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

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)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 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 ≤ 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.