Crystal Structure of the Transition‐Metal Molybdates and Tungstates. II. Diamagnetic Sc2(WO4)3
15 Oct 1966-Journal of Chemical Physics (American Institute of Physics)-Vol. 45, Iss: 6, pp 2745-2752
TL;DR: Sc2(WO4)3, diamagnetic above 30°K, crystallizes in the orthorhombic system, Space Group Pnca, with lattice constants a=9.596±0.004, b=13.330± 0.003, and c= 9.512±0.004 A at 298°K as mentioned in this paper.
Abstract: Sc2(WO4)3, diamagnetic above 30°K, crystallizes in the orthorhombic system, Space Group Pnca, with lattice constants a=9.596±0.004, b=13.330±0.003, and c=9.512±0.004 A at 298°K. The complete x‐ray scattering pattern within a reciprocal lattice hemisphere of radius (sinθ)/λ=1.02 A−1 was measured with PEXRAD. The crystal structure was solved by use of three‐dimen sional Patterson and Fourier series and refined by the method of least squares, using 1731 independent structure factors. The final agreement factor R is 0.0622. Scandium atoms occupy slightly distorted octahedra, with average Sc–O=2.063 A and Sc–O distances ranging from 2.026±0.015 to 2.124±0.010 A. Two crystallographically independent W atoms are surrounded by somewhat distorted tetrahedra: the W–O distances vary from 1.695±0.009 to 1.829±0.016 A, the average being 1.761 A. The thermal vibrations are significantly anisotropic. Sc2(WO4)3 forms the structure type for 23 trivalent metal tungstates and molybdates, including the nine smaller rare‐earth tungstates. The larger rare‐earth tungstates, crystallizing in the Eu2(WO4)3 structure type, have 8 coordination about the rare‐earth ion; the smaller have 6 coordination. A simple correlation is found between the variation in radius ratio due to the lanthanide contraction and the change in coordination.
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TL;DR: In this article, it was shown that Darwin's formula for the secondary extinction correction, which has been universally accepted and extensively used, contains an appreciable error in the x-ray diffraction case.
Abstract: It is shown that Darwin's formula for the secondary extinction correction, which has been universally accepted and extensively used, contains an appreciable error in the x-ray diffraction case. The correct formula is derived. As a first order correction for secondary extinction, Darwin showed that one should use an effective absorption coefficient mu + gQ where an unpolarized incident beam is presumed. The new derivation shows that the effective absorption coefficient is mu + 2gQ(1 + cos/sup 4/2 theta )/(1 plus or minus cos/sup 2/2 theta )/s up 2/, which gives mu + gQ at theta =0 deg and theta = 90 deg , but mu + 2gQ at theta = 45 deg . Darwin's theory remains valid when applied to neutron diffraction. (auth)
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