Ab initio constrained crystal-chemical Rietveld refinement of Ca10(VxP1-xO4)6F2 apatites
Mercier, Patrick H. J.
Page, Yvon Le
White, Timothy John
Whitfield, Pamela S.
Mitchel, Lyndon D.
Date of Issue2007
School of Materials Science and Engineering
Extraction of reliable bond distances and angles for Ca10(VxP1-O4)6F2 apatites using standard Rietveld refinement with Cu Kα 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 AII 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.
Acta crystallographica B
© 2007 International Union of Crystallography. This paper was published in Acta Crystallographica B and is made available as an electronic reprint (preprint) with permission of International Union of Crystallography. The paper can be found at the following DOI: http://dx.doi.org/10.1107/S0108768106045538. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.