Ab initio constrained crystal-chemical Rietveld refinement of Ca ₁₀(V_xP_1-xO₄)₆F ₂

Extraction of reliable bond distances and angles for Ca10(V x P1 - x O4)6F2 apatites using standard Rietveld refinement with Cu K X-ray powder data was significantly impaired by large imprecision for the O-atom coordinates. An initial attempt to apply crystal-chemical Rietveld refinements to the same compounds was partly successful, and exposed the problematic determination of two oxygen-metal-oxygen angles. Ab initio modeling with VASP in space groups P63/m, P21/m and Pm showed that both these angular parameters exhibited a linear dependence with the vanadium content. Stable crystal-chemical Rietveld refinements in agreement with quantum results were obtained by fixing these angles at the values from ab initio simulations. Residuals were comparable with the less precise standard refinements. The larger vanadium ion is accommodated primarily by uniform expansion and rotation of BO4 tetrahedra combined with a rotation of the Ca-Ca-Ca triangular units. It is proposed that the reduction of symmetry for the vanadium end-member is necessary to avoid considerable departures from formal valences at the A ^II and B sites in P63/m. The complementarity of quantum methods and structural analysis by powder diffraction in cases with problematic least-squares extraction of the crystal chemistry is discussed.