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

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[ A I] 4[ A II] 6( BO 4) 6 X 2 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 A IO 6 metaprism twist angle, φ. These systematics are illustrated through powder neutron diffraction refinement of the crystal chemistry of A 10(PO 4) 6F 2 ( A=Ca, Sr) fluorapatites. Variations in φ reflect changes in the relative size of the A I 4( BO 4) 6 framework and A II 6 X 2 tunnel content and can be used to quantitatively assess the reliability of A I/ A II cation partitioning coefficients determined by Rietveld analysis. In the simplest cases of bi-ionic substitution, the metaprism twist systematics conform to three principle trends (i) For A-type divalent substitution, the larger A 2 + species preferentially enters the channel before partitioning to the framework. This leads to parabolic modification in φ across the compositional series; (ii) For B-type pentavalent compounds, the φ variation will be linear in accord with the relative B 5+ ionic size; and (iii) For X-type substitution of halide anions, φ will be reduced as the average size increases. Departures from these trends may indicate polymorphism, compositional anomalies, A I /A II order disequilibrium, or poor structure refinement, and may be extended to chemically complex apatites with simultaneous substitutions over the A, B and X sites.