Structural derivation and crystal chemistry of apatites

Abstract
The crystal structures of the [A(1)2][A(2)3](BO4)3 X apatites and the related compounds [A(1)2][A(2)3](BO5)3 X and [A(1)2][A(2)3](BO3)3 X 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 P63 cm. 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)3 X apatites that were surveyed was P63/m (57%), with progressively more complex chemistries adopting P63 (21%), P\bar 3 (9%), P\bar 6 (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.
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