Structural derivation and crystal chemistry of apatites

The crystal structures of the [A(1)₂][A(2)₃](BO₄)₃X apatites and the related compounds [A(1)₂][A(2)₃](BO₅)₃X and [A(1)₂][A(2)₃](BO₃)₃X are collated and reviewed. The structural aristotype for this family is Mn₅Si₃ (D8₈ type, P6₃/mcm symmetry), whose cation array approximates that of all derivatives and from which related structures arise through the systematic insertion of anions into tetrahedral, triangular or linear interstices. The construction of a hierarchy of space-groups leads to three apatite families whose high-symmetry members are P6₃/m, Cmcm and P6₃cm. Alternatively, systematic crystallographic changes in apatite solid-solution series may be practically described as deviations from regular anion nets, with particular focus on the O(1)—A(1)—O(2) twist angle φ projected on (001) of the A(1)O₆ metaprism. For apatites that contain the same A cation, it is shown that φ decreases linearly as a function of increasing average ionic radius of the formula unit. Large deviations from this simple relationship may indicate departures from P6₃/m symmetry or cation ordering. The inclusion of A(1)O₆ metaprisms in structure drawings is useful for comparing apatites and condensed-apatites such as Sr₅(BO₃)₃Br. The most common symmetry for the 74 chemically distinct [A(1)₂][A(2)₃](BO₄)₃X apatites that were surveyed was P6₃/m (57%), with progressively more complex chemistries adopting P6₃ (21%), P (9%), P (4.3%), P2₁/m (4.3%) and P2₁ (4.3%). In chemically complex apatites, charge balance is usually maintained through charge-coupled cation substitutions, or through appropriate mixing of monovalent and divalent X anions or X-site vacancies. More rarely, charge compensation is achieved through insertion/removal of oxygen to produce BO₅ square pyramidal units (as in ReO₅) or BO₃ triangular coordination (as in AsO₃). Polysomatism arises through the ordered filling of [001] BO₄ tetrahedral strings to generate the apatite–nasonite family of structures.