RIETVELD REFINEMENT OF THE INCOMMENSURATE STRUCTURES OF FERROELECTRIC AND SUPERCONDUCTING PEROVSKITES.

G. Baldinozzi¹, O. Perez², D. Grebille², J.-F. Berar and G. Calvarin¹

¹Laboratoire de Chimie Physique du Solide, URA CNRS 453, Ecole Centrale Paris F 92995 Chatenay-Malabry Cedex, France. E-Mail: baldinozzi@cps.ecp.fr
²Laboratoire CRISMAT, UMR CNRS 6508, ISMRa F 14050 Caen Cedex, France.Laboratoire de Cristallographie, CNRS BP 166 F 38042 Grenoble Cedex, France.

Keywords: Incommensurate crystals, neutron diffraction, single-crystal and powder diffraction, disordered structures.

In the past years, the study of compounds presenting modulated phases has reached a considerable extension. Moreover, these studies have overcome the specialized domains where they appeared (metallurgy and magnetism) and many other branches of solid state physics constitute a fruitful field of application. Ionic conductors, superconductors and insulators exhibit modulated phases. These studies point out that the onset of an incommensurate structure is not characteristic of low dimensionality solids but full three dimensional systems can be interested as well.

Most of the structural studies of incommensurately modulated phases are developed using single crystal diffraction data. Nevertheless, many compounds are not easily synthesized as single crystals or the interesting phases present complex polydomain structures. Therefore, the study of the structure by single crystal techniques becomes very complex, or even not possible.

The Rietveld program XND [1], already developed for non modulated structures, has been modified and the 4D formalism for mono-incommensurate modulated phases (superspace group symmetry, intensity and positioning of satellite reflections) has been implemented [2,3].

Detail of the refinement (experimental, fitted and difference profile) of the neutron powder diffraction pattern of Pb₂CoWO₆ in the monoclinic incommensurate phase at 250 K. The ticks represent the positions of zeroth, first and second order satellite peaks.

The refinement of the incommensurately modulated structures of different perovskites is presented: these compounds represent a challenging problem because in ferroelectric perovskites the onset of the modulated phase takes place at a ferroelastic phase transition. Moreover, light and heavy scatterers are present in the structure of ferroelectrics and superconductors. Therefore, the use of complementary sources of radiation is very interesting to increase the contrast. In particular, neutron diffraction experiments are invaluable to give an accurate description of the oxygen framework.

Examples of refinements, involving compositional and / or displacive modulations, are presented, illustrating the possibilities and the advantages of the method. The refinement of the low temperature incommensurate structure (at 6 K) of Pb₂MgTeO₆[4] a perovskite for which no single crystals have been synthesized yet, is presented. Two other particularly interesting examples will be discussed: the structures of the antiferroelectric perovskite Pb₂CoWO₆ [5,6] at 250 K and of B_2+xSr_3-xFe₂O_9+d [7,8] at room temperature for which single crystal X-ray diffraction data and structural refinements are available, so the methods, the results and their efficiency can be compared. The specific contribution of the Rietveld method is outlined.

These results prove the accuracy of the Rietveld refinements and let foresee its extension to a broader class of compounds presenting modulated phases.

J.-F. Berar and P. Garnier, APD 2nd Conference. Gaithersburg, USA: NIST (1992); XND is available on ftp://labs.polycnrs-gre.fr/pub/xnd.

Baldinozzi G, Grebille D and Berar J-F, Rietveld refinement of incommensurate modulated phases, Proceedings of Aperiodic 97, World Scientific (at press).

Grebille D, Baldinozzi G, Berar J-F, Perez O and Boullay, Ph Resolution de structures modulees incommensurables par la methode de Rietveld, AFC 98 Orleans February, 24--27 (1998).

Baldinozzi G, Grebille D, Sciau Ph, Kiat J-M, Moret J and Berar J-F, J. Phys.: Condens. Matter (1998) (at press).

Bonin M, Paciorek W, Schenk K J and Chapuis G, Acta Crystallogr. B 51 48-54 (1998).

Baldinozzi G, Sciau Ph, Calvarin G, Grebille D and Suard E, Rietveld refinement of the incommensurate phase of the elpasolite (ordered perovskite) Pb₂CoWO₆ (to be published).

Perez O, Leligny H, Grebille D, Greneche J-M, Labb'e Ph, Groult D and Raveau B, Phys. Rev. B 55 1236-1245 (1997).

Perez O, Baldinozzi G and Grebille D, t Joint refinement of X-ray single crystal and neutron powder diffraction data of the crystal structure of the modulated-phase B_2+xSr_3-xFe₂O_9+d. (to be published).