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

Abstract 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 (0 β 0)0, β = 1/3, for commensurately modulated In(PO 3 ) 3 , and Cc (0 β 0)0, β = 0.36564(7), for incommensurately modulated Y(PO 3 ) 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 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.