Apatite metaprism twist angle (φ) as a tool for crystallochemical diagnosis

[AI]4[AII]6(BO4)6X2 apatites can flexibly accommodate numerous cationic, metalloid and anionic substitutions. Using a combination of new refinements and published structures, this paper reviews correlations between substituent type and framework adaptation through adjustment of the AIO6 metaprism twist angle, φ. These systematics are illustrated through powder neutron diffraction refinement of the crystal chemistry of A10(PO4)6F2 (A=Ca, Sr) fluorapatites. Variations in φ reflect changes in the relative size of the AI4(BO4)6 framework and AII6X2 tunnel content and can be used to quantitatively assess the reliability of AI/AII cation partitioning coefficients determined by Rietveld analysis. In the simplest cases of bi-ionic substitution, the metaprism twist systematics conform to three principle trends For A-type divalent substitution, the larger A2 species preferentially enters the channel before partitioning to the framework. This leads to parabolic modification in φ across the compositional series;For B-type pentavalent compounds, the φ variation will be linear in accord with the relative B5 ionic size; andFor X-type substitution of halide anions, φ will be reduced as the average size increases. Departures from these trends may indicate polymorphism, compositional anomalies, AI/AII order disequilibrium, or poor structure refinement, and may be extended to chemically complex apatites with simultaneous substitutions over the A, B and X sites