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

Experimental structure refinements and ab initio simulation results for 18 published, fully ordered P63/m ()()(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 …–AII–O3–B–O3–AII–⋯ atoms, whereas that of a was determined from those describing (AIO6)–(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.