95 research outputs found

    Dynamic displacement disorder of cubic BaTiO3

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    The three-dimensional distribution of the x-ray diffuse scattering intensity of BaTiO3 has been recorded in a synchrotron experiment and simultaneously computed using molecular dynamics simulations of a shell model. Together, these have allowed the details of the disorder in paraelectric BaTiO3 to be clarified. The narrow sheets of diffuse scattering, related to the famous anisotropic longitudinal correlations of Ti ions, are shown to be caused by the overdamped anharmonic soft phonon branch. This finding demonstrates that the occurrence of narrow sheets of diffuse scattering agrees with a displacive picture of the cubic phase of this textbook ferroelectric material. The presented methodology allows one to go beyond the harmonic approximation in the analysis of phonons and phonon-related scattering

    Structural origins of relaxor behavior in a 0.96(Bi1/2Na1/2)TiO3-0.04BaTiO(3) single crystal under electric field

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    Diffuse x-ray scattering intensities from a single crystal of 0.96(Bi1/2Na1/2TiO3)-0.04(BaTiO3) have been collected at room temperature with and without application of an electric field along the [100] direction. Distinct features in the diffuse scattering intensities indicate correlations on a nanometer length scale. It is shown that locally correlated planar-like structures and octahedral tilt-domains within the room temperature rhombohedral R3c phase are both electrically active and are irreversibly affected by application of an electric field of 4.3 kV/mm. The field dependence of these nanoscale structures is correlated with the relaxor behavior of the material by macroscopic permittivity measurementsopen221

    Measurement of disorder – diffuse X-ray scattering using a diffractometer

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    Local structure evolution in polycrystalline Zn1−x_{1-x}Mgx_xO (0≀x≀0.150\leq{x}\leq{0.15}) studied by Raman and by synchrotron x-ray pair distribution analysis

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    The local structures of Zn1−x_{1-x}Mgx_xO alloys have been studied by Raman spectroscopy and by synchrotron x-ray pair distribution function (PDF) analysis. Within the solid solution range (0≀x≀0.150\leq{x}\leq{0.15}) of Zn1−x_{1-x}Mgx_xO, the wurtzite framework is maintained with Mg homogeneously distributed throughout the wurtzite lattice. The E2highE_2^\mathrm{high} Raman line of Zn1−x_{1-x}Mgx_xO displays systematic changes in response to the evolution of the crystal lattice upon the Mg-substitution. The red-shift and broadening of the E2highE_2^\mathrm{high} mode are explained by the expansion of hexagonal abab-dimensions, and compositional disorder of Zn/Mg, respectively. Synchrotron x-ray PDF analyses of Zn1−x_{1-x}Mgx_xO reveal that the Mg atoms have a slightly reduced wurtzite parameter uu and more regular tetrahedral bond distances than the Zn atoms. For both Zn and Mg, the internal tetrahedral geometries are independent of the alloy composition.Comment: 10 pages, 12 figures RevTe

    Diffractive point sets with entropy

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    After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of lattice gases. We show that taking the site occupation of a model set stochastically results, with probabilistic certainty, in well-defined diffractive properties augmented by a constant diffuse background. We discuss both the case of independent, but identically distributed (i.i.d.) random variables and that of independent, but different (i.e., site dependent) random variables. Several examples are shown.Comment: 25 pages; dedicated to Hans-Ude Nissen on the occasion of his 65th birthday; final version, some minor addition

    Urotropin azelate: a rather unwilling co-crystal

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    Urotropin (U) and azelaic acid (AA) form 1:1 co-crystals (UA) that give rise to a rather complex diffraction pattern, the main features of which are diffuse rods and bands in addition to the Bragg reflections. UA is characterized by solvent inclusions, parasite phases, and high vacancy and dislocation densities. These defects compounded with the pronounced tendency of U to escape from the crystal edifice lead to at least seven exotic phase transitions (many of which barely manifest themselves in a differential scanning calorimetry trace). These involve different incommensurate phases and a peritectoid reaction in the recrystallization regime (T-h >0.6). The system may be understood as an OD (order-disorder) structure based on a layer with layer group P(c)c2 and cell a(o) similar or equal to 4.7, b similar or equal to 26.1 and c similar or equal to 14.4 Angstrom. At 338 K the layer stacking is random, but with decreasing temperature the build-up of an orthorhombic MDO (maximal degree of order) structure with cell a(1) = 2a(o), b(1) = b, c(1) = c and space group Pcc2 is begun (at similar to 301 K). The superposition structure of the OD system at T = 286 (1) K with space group Bmmb and cell (a) over cap = 2a(o), (b) over cap = b and (c) over cap = c/2 owes its cohesion to van der Waals interactions between the AA chains and to three types of hydrogen bonds of varied strength between U-U and U-AA. Before reaching completion, this MDO structure is transformed, at 282 K, into a monoclinic one with cell a(m) = a(o) + c/4, b(m) = b, c(m) = -2(a(o) + c/2), space group P2(1)/c, spontaneous deformation similar to2degrees, and ferroelastic domains. This transformation is achieved in two steps: first a furtive triggering transition, which is not yet fully understood, and second an improper ferroelastic transition. At similar to 233 K, the system reaches its ground state (cell a(M) = a(m), bM = b, c(M) = c(m) and space group P2(1)/c) via an irreversible transition. The phase transitions below 338 K are described by a model based on the interaction of two thermally activated slip systems. The OD structure is described in terms of a three-dimensional Monte Carlo model that involves first- and second-neighbour interactions along the a axis and first-neighbour interactions along the b and c axes. This model includes random shifts of the chains along their axes and satisfactorily accounts for most features that are seen in the observed diffraction pattern

    Stacking faults and superstructures in a layered brownmillerite

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    Stacking faults in Ca4Fe2Mn0.5Ti0.5O9 have been examined using X-ray diffraction and high-resolution transmission electron microscopy. Electron diffraction revealed two superstructures with ordered stacking sequences
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