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

[A^I]₄[A^II]₆(BO ₄)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 A^IO₆ 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 A^I ₄(BO₄)₆ framework and A ^II ₆X₂ 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 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, 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.