The restrained Rietveld refinement of modulated trivalent metal polyphosphates M(PO_3)_3

摘要

Room temperature X-ray powder diffraction data were used to investigate modulated crystal structures of two monoclinic polyphosphates of crystal form C, In(PO_3)_3 and Y(PO_3)_3, by the Rietveld refinement. The structures were refined with the program JANA2006 in the superspace groups Xc(00)0, = 1/3, for commensurately modulated In(PO_3)_3, and Cc(0β0)0, β = 0.36564(7), for incommensurately modulated Y(PO_3)_3. The positional modulations were described with the firstorder harmonic functions. The Rietveld refinement was performed with soft restraints on bond lengths and valence angles in PO_4 tetrahedra, as well as on angles in MO_6 octahedra. No initial information about modulation parameters was used. A good agreement of the observed and calculated intensities of main and satellite reflections was achieved for both compounds. Obtained modulated structures of In(PO_3)-3 and Y(PO_3)_3 are close to published single crystal data.