Fractional Coordinates

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M. Lang - One of the best experts on this subject based on the ideXlab platform.

  • the magnetic and crystal structure of azurite cu _3 co _3 _2 oh _2 as determined by neutron diffraction
    Physical Review B, 2011
    Co-Authors: K C Rule, M C R Gibson, S Gerischer, J.-u. Hoffmann, M Reehuis, Matthias J. Gutmann, B. Ouladdiaf, Daniel A Tennant, S. Süllow, M. Lang
    Abstract:

    Here we present neutron diffraction results on the mineral azurite. We have found that the crystal structure of azurite can be described in the space group $P2_1$ which is the next lower symmetric group of $P2_1/c$ as found in earlier work. This small change in symmetry does not greatly influence the lattice parameters or atomic Fractional Coordinates which are presented here for single crystal diffraction refinements. The ordered magnetic moment structure of this material has been determined and is comprised of two inequivalent magnetic moments on copper sites of magnitude 0.68(1) and 0.25(1) $\mu_{B}$. This result is discussed in terms of the anisotropic exchange and Dzyaloshinskii-Moriya interactions. It is found that the system is likely governed by one-dimensional behaviour despite the long-range ordered ground state. We also highlight the significance of strain in this material which is strongly coupled to the magnetism.

  • The magnetic and crystal structure of azurite Cu$_3$(CO$_3$)$_2$(OH)$_2$ as determined by neutron diffraction
    Physical Review B, 2011
    Co-Authors: K C Rule, M C R Gibson, S Gerischer, J.-u. Hoffmann, M Reehuis, Matthias J. Gutmann, B. Ouladdiaf, Daniel A Tennant, S. Süllow, M. Lang
    Abstract:

    Here we present neutron diffraction results on the mineral azurite. We have found that the crystal structure of azurite can be described in the space group $P2_1$ which is the next lower symmetric group of $P2_1/c$ as found in earlier work. This small change in symmetry does not greatly influence the lattice parameters or atomic Fractional Coordinates which are presented here for single crystal diffraction refinements. The ordered magnetic moment structure of this material has been determined and is comprised of two inequivalent magnetic moments on copper sites of magnitude 0.68(1) and 0.25(1) $\mu_{B}$. This result is discussed in terms of the anisotropic exchange and Dzyaloshinskii-Moriya interactions. It is found that the system is likely governed by one-dimensional behaviour despite the long-range ordered ground state. We also highlight the significance of strain in this material which is strongly coupled to the magnetism.

Fujio Izumi - One of the best experts on this subject based on the ideXlab platform.

  • vesta a three dimensional visualization system for electronic and structural analysis
    Journal of Applied Crystallography, 2008
    Co-Authors: Koichi Momma, Fujio Izumi
    Abstract:

    A cross-platform program, VESTA, has been developed to visualize both structural and volumetric data in multiple windows with tabs. VESTA represents crystal structures by ball-and-stick, space-filling, polyhedral, wireframe, stick, dot-surface and thermal-ellipsoid models. A variety of crystal-chemical information is extractable from Fractional Coordinates, occupancies and oxidation states of sites. Volumetric data such as electron and nuclear densities, Patterson functions, and wavefunctions are displayed as isosurfaces, bird's-eye views and two-dimensional maps. Isosurfaces can be colored according to other physical quantities. Translucent isosurfaces and/or slices can be overlapped with a structural model. Collaboration with external programs enables the user to locate bonds and bond angles in the `graphics area', simulate powder diffraction patterns, and calculate site potentials and Madelung energies. Electron densities determined experimentally are convertible into their Laplacians and electronic energy densities.

  • Chapter 7 The rietveld method and its applications to synchrotron X-ray powder data
    Analytical Spectroscopy Library, 2007
    Co-Authors: Fujio Izumi
    Abstract:

    Publisher Summary The Rietveld method is a technique for refining structure and lattice parameters directly from whole X-ray or neutron powder diffraction patterns without separating peaks contained in them. The Rietveld method substantially contains the following data-processing procedures: (i) separation of overlapping peaks in diffraction patterns, (ii) separation of Kα I and Kα 2 peaks when using characteristic X-rays, (iii) background subtraction, (iv) refinement of lattice parameters, (v) refinement of structure parameters (Fractional Coordinates, occupation factors, and thermal-displacement parameters), (vi) correction of preferred orientation, (vii) determination of mixing ratios, (viii) identification of impurity peaks, (ix) indexing of reflections, and (x) determination of integrated intensities, full-widths at half-maximum intensities (FWHM), and peak positions. The Rietveld method, in which these complex calculations are executed simultaneously, is an exquisite technique for the analysis of powder-diffraction data. The Rietveld method is widely applicable to metals, inorganic compounds, and organic compounds of low molecular weights only if they are crystalline.

  • Neutron and X-Ray Powder Diffraction Studies of LiMn2−yCryO4
    IEEE Journal of Solid-state Circuits, 1999
    Co-Authors: K. Oikawa, Fujio Izumi, Takashi Kamiyama, D Nakazato, Hiromasa Ikuta, Masataka Wakihara
    Abstract:

    The crystal structures of chromium-doped spinel-type lithium manganese oxides, LiMn[sub 2[minus]y]Cr[sub y]O[sub 4] (y = 0, 1/9, 1/6, and 1/3), have been studied by neutron and X-ray powder diffraction. Rietveld refinements of their neutron diffraction data revealed that Cr is substituted for Mn selectively and that Li occupies only the 8a site. Thus, the above solid solutions can be expressed as Li(Mn[sub 2[minus]y]Cr[sub y])O[sub 4]. The Fractional Coordinates of oxygen were almost the same in all the samples while the lattice parameter a decreased linearly with increasing Cr content. The lengths of (Mn, Cr)-O bonds in (Mn, Cr)O[sub 6] octahedra changed in a manner expected from average ionic radii for Mn[sub 2[minus]y]Cr[sub y]. Rietveld analyses of the X-ray diffraction data showed the crystallite size and anisotropic strain to decrease with increasing Cr content.

K C Rule - One of the best experts on this subject based on the ideXlab platform.

  • the magnetic and crystal structure of azurite cu _3 co _3 _2 oh _2 as determined by neutron diffraction
    Physical Review B, 2011
    Co-Authors: K C Rule, M C R Gibson, S Gerischer, J.-u. Hoffmann, M Reehuis, Matthias J. Gutmann, B. Ouladdiaf, Daniel A Tennant, S. Süllow, M. Lang
    Abstract:

    Here we present neutron diffraction results on the mineral azurite. We have found that the crystal structure of azurite can be described in the space group $P2_1$ which is the next lower symmetric group of $P2_1/c$ as found in earlier work. This small change in symmetry does not greatly influence the lattice parameters or atomic Fractional Coordinates which are presented here for single crystal diffraction refinements. The ordered magnetic moment structure of this material has been determined and is comprised of two inequivalent magnetic moments on copper sites of magnitude 0.68(1) and 0.25(1) $\mu_{B}$. This result is discussed in terms of the anisotropic exchange and Dzyaloshinskii-Moriya interactions. It is found that the system is likely governed by one-dimensional behaviour despite the long-range ordered ground state. We also highlight the significance of strain in this material which is strongly coupled to the magnetism.

  • The magnetic and crystal structure of azurite Cu$_3$(CO$_3$)$_2$(OH)$_2$ as determined by neutron diffraction
    Physical Review B, 2011
    Co-Authors: K C Rule, M C R Gibson, S Gerischer, J.-u. Hoffmann, M Reehuis, Matthias J. Gutmann, B. Ouladdiaf, Daniel A Tennant, S. Süllow, M. Lang
    Abstract:

    Here we present neutron diffraction results on the mineral azurite. We have found that the crystal structure of azurite can be described in the space group $P2_1$ which is the next lower symmetric group of $P2_1/c$ as found in earlier work. This small change in symmetry does not greatly influence the lattice parameters or atomic Fractional Coordinates which are presented here for single crystal diffraction refinements. The ordered magnetic moment structure of this material has been determined and is comprised of two inequivalent magnetic moments on copper sites of magnitude 0.68(1) and 0.25(1) $\mu_{B}$. This result is discussed in terms of the anisotropic exchange and Dzyaloshinskii-Moriya interactions. It is found that the system is likely governed by one-dimensional behaviour despite the long-range ordered ground state. We also highlight the significance of strain in this material which is strongly coupled to the magnetism.

Matthias J. Gutmann - One of the best experts on this subject based on the ideXlab platform.

  • Glycine zinc sulfate penta-hydrate: redetermination at 10 K from time-of-flight neutron Laue diffraction.
    Acta Crystallographica Section E: Crystallographic Communications, 2016
    Co-Authors: Andrew Dominic Fortes, Ian G. Wood, C.m. Howard, Matthias J. Gutmann
    Abstract:

    Single crystals of glycine zinc sulfate penta­hydrate [systematic name: hexa­aqua­zinc tetra­aquadiglycinezinc bis­(sulfate)], [Zn(H2O)6][Zn(C2H5NO2)2(H2O)4](SO4)2, have been grown by isothermal evaporation from aqueous solution at room temperature and characterized by single-crystal neutron diffraction. The unit cell contains two unique ZnO6 octa­hedra on sites of symmetry -1 and two SO4 tetra­hedra with site symmetry 1; the octa­hedra comprise one [tetra­aqua-diglycine zinc]2+ ion (centred on one Zn atom) and one [hexa­aqua­zinc]2+ ion (centred on the other Zn atom); the glycine zwitterion, NH3+CH2COO−, adopts a monodentate coordination to the first Zn atom. All other atoms sit on general positions of site symmetry 1. Glycine forms centrosymmetric closed cyclic dimers due to N—H⋯O hydrogen bonds between the amine and carboxyl­ate groups of adjacent zwitterions and exhibits torsion angles varying from ideal planarity by no more than 1.2°, the smallest values for any known glycine zwitterion not otherwise constrained by a mirror plane. This work confirms the H-atom locations estimated in three earlier single-crystal X-ray diffraction studies with the addition of independently refined Fractional Coordinates and Uij parameters, which provide accurate inter­nuclear X—H (X = N, O) bond lengths and consequently a more accurate and precise depiction of the hydrogen-bond framework.

  • the magnetic and crystal structure of azurite cu _3 co _3 _2 oh _2 as determined by neutron diffraction
    Physical Review B, 2011
    Co-Authors: K C Rule, M C R Gibson, S Gerischer, J.-u. Hoffmann, M Reehuis, Matthias J. Gutmann, B. Ouladdiaf, Daniel A Tennant, S. Süllow, M. Lang
    Abstract:

    Here we present neutron diffraction results on the mineral azurite. We have found that the crystal structure of azurite can be described in the space group $P2_1$ which is the next lower symmetric group of $P2_1/c$ as found in earlier work. This small change in symmetry does not greatly influence the lattice parameters or atomic Fractional Coordinates which are presented here for single crystal diffraction refinements. The ordered magnetic moment structure of this material has been determined and is comprised of two inequivalent magnetic moments on copper sites of magnitude 0.68(1) and 0.25(1) $\mu_{B}$. This result is discussed in terms of the anisotropic exchange and Dzyaloshinskii-Moriya interactions. It is found that the system is likely governed by one-dimensional behaviour despite the long-range ordered ground state. We also highlight the significance of strain in this material which is strongly coupled to the magnetism.

  • The magnetic and crystal structure of azurite Cu$_3$(CO$_3$)$_2$(OH)$_2$ as determined by neutron diffraction
    Physical Review B, 2011
    Co-Authors: K C Rule, M C R Gibson, S Gerischer, J.-u. Hoffmann, M Reehuis, Matthias J. Gutmann, B. Ouladdiaf, Daniel A Tennant, S. Süllow, M. Lang
    Abstract:

    Here we present neutron diffraction results on the mineral azurite. We have found that the crystal structure of azurite can be described in the space group $P2_1$ which is the next lower symmetric group of $P2_1/c$ as found in earlier work. This small change in symmetry does not greatly influence the lattice parameters or atomic Fractional Coordinates which are presented here for single crystal diffraction refinements. The ordered magnetic moment structure of this material has been determined and is comprised of two inequivalent magnetic moments on copper sites of magnitude 0.68(1) and 0.25(1) $\mu_{B}$. This result is discussed in terms of the anisotropic exchange and Dzyaloshinskii-Moriya interactions. It is found that the system is likely governed by one-dimensional behaviour despite the long-range ordered ground state. We also highlight the significance of strain in this material which is strongly coupled to the magnetism.

Michal Dušek - One of the best experts on this subject based on the ideXlab platform.

  • Structure determination of KScS₂, RbScS₂ and KLnS₂ (Ln = Nd, Sm, Tb, Dy, Ho, Er, Tm and Yb) and crystal-chemical discussion.
    Acta crystallographica. Section C Structural chemistry, 2015
    Co-Authors: Lubomír Havlák, Jan Fábry, Margarida Henriques, Michal Dušek
    Abstract:

    The title structures of KScS2 (potassium scandium sulfide), RbScS2 (rubidium scandium sulfide) and KLnS2 [Ln = Nd (potassium neodymium sufide), Sm (potassium samarium sulfide), Tb (potassium terbium sulfide), Dy (potassium dysprosium sulfide), Ho (potassium holmium sulfide), Er (potassium erbium sulfide), Tm (potassium thulium sulfide) and Yb (potassium ytterbium sulfide)] are either newly determined (KScS2, RbScS2 and KTbS2) or redetermined. All of them belong to the α-NaFeO2 structure type in agreement with the ratio of the ionic radii r(3+)/r(+). KScS2, the member of this structural family with the smallest trivalent cation, is an extreme representative of these structures with rare earth trivalent cations. The title structures are compared with isostructural alkali rare earth sulfides in plots showing the dependence of several relevant parameters on the trivalent cation crystal radius; the parameters thus compared are c, a and c/a, the thicknesses of the S-S layers which contain the respective constituent cations, the sulfur Fractional Coordinates z(S(2-)) and the bond-valence sums.

  • Structure determination of KScS2, RbScS2 and KLnS2 (Ln = Nd, Sm, Tb, Dy, Ho, Er, Tm and Yb) and crystal–chemical discussion
    Acta Crystallographica Section C-crystal Structure Communications, 2015
    Co-Authors: Lubomír Havlák, Jan Fábry, Margarida S. Henriques, Michal Dušek
    Abstract:

    The title structures of KScS2 (potassium scandium sulfide), RbScS2 (rubidium scandium sulfide) and KLnS2 [Ln = Nd (potassium neodymium sufide), Sm (potassium samarium sulfide), Tb (potassium terbium sulfide), Dy (potassium dysprosium sulfide), Ho (potassium holmium sulfide), Er (potassium erbium sulfide), Tm (potassium thulium sulfide) and Yb (potassium ytterbium sulfide)] are either newly determined (KScS2, RbScS2 and KTbS2) or redetermined. All of them belong to the α-NaFeO2 structure type in agreement with the ratio of the ionic radii r3+/r+. KScS2, the member of this structural family with the smallest trivalent cation, is an extreme representative of these structures with rare earth trivalent cations. The title structures are compared with isostructural alkali rare earth sulfides in plots showing the dependence of several relevant parameters on the trivalent cation crystal radius; the parameters thus compared are c, a and c/a, the thicknesses of the S—S layers which contain the respective constituent cations, the sulfur Fractional Coordinates z(S2−) and the bond-valence sums.