Geographic style maps for two-dimensional lattices

Bright, Matthew, Cooper, Andrew I and Kurlin, Vitaliy ORCID: 0000-0001-5328-5351 (2023) Geographic style maps for two-dimensional lattices. ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES, 79 (Pt 1). pp. 1-13.

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Official URL: http://dx.doi.org/10.1107/s2053273322010075

Abstract

This paper develops geographic style maps containing two-dimensional lattices in all known periodic crystals parameterized by recent complete invariants. Motivated by rigid crystal structures, lattices are considered up to rigid motion and uniform scaling. The resulting space of two-dimensional lattices is a square with identified edges or a punctured sphere. The new continuous maps show all Bravais classes as low-dimensional subspaces, visualize hundreds of thousands of lattices of real crystal structures from the Cambridge Structural Database, and motivate the development of continuous and invariant-based crystallography.

Item Type:	Article
Uncontrolled Keywords:	two-dimensional lattices, reduced basis, obtuse superbase, isometry, complete invariants, metric tensor, continuity
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	11 Jan 2023 11:37
Last Modified:	22 Feb 2023 15:08
DOI:	10.1107/S2053273322010075
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3166993