Rotational Disorder in Scheelite-Type NaRE(MO4)2 (RE = Rare-Earth, Y; M = Mo, W)

The average and local crystal structures of scheelite-type double molybdates and tungstates of formula NaRE(MO4)(2) (RE = rare-earth, Y; M = Mo, W) are probed using a dual-space approach that combines Rietveld and PDF analyses of X-ray scattering data. The evolution of metal-oxygen distances as a function of the ionic radius of the rare-earth cation reveals that the crystal-chemical pictures derived from Rietveld and PDF analyses differ in their description of (1) the rigidity of M-VI-O bonds defining MO4 tetrahedra and (2) the extent of Na/RE-O bond distance distortions in (Na/RE)O-8 dodecahedra. Analysis of the thermal ellipsoids of the oxygen atoms reveals that these differences stem from the presence of rotational disorder of MO4 tetrahedra. Rietveld analysis averages random rotations of these tetrahedra yielding an abnormally broad range of Mo-O and W-O bond distances across the rare-earth series. By contrast, bond distances extracted from PDF analysis remain unchanged upon chemical substitution, in agreement with the well-known rigidity of M-VI-O bonds. In addition, PDF analysis shows that the rotational disorder of MO4 tetrahedra translates into local distortions of Na/RE-O bond distances defining (Na/RE)O-8 dodecahedra. These results highlight the complementarity of Rietveld and PDF analyses and the significance of coupling both approaches to accurately probe local structural distortions through a single scattering measurement.