Rietveld refinement of the incommensurate structure of the elpasolite (ordered perovskite)

Abstract

Lead magnesium tellurate, , undergoes two structural phase transitions at about 194 K and 142 K. The structures of the cubic and of the lower-temperature phase have been refined by the Rietveld method at three different temperatures (350, 220 and 6 K). The relative simplicity of the structure has allowed the incommensurately modulated structure for powder samples to be characterized. The modulated displacements of O atoms give rise to a large spread of bond lengths. Pb atoms are disordered and their average positions are away from the threefold axis. The structural resolution is compared to that from the analysis of the symmetry-adapted coordinates of the optic modes becoming totally symmetric in the lower-temperature phase.

Étude de la Solution Solide Entre Tungstate et Tellurate de Magnésium: Pb2MgWxTe(1−x)O6

“…L'analyse du diagramme de diffraction de Pb MgTeO conduit aux groupes quadridimensionnels R3 m( ) et R3 ( ) (9). Les deux solutions ont e´te´envisa-ge´es lors de l'e´tude structurale, a`6 K, et seul le second groupe donne une solution acceptable (10). Dans l'hypothe`-se, tre`s vraisemblable, ou il existe une seconde transition de phase vers 142 K cette solution correspondrait donc a`la structure de la phase a`plus basse tempe´rature.…”

“…D'apre`s une e´tude par diffusion Raman il existerait une seconde transition de phase vers 142 K avec se´paration de la phase incommensurable en deux nouvelles phases (9). La structure incommensurable, a`6 K, a e´te´re´cemment de`termine´e par diffraction de neutrons sur poudre (10,11 La caracte´risation structurale a e´te´effectue´e par diffraction X sur un goniome`tre prototype Microcontrole conc ,u au laboratoire (12) et par diffraction de neutrons sur le diffractome`tre D1A de l'ILL a`Grenoble. Les conditions de mesure des enregistrements utilise´s dans les affinements structuraux sont donne´es dans le Tableau 1.…”

Atomistic mechanism leading to complex antiferroelectric and incommensurate perovskites

“…Refs. 14-16 and references therein) and even incommensurate phases 17,18 in various perovskites possessing a structural complexity that has acted as a major deterrent of detailed studies. In other words, the presently discovered couplings also provide an unified description of many antiferroelectric and incommensurate perovskites.…”

First-principles determination of the dynamical properties ofPb2MgTeO6

“…For insulating systems, mechanisms governing the phase transition have not yet been characterized from first principles. There are a few perovskite insulators presenting such phases and all are rock-salt ordered perovskites: Pb 2 CoWO 6 , 5 Pb 2 CdWO 6 , 6 PbSc 1/2 Ta 1/2 O 3 , 7 Pb 2 MgNbO 6 , 8,9 and Pb 2 MgTeO 6 ͑Refs. 8 and 9͒ ͑PMT͒.…”

“…The experimental studies 8,9 of PMT show an ordered face-centered-cubic structure at high temperature with the Fm3m space group ͑phase I͒. This phase transforms to a first incommensurately modulated phase at 194 K with the R3m average structure ͑phase II͒.…”