The discontinuity challenge of cell-based representations of crystals.

17^th October 2025, 15:00
Vitaliy Kurlin
MIF

Abstract

After the previous meetings discussed the fundamental concepts of equivalences and invariants, the final introductory discussion this year will focus on periodic crystals. Over many years, crystallography developed standard settings for a canonical representation of any periodic crystal in a conventional or a reduced cell. However, a reduced cell discontinuously scales up under almost any displacement of atoms, within the space of all periodic crystals. Our earliest reference to the experimentally demonstrated discontinuity is The reduced cell and its crystallographic applications (part B from page 80) in 1965. As a result, many materials databases accumulated numerous near-duplicates, which we reported in NeurIPS 2022 (the extended version and the latest higher-order version), IUCrJ 2024, CGD 2024, SR 2025, PR 2026, and will present at future MIF++ seminars, while this open-table discussion will focus on the discontinuity problem itself.