What is it about?

More than 2.6 million 2-dimensional lattices that naturally appear in real crystals from the Cambridge Structural Database are mapped by geographic-style coordinates similar to our plane Earth. All Bravais classes are visualised as subspaces in the full continuous space of lattices.

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Why is it important?

For centuries, crystallography studied periodic structures almost exclusively by discrete tools such as Bravais classes symmetry groups that are discontinuous under almost any tiny perturbation. We uniquely parameterise all 2-dimensional lattices by continuous coordinates that are provably stable under noise.

Perspectives

This paper opens the new era of continuous crystallography studying periodic structures by stable-under-noise invariants.

Vitaliy Kurlin
University of Liverpool

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This page is a summary of: Geographic style maps for two-dimensional lattices, Acta Crystallographica Section A Foundations and Advances, January 2023, International Union of Crystallography, DOI: 10.1107/s2053273322010075.
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