances satisfying metric axioms. This article analyzes these and newer G-chiral distances for millions of two-dimensional lattices that are extracted from thousands of available two-dimensional materials and real crystal structures in the Cambridge Structural Database.
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