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Ab initio constrained crystal-chemical Rietveld refinement of Ca10(VxP1–xO4)6F2 apatites

Acta Cryst. (2007). B63, 37–48 [doi:10.1107/S0108768106045538]

[Rietveld diagram]Standard (red) and ab initio constrained crystal chemical (blue) Rietveld refinement results for Ca10(VxP1-xO4)6F2 apatites compared with accurate single-crystal refinements and ab initio simulations for known P63/m end-member structures (black).
Extraction of reliable distances and angles for Ca10(VxP1–xO4)6F2 apatites using standard Rietveld refinement was impaired by large imprecision for O-atom coordinates with X-ray powder data. Constraining crystal-chemical Rietveld refinements for two oxygen–metal–oxygen angles with results from ab initio modeling produced experimental results in agreement with quantum ones and residuals similar to unconstrained standard refinements. Ab initio simulations were performed with VASP and Materials Toolkit ( Expansion of BO4 tetrahedra and rotation of Ca–Ca–Ca triangular units are observed upon replacement of phosphorus by vanadium. The crystal-chemical refinement method provides more accurate bond angles than standard refinement of the same data. Complementarity of quantum methods and problematic least-squares structural analyses of crystal chemistry is discussed.
P.H.J. Mercier, Z. Dong, T. Baikie, Y. Le Page, T.J. White, P.S. Whitfield and L.D. Mitchel