The restrained Rietveld refinement of modulated trivalent metal polyphosphates M(PO3)3

Abstract

Abstract Room temperature X-ray powder diffraction data were used to investigate modulated crystal structures of two monoclinic polyphosphates of crystal form C, In(PO3)3 and Y(PO3)3, by the Rietveld refinement. The structures were refined with the program JANA2006 in the superspace groups Xc(0β0)0, β = 1/3, for commensurately modulated In(PO3)3, and Cc(0β0)0, β = 0.36564(7), for incommensurately modulated Y(PO3)3. The positional modulations were described with the first-order harmonic functions. The Rietveld refinement was performed with soft restraints on bond lengths and valence angles in PO4 tetrahedra, as well as on angles in MO6 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(PO3)3 and Y(PO3)3 are close to published single crystal data.