Introduction to Periodic Geometry for applications in Crystallography and Materials Discovery.

13^th December 2020, 15:15
Vitaliy Kurlin
MIF

Abstract

A periodic crystal is modeled as a periodic set of zero-sized points in 3-space. Such a periodic set is usually given by a unit cell (a parallelepiped defined by 3 edge-lengths and 3 angles) and a motif of points with fractional coordinates in this cell. Representing a crystal as a unit cell plus a motif is highly ambiguous. Hence a reliable comparison of rigid crystals should be based on isometry invariants that are preserved under any rigid motions, hence are independent of a unit cell and a motif. The talk will discuss a stable isometry classification of periodic crystals. Most past invariants of crystals such as symmetry groups are discontinuous under atomic vibrations. The new classification establishes foundations of periodic geometry. Based on joint papers with Andy Cooper, Angeles Pulido, Herbert Edelsbrunner, Mathijs Wintraecken, Teresa Heiss, Phil Smith, Marco Mosca, Dan Widdowson, e.g. arxiv:2009.02488.