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

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

[Model predictions] Model predictions made from crystal-chemical parameters as a function of the observed c/a. Legend for symbols: red= single-crystal refinements; blue= ab initio optimizations.
Experimental single-crystal and Rietveld analysis results of apatite materials are compared with ab initio simulations using a geometric crystal-chemical model involving 10 parameters and 4 constraints equivalent to unit-cell parameters (a and c) and 12 independent atom coordinates. From crystal-chemical parameters representing polyhedral distortions, the magnitude of a and c is reproduced to ±0.025Å accuracy whereas the c/a ratio is predicted to ±0.2%. Comparison of ab initio optimized structures with experimental ones shows good agreement (within ±0.5–2.0%) with only the most reliable single-crystal refinements.
P. H. J. Mercier, Y. Le Page, P. S. Whitfield, L. D. Mitchell, I. J. Davidson and T. J. White