The solution of unknown crystal structures from X-ray powder diffraction data. Technique and an example, ZrNaH(PO4)2

An integrated system whereby the structure of an unknown polycrystalline compound can be solved from X-ray powder data, collected on a powder diffractometer, is described. The method developed falls into three main sections: accurate data collection and analysis of the pattern to give unit-cell parameters and space group; structure analysis, via Patterson/direct methods and Fourier/difference Fourier techniques using integrated intensities of unambiguously indexed peaks in the pattern; and lastly a complete Rietveld refinement analysis of the entire powder profile. The method is illustrated by the solution of the crystal structure of ZrNaH(PO4)2. This compound is monoclinic with Rietveld-refined cell parameters of a=8.8666 (3), b=5.3583 (2), c=16.1284(5) A, β=115.96 (8)0; space group P2/c and Z=4. The Na+ ions are in twofold special positions halfway between the α-zirconium phosphate layers. One of them is six coordinate with Na-O bond distances of 2.29 (9) to 2.49 (6) A. The other Na+ ion is eight coordinate with Na-O interatomic distances of 2.63(7) to 2.99 (7) A. The Zr-O and P-O bond distances and angles were found to be quite regular. Final agreement factors were Rsub(wp)=0.164, Rsub(F)=0.044 and Rsub(I)=0.07. (orig.)