Copernican Crystallography

TL;DR

This paper proposes a new framework for quasiperiodic crystallography that avoids redundancies by redefining point groups based on indistinguishability rather than strict periodicity, broadening the scope of crystallography.

Contribution

It introduces a novel approach to quasiperiodic crystallography by redefining point groups, moving beyond the outdated periodicity paradigm.

Findings

Redundancies in current quasiperiodic crystallography are identified.

A new definition of point groups based on indistinguishability is proposed.

The approach broadens the applicability of crystallography to quasiperiodic materials.

Abstract

Redundancies are pointed out in the widely used extension of the crystallographic concept of Bravais class to quasiperiodic materials. Such pitfalls can be avoided by abandoning the obsolete paradigm that bases ordinary crystallography on microscopic periodicity. The broadening of crystallography to include quasiperiodic materials is accomplished by defining the point group in terms of indistinguishable (as opposed to identical) densities.