Geometrical parameterization of the crystal chemistry of P6(3)/m apatites: comparison with experimental data and ab initio results

摘要

Experimental structure refinements and ab initio simulation results for 18 published, fully ordered P6(3)/m (A(4)(I))(A(6)(II))(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 angstrom, 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))-(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)(6)Cl-2 and (Ca,Pb,Cd)(10)(CrO4)(6)Cl-2.