Validating the model of a (3 + 1)-dimensional incommensurately modulated structure as generator of a family of compounds for the Eu 2 (MoO 4 ) 3 scheelite structure (original) (raw)
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KNd(MoO 4 ) 2 : A New Incommensurate Modulated Structure in the Scheelite Family
Chemistry of Materials, 2006
Potassium neodymium molybdenum oxide, KNd(MoO 4 ) 2 , has been synthesized by the solid-state method. The structure and microstructure have been studied by X-ray powder diffraction and transmission electron microscopy (TEM). TEM revealed that the KNd(MoO 4 ) 2 structure is incommensurately modulated. The scheelite-like structure of KNd(MoO 4 ) 2 has been refined from X-ray powder diffraction intensities in the (3 + 1)D superspace group I2/b(R 0)00 with a ) 5.5202(2) Å, b ) 5.33376(5) Å, c ) 11.8977(3) Å, γ ) 90.9591(7)°, and modulation vector q ) 0.57789(4)a* -0.14748(6)b* (R P ) 3.09%, R wP ) 4.04%). The ordering of the K and Nd cations appears to be the primary parameter of the structure modulations. The compositional wave of the {KMoO 4 } and {NdMoO 4 } distribution is observed in the ab structure projection. The incommensurability of the compositional wave direction with respect to the a and b lattice constants is regarded as the origin of the incommensurate structure modulations.
Inorganic chemistry, 2014
The factors mediating cation ordering in the scheelite-based molybdates and tungstates are discussed on the basis of the incommensurately modulated crystal structures of the CaEu2(BO4)4 (B = Mo, W) red phosphors solved from high-resolution synchrotron powder X-ray diffraction data. Monoclinic CaEu2(WO4)4 adopts a (3 + 1)-dimensionally modulated structure [superspace group I2/b(αβ0)00, a = 5.238 73(1)Å, b = 5.266 35(1) Å, c = 11.463 19(9) Å, γ = 91.1511(2)°, q = 0.56153(6)a* + 0.7708(9)b*, R(F) = 0.050, R(P) = 0.069], whereas tetragonal CaEu2(MoO4)4 is (3 + 2)-dimensionally modulated [superspace group I4₁/a(αβ0)00(-βα0)00, a = 5.238 672(7) Å, c = 11.548 43(2) Å, q1 = 0.55331(8)a* + 0.82068(9)b*, q2 = -0.82068(9)a* + 0.55331(8)b*, R(F) = 0.061, R(P) = 0.082]. In both cases the modulation arises from the ordering of the Ca/Eu cations and the cation vacancies at the A-sublattice of the parent scheelite ABO4 structure. The cation ordering is incomplete and better described with harmonic ...
Quantitative crystal structure descriptors from multiplicative congruential generators
Acta crystallographica. Section A, Foundations of crystallography, 2012
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Acta Crystallographica Section B-structural Science, 2002
The basic principles of a model predicting new lattices from a known crystal structure is described. The first of the two-step procedure consists in extracting one-or two-dimensional periodic fragments (PF) from the mother structure. In the second step, symmetry operators are added to the PFs in order to generate one or several new three-dimensional lattices consistent with the 230 space groups. Most of the examples are related to polymorphism, but relationships between racemic compounds and enantiomers, twinning and lamellar epitaxy phenomena are also exemplified.
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