Combined X-ray single-crystal and neutron powder refinement of modulated structures and application to the incommensurately modulated structure of Bi₂Sr₂CaCu₂O_8+y

A method is described for the refinement of modulated structures from a combined set of single-crystal and powder diffraction data or from powder data only. The method is especially useful when information on light atoms is to be obtained and no single crystals of suitable size for neutron diffraction are available. The program in which the method is encoded allows for differences in composition between the single-crystal and powder samples. Application to the incommensurately modulated superconductor Bi₂Sr₂CaCu₂O_8+y (2212) using powder neutron and single-crystal X-ray data confirms that the oxygen modulation in the Bi-O layer is saw-tooth-like, as observed in the preceding study based solely on X-ray data [Petricek, Gao, Lee & Coppens (1990). Phys. Rev. B, 42, 387-392], but with improved accuracy in the resulting parameters. The extra oxygen content is explicitly related to the modulation model and corresponds to 0.14-(4) per formula unit. With the refined site occupancies for the heavy atoms and the results of an anomalous-scattering study on the bismuth distribution [Coppens, Lee, Gao & Sheu (1991). J. Phys. Chem. Solids, 52, 1267-1272], a copper valency of 2.31 is obtained for the single-crystal sample. The powder value of 2.40 is somewhat less reliable as no anomalous-scattering data are available for the powder sample.