Rietveld refinement of the langbeinite-type mixed-metal phosphate K2Ni0.5Zr1.5(PO4)3

Dipotassium [nickel(II) zirconium(IV)] tris(orthophosphate) was prepared from a self-flux in the system K2O–P2O5–NiO–K2ZrF6. The title compound belongs to the langbeinite family and is built up from two [MO6] octahedra [M = Ni:Zr with mixed occupancy in ratios of 0.21 (4):0.79 (4) and 0.29 (4):0.71 (4), respectively] and [PO4] tetrahedra interlinked via vertices into a 3 ∞[M 2(PO4)3] framework. Two independent K+ cations are located in large cavities of the framework, with coordination numbers to O2− anions of nine and twelve. The K, Ni, and Zr sites are located on threefold rotation axes.

Supporting information for this paper is available from the IUCr electronic archives (Reference: WM5021).

Experimental
A well-ground mixture of 11.8 g KPO 3 and 1.12 g NiO was placed in a platinum crucible and then was heated up to 1273 K. The temperature was kept constant during one hour and after that it was decreased to 1173 K. 4.25 g of K 2 ZrF 6 were added to the flux under stirring with a platinum stirrer (initial K:P, Zr:P and Zr:Ni ratio equal to 1.3, 0.15, and 1.0, respectively). The crystallization of the melt was performed in the temperature range from 1173 to 913 K at an rate of 25 K/h. Finally, the crucible was cooled down to room temperature. The obtained material of (I) was recovered by washing with hot deionized water. The small crystals of (I) had the form of regular tetrahedra and were of light-yellow colour. The atomic ratio of the elements in (I) was found to be 4:1:3:6 for K/Ni/Zr/P, respectively: The sample was dissolved in 80% sulfuric acid under heating. The amount of the elements was then determined by atomic emission spectroscopy with inductive coupled plasma, AES-ICP, Spectroflame Modula ICP "Spectro".

Refinement
The powder pattern of (I) was indexed in the cubic system using DICVOL-2004 (Boultif & Louër, 2004). The pattern indexing showed that the sample was a single phase. Atomic coordinates of K 1.96 Mn 0.57 Zr 1.43 (PO 4 ) 3 (Ogorodnyk et al., 2007a) were used during Rietveld refinement as a starting model. For profile refinement a pseudo-Voigt function with axial divergence asymmetry (Thompson et al., 1987) was used. First, the scaling factor, background, cell parameters etc.
were refined during profile matching. Atomic coordinates were then refined during the next step. Atomic coordinates and displacement parameters of corresponding Zr and Ni sites were constrained to be the same. Isotropic displacement parameters of all atoms were appended to the refinement. The occupancies of K, Ni and Zr were refined taking into account that the occupancies of the hexacoordinated metal site should be equal to unity which was done using occupancy constraints. As the occupancy of the K sites was found to be 1, the occupancy factors of K1 and K2 were fixed at 1. The displacement factors of the O atoms were spread over a large range which is meaningless in this case due to the quality of the powder diffraction data. Thus U iso values for all O atoms were constrained to be equal. As a result, the values of U iso and their e.s.d.'s have close values. At the final refinement cycles two geometric restraints were applied to the lengths of P-O bonds because their values were unsatisfactory for the model (without restraints, one was ≈ 1.44 Å while another was close to 1.57 Å). Experimental, calculated and difference patterns are shown in Fig. 1.

Figure 1
Results of the Rietveld refinement of K 2 Ni 0.5 Zr 1.5 (PO 4 ) 3 . Experimental (dots), calculated (red curve) and difference (blue curve) data.    The O environment of K1 + and K2 + cations for (I). Displacement ellipsoid are drawn at the 50% probability level.