The aperiodic nature of incommensurately modulated structures

Abstract

The discovery of aperiodic crystals is perhaps one of the most important event which has changed our vision on crystalline architectures since the discovery of diffraction hundred years ago. It was the merit of a dutch crystallographer, P.M. de Wolff, to interpret their diffraction pattern as a three dimensional projection of a higher dimensional reciprocal lattice, idea which led directly to the generalization of the concept of crystal. Aperiodic crystals are currently described as periodic objects in higher-dimensional space, i .e. the superspace and their structures can be described in terms of 3-d cuts. Incommensurate structures, composite structures and quasicrystals all belong to aperiodic structures.Many interesting properties of superspace have been discovered which are also directly applicable to crystals in the conventional sense, i .e. crystals with 3-d periodicity. In particular the concept of structure type can be extended for a better understanding of structure relations. The notion of solid solution has also benefited from superspace considerations. Moreover, superspace is a very powerful tool for a better understanding of structure-property relations in material science, e.g. luminescence properties could be directly associated to the description of structures in superspace. Recently, this concept has been used for the prediction of new structural modifications including polytypes and even polytypic modifications of a well known pharmaceutical product.

Weak coupling of pseudoacoustic phonons and magnon dynamics in the incommensurate spin-ladder compound Sr14Cu24O41

“…Incommensurate compounds consist of two or more interpenetrating sublattices with lattice periods incommensurate along one or more crystal axes. They belong to the broad class of aperiodic crystals, 1 which also includes the celebrated quasicrystals. 2 These compounds usually show anisotropies in electronic, optical, magnetic, and thermal properties.…”

Could incommensurability in sulfosalts be more common than thought? The case of meneghinite, CuPb13Sb7S24

“…Refined cation population at the site: Pb 0.28 Sb 0.72 . (Chapuis & Arakcheeva, 2013;Pina & Ló pez-Acevedo, 2016). Unfortunately, all these great advantages have been accompanied by a turning of the diffractometer more into a black box that operates in a push-button mode.…”