Geometrical parameterization of the crystal chemistry of P 6 3 / m apatites: comparison with experimental data and ab initio results

• Published in: Acta crystallographica. Section B, Structural science Structural science, 2005-12, Vol.61 (6), p.635-655
• Main Authors: Mercier, Patrick H. J., Le Page, Yvon, Whitfield, Pamela S., Mitchell, Lyndon D., Davidson, Isobel J., White, T. J.
• Format: Article
• Language: English
• ISSN: 0108-7681
• DOI: 10.1107/S0108768105031125

Experimental structure refinements and ab initio simulation results for 18 published, fully ordered P 6 3 / m (A^{\rm I}_4)(A^{\rm II}_6)( B O 4 ) 6 X 2 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 I O 6 )–( B O 4 ) 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 ≤ 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 (PO 4 ) 6 (Cl,F) 2 , (Ca,Cd) 10 (VO 4 ) 6 Cl 2 and (Ca,Pb,Cd) 10 (CrO 4 ) 6 Cl 2 .