Abstract: Synthetic and naturally occurring forms of tricopper orthotellurate, (Cu3TeO6)-Te-II-O-IV (the mineral mcalpineite) have been investigated by 3D electron diffraction (3D ED), X-ray powder diffraction (XRPD), Raman and infrared (IR) spectroscopic measurements. As a result of the diffraction analyses, (Cu3TeO6)-Te-II-O-IV is shown to occur in two polytypes. The higher-symmetric (Cu3TeO6)-Te-II-O-IV-1C polytype is cubic, space group 1a (3) over bar, with a = 9.537 (1) angstrom and V = 867.4 (3) angstrom(3) as reported in previous studies. The 1C polytype is a well characterized structure consisting of alternating layers of (CuO6)-O-II octahedra and both (CuO6)-O-II and (TeO6)-O-VI octahedra in a patchwork arrangement. The structure of the lower-symmetric orthorhombic (Cu3TeO6)-Te-II-O-IV-2O polytype was determined for the first time in this study by 3D ED and verified by Rietveld refinement. The 2O polytype crystallizes in space group Pcca, with a = 9.745 (3) angstrom, b = 9.749 (2) angstrom, c = 9.771 (2) angstrom and V = 928.3 (4) angstrom(3) . High-precision XRPD data were also collected on (Cu3TeO6)-Te-II-O-IV-2O to verify the lower-symmetric structure by performing a Rietveld refinement. The resultant structure is identical to that determined by 3D ED, with unit-cell parameters a = 9.56157 (19) angstrom, b = 9.55853 (11) angstrom, c = 9.62891 (15) angstrom and V = 880.03 (2) angstrom(3) . The lower symmetry of the 2O polytype is a consequence of a different cation ordering arrangement, which involves the movement of every second (CuO6)-O-II and (TeO6)-O-VI octahedral layer by (1/4, 1/4, 0), leading to an offset of (TeO6)-O-VI and (CuO6)-O-II octahedra in every second layer giving an ABAB* stacking arrangement. Syntheses of (Cu3TeO6)-Te-II-O-IV showed that low-temperature (473 K) hydrothermal conditions generally produce the 2O polytype. XRPD measurements in combination with Raman spectroscopic analysis showed that most natural mcalpineite is the orthorhombic 2O polytype. Both XRPD and Raman spectroscopy measurements may be used to differentiate between the two polytypes of (Cu3TeO6)-Te-II-O-IV. In Raman spectroscopy, (Cu3TeO6)-Te-II-O-IV-1C has a single strong band around 730 cm(-1), whereas (Cu3TeO6)-Te-II-O-IV-2O shows a broad double maximum with bands centred around 692 and 742 cm(-1).

Abstract: The crystal structure solution of modulated compounds is often very challenging, even using the well established methodology of single-crystal X-ray crystallography. This task becomes even more difficult for materials that cannot be prepared in a single-crystal form, so that only polycrystalline powders are available. This paper illustrates that the combined application of transmission electron microscopy (TEM) and powder diffraction is a possible solution to the problem. Using examples of anion-deficient perovskites modulated by periodic crystallographic shear planes, it is demonstrated what kind of local structural information can be obtained using various TEM techniques and how this information can be implemented in the crystal structure refinement against the powder diffraction data. The following TEM methods are discussed: electron diffraction (selected area electron diffraction, precession electron diffraction), imaging (conventional high-resolution TEM imaging, high-angle annular dark-field and annular bright-field scanning transmission electron microscopy) and state-of-the-art spectroscopic techniques (atomic resolution mapping using energy-dispersive X-ray analysis and electron energy loss spectroscopy).

Abstract: We computed Debye-Waller factors in the temperature range from 0.1 to 1000 K for AlN, GaN, InN, ZnO and CdO with the wurtzite-type structure. The Debye-Waller factors were derived from phonon densities of states obtained from Hellmann-Feynman forces computed within the density-functional-theory formalism. The temperature dependences of the Debye-Waller factors were fitted and fit parameters are given.

Abstract: The incommensurately modulated scheelite-like KSm( MoO4)(2) structure has been refined in the monoclinic superspace group I2/b(alpha beta 0)00 by the Rietveld method on the basis of synchrotron radiation powder diffraction data. The systematic broadening of satellite reflections has been accounted for by applying anisotropic microstrain line-broadening. The microstructure has been studied by transmission electron microscopy (TEM). The partial disorder of the K and Sm cations in the A position is best approximated by a combination of harmonic and complex crenel functions with (0.952Sm + 0.048K) and (0.952K + 0.048Sm) atomic domains. This combination yields a compositional wave distribution from {KMoO4} to {SmMoO4} observed in the ab structure projection along q. The specific features of KSm(MoO4)(2) and degree of the A-cation ordering are discussed in comparison with the previously reported structure of KNd(MoO4)(2).