Superstructure reflexions in tilted perovskites Part 1

TL;DR

This paper presents a crystallographic approach to understanding superstructure reflections in tilted perovskites, providing conditions for their appearance based on distortion modes and structure factors.

Contribution

It introduces a method to derive Boolean conditions for first order superstructure reflections in tilted perovskites using structure factor equations.

Findings

Boolean conditions for first order superstructure reflections derived

Method applicable to electron diffraction pattern analysis

Foundation for analyzing second order reflections in future work

Abstract

The superstructure spots that appear in diffraction patterns of tilted perovskites are well documented and easily calculated using crystallographic software. Here, by considering a distortion mode as a perturbation of the prototype perovskite structure, we show how the structure factor equation yields Boolean conditions for the presence of first order superstructure reflexions. A subsequent article describes conditions for second order reflexions, which appear only in structures with mixed in-phase and anti-phase oxygen octahedral tilting. This approach may have some advantages for the analysis of electron diffraction patterns of perovskites.