Superspace formalism to crack complex codes in material chemistry
Olivier Pérez, Luis Elcoro · Acta Crystallographica Section A Foundations of Crystallography · 2008
In the study of incommensurate modulated compounds, transmission electron microscopy (TEM) is an invaluable tool for characterisation.In cases where large single crystals are not available, TEM will still allow to clearly distinguish the satellite reflections.This allows to determine the superspace symmetry and modulation vector.Several examples will be presented of materials whose structure could only be solved by first turning to TEM.First, AxMnO2 (x<1) tunnel structures will be presented.The tunnel walls are built from rutiletype chains of edge-sharing MnO6 octahedra forming a variety of tunnel structures by being combined in different manners.The A-cation strings in the tunnels can contain ordered vacancies and, along with a displacement of the A-cations, this results in modulated structures.The shape of the tunnels and the order of the A-cations vary depending on the size of the A-cation and the A/Mn ratio, linking the modulation to the composition.[e.g.1-2] The second example is the new family of perovskite based structures having crystallographic shear planes.This requires a cation with a lone electron pair in the A-position, such as Pb 2+ .The crystallographic orientation of the shear planes can be controlled through the choice and amount of other A-cations substituting for Pb, resulting in a series of incommensurately modulated materials.The building principles, features of the diffraction patterns and chemical compositions of this series will be shown as found in different variants of '(Pb,A)2Fe2O5'.[3][4]