**1.4. Chemical composition of apatite supergroup minerals**

The general formula of apatite compounds several times mentioned above (Ca10(PO4)6(F,Cl,O)2 or 3Ca3(PO4)2·Ca(F2,Cl2,O) was given by VOELCKER [74] and HOSKYNS-ABRAHALL [137]. RAMMELSBERG [138] assumed the existence of compound Ca10P6O25 (equiva‐ lent to 3Ca3(PO4)2⋅CaO) to explain the chemical composition of various apatites, although he thought the presence of this molecule was due to alteration. GROTH [139] substituted hydrox‐ yl for oxygen and gave the formula (PO4)3(Cl,F,OH)Ca5. He was followed by LACROIX, NAUMANN-ZIRKEL and others [73]. Many minerals of the apatite group are deficient in com‐ bined fluorine and chlorine [73],[74],[140]. This deficiency was generally explained by assuming the compound 3Ca3(PO4)2·Ca(OH)2 [73].

Based on the results of chemical analysis, the calculation of apatite formula (M5(XO4)3Z) can be determined according to the following criteria [45]:


**Fig. 10.** Schematic representation of *α* and *β*, M5X3O18Z2 apatite modules (assuming a hexagonal basal plane), which are related by [0001]hex 60°rotation twinning. The principal idealization is that the MFO6 polyhedron is represented as a trigonal prism, but in real polysomes, twisting of the triangular faces through an angle *φ* creates a metaprism (a). Stacking of a and b modules show the construction of …*β*(*αβ*)*α*… apatite–2H M10(XO4)6Z2 (1) and the hypothetical structure …*α*(*α*)*α*… apatite–1H M5(X3O9)Z polysome end members (2). The coincident lattice where the condensation

An idealized polysome module of apatite has the composition of **M**(1)2**M**(2)3**X**3O18**Z** and the thickness of ~3.5Å. These modules can occupy a hexagonal unit cell in two orientations, designated **α** and **β** layers **Fig. 10**(**a**), which are rotated by 60° with respect to each other, with the condensation leading to the elimination of oxygen from coincident lattice position. The layers joint without the rotation create corner-connected B*n*O3*n*+1 (*n* = ∞) tetrahedral strings,

**Fig. 11.** Expanded apatite phase space containing all permutations of polymorphs, pseudomorphs, polysomes and hy‐

brid structures, which may be feasible [109].

and elimination of oxygen take place is emphasized by brackets (MT and Z ions are not included) (b) [109].

22 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

In principle, criterion a is preferable to criteria b and c. In fact, the calculation based on any subset of all atoms does not affect the stoichiometric ration between them but automatically shifts the analytical error to the atoms not belonging to that subset. Criteria b and c would be best to use in cases in which structural vacancies are possible at some sites, but this does not seem to be the case for any apatite supergroup minerals [45].

Cations P5+, As5+, V5+, Si4+ and S6+ can be assumed to be in tetrahedral coordination and assigned to *X* site in the formula of apatite. The total sum of these cation should be equal to 3 apfu36 (in the single formula M(1)2M(2)3(XO4)3Z). All remaining cations enter **M**(1) and **M**(2) sites. The elucidation of partitioning between these two sites is almost impossible without an accurate evaluation of the electron density at each of them, which makes the structural study manda‐

<sup>36</sup> The abbreviation for **a**toms **p**er **f**ormula **u**nit (**apfu**).

tory. Generally, **M**(1) sites (Wyckoff positions *4f* in P63/M structure, **Table 5**) are occupied by smaller cations (in particular Ca) and **M**(2) sites (Wyckoff positions *6h*) accommodate larger cation37 such as Ba2+ or Pb2+ [45].
