Acta Crystallographica Section B

Structural Science

Volume 61, Part 6 (December 2005)

research papers

Acta Cryst. (2005). B61, 635-655 [ doi:10.1107/S0108768105031125 ]

Geometrical parameterization of the crystal chemistry of P6₃/m apatites: comparison with experimental data and ab initio results

P. H. J. Mercier, Y. Le Page, P. S. Whitfield, L. D. Mitchell, I. J. Davidson and T. J. White

Abstract: Experimental structure refinements and ab initio simulation results for 18 published, fully ordered P6₃/m ( $A^{\rm I}_4$ )( $A^{\rm II}_6$ )(BO₄)₆X₂ apatite end-member compositions have been analyzed in terms of a geometric crystal-chemical model that allows the prediction of unit-cell parameters (a and c) and all atom coordinates. To an accuracy of ± 0.025 Å, the magnitude of c was reproduced from crystal-chemical parameters characterizing chains of ...-A^II-O3-B-O3-A^II- atoms, whereas that of a was determined from those describing (A^IO₆)-(BO₄) polyhedral arrangements. The c/a ratio could be predicted to ±0.2% using multi-variable functions based on geometric crystal-chemical model predictions, but could not be ascribed to the adjustment of a single crystal-chemical parameter. The correlations observed between algebraically independent crystal-chemical parameters representing the main observed polyhedral distortions reveal them as the minimum-energy solution to accommodate misfit components within this flexible structure type. For materials with given composition, good agreement (within ± 0.5-2.0%) of ab initio crystal-chemical parameters was observed with only those from single-crystal refinements with R [less-than or equal to] 4.0%. Agreement with single-crystal work with R > 4.0% was not as good, while the scatter with those from Rietveld refinements was considerable. Accordingly, ab initio cell data, atomic coordinates and crystal-chemical parameters were reported here for the following compositions awaiting experimental work: (Zn,Hg)₁₀(PO₄)₆(Cl,F)₂, (Ca,Cd)₁₀(VO₄)₆Cl₂ and (Ca,Pb,Cd)₁₀(CrO₄)₆Cl₂.

Keywords: apatite; crystal chemistry; geometric crystal-chemical modelling; ab initio calculations; crystal structure analysis.


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