STRUCTURE REFINEMENT OF COMMENSURATELY MODULATED BISMUTH TUNGSTATE, BI2WO6

The displacive ferroelectric Bi2WO6[M(r) = 697.81, a = 5.4559 (4), b = 5.4360 (4), c = 16.4298 (17) angstrom, Z = 4, D(x) = 9.512 g cm-3, Mo K-alpha, lambda = 0.7107 angstrom, mu = 958.6 cm-1, F(000) = 1151.73], is described at room temperature as a commensurate modulation of an idealized Fmmm parent structure derived from an I4/mmm structure. Transmission electron microscopy clearly showed that there are coherent intergrowths of two distinct modulated variants in Bi2WO6 crystals. Displacive modes of inherent F2mm and Bmab symmetry are substantial and coherent over a large volume. They reduce the space-group symmetry to B2ab. A further substantial displacive mode corresponds to rotation of corner-connected WO6 octahedra about axes parallel to c and has either of two inherent symmetries, Abam or Bbam, the difference being associated with the way this mode propagates along c. The dominant Abam mode reduces the space-group symmetry to P2(1)ab, while the existence of the Bbam mode reduces the intensity of h + l = 2n + 1 data and acts like a stacking fault. Group theoretical analysis of the problem details how the X-ray data can be classified so as to monitor the refinement. Anomalous dispersion selects the overall sign of the F2mm mode and determines the polarity. The overall signs chosen for the Bmab and Abam symmetry components of atom displacements select between equivalent origins. The overall signs of induced modes of inherent Amam, Bbab and Ccma symmetry had to be determined by comparative refinement since the assumption that calculated phases are best estimates can retain the initial overall sign choice for these modes during least-squares refinement. Correlations between the dominant modes and the induced modes allowed a meaningful choice of signs to resolve the pseudo homometry. Only the sign of the Bbab mode was capable of self-correction during refinement. A further induced mode of inherent Cmma symmetry was constrained to have zero amplitude because it required the interaction of three, rather than two, of the dominant modes for its induction. A final value of 0.037 for R1 = SIGMA-h\\F(obs)(h)\ - \F(calc)(h)\\/SIGMA-h\F(obs)(h)\ was obtained for 2351 unmerged data with I(h) > 3-sigma[I(h)].