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

Extraction of reliable bond distances and angles for Ca10(VxP1-xO4)6F2 apatites using standard Rietveld refinement with Cu Kalpha 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 P6(3)/m, P2(1)/m and Pm showed that both these angular parameters exhibited a linear dependence with the vanadium content.