Continuous metrics and chiral distances for 2-dimensional lattices.

11^th March 2022, 14:00
Vitaly Kurlin
MIF

Abstract

The paper "Mathematics of 2-dimensional lattices" (the latest pdf, an early version in arxiv:2201.05150) introduced continuous metrics on the spaces of 2-dimensional lattices considered up to isometry, rigid motion, similarity (with uniform scaling) in the plane. These spaces contain the non-oblique Bravais classes (hexagonal, tetragonal (square), rectangular, centered-rectangular) as low-dimensional strata. A continuous distance from a lattice to the subspace of non-oblique lattices can be considered as a real-valued chiral measure for a deviation of a given lattice from its closest higher-symmetry neighbor. We will discuss explicit formulae of metrics and chiral distances, and their computations for millions of crystal lattices extracted from the Cambridge Structural Database in the joint work with Matt Bright and Andy Cooper.