**1.3 Polysomatic apatites**

Less known polysomes of apatite are **ganomalite**34 (Pb3Ca2(SiO4)(Si2O7) [121],[122],[123]) and **nasonite**35 (Ca4Pb6(Si2O7)3Cl2 [124]) [109],[125],[126]. The concept of polysomatism was extensively developed by THOMPSON [127] and VEBLEN [128] for the crystallochemical analysis of rock-forming silicates and is a widely applied taxonomic principle for the description of condensed matter. Numerous polysome families include perovskite derivatives such as layered high **T**c superconductors [129],[130],[131],[132], fluorite superstructures found in highlevel nuclear ceramics [133] and **β**-alumina-hibonite (CaAl12O19) materials [134],[135],[136], which are encountered in superionic conductivity [109].


<sup>34</sup> Greek name reflecting luster appearance of mineral.

<sup>35</sup> Mineral is named according to American geologist LEWIS NASON.


**Table 6.** Staking sequence and compositions of polysomic apatites [109].

**5.** Polymorphic transformations initiated by the application of temperature/pressure that

**6.** Pseudomorfism whereby quite compositional adjustments lead to breaches in the critical

**7.** Polysomatism that arises by rotational twinning of M5X3O18Zδ modules in ordered and

extensively developed by THOMPSON [127] and VEBLEN [128] for the crystallochemical analysis of rock-forming silicates and is a widely applied taxonomic principle for the description of condensed matter. Numerous polysome families include perovskite derivatives such as layered high **T**c superconductors [129],[130],[131],[132], fluorite superstructures found in highlevel nuclear ceramics [133] and **β**-alumina-hibonite (CaAl12O19) materials [134],[135],[136],

*N* **Crystallochemical formulae Chemical formulae Stacking sequence**

2 M10(XO4)6Z2δ M10X6O24Z2δ 1) …*β*(*αβ*)*α*… 3 M15(X2O7)3(XO4)3Z3δ M15X9O33Z3δ 2) …*β*(*ααβ*)*α*… 4 M20(X3O10)3(XO3)3Z4δ M20X12O42Z4δ …*β*(*αααβ*)*α*… M20(X2O7)6Z4δ M20X12O42Z4δ 3) …*β*(*ααββ*)*α*… 5 M25(X4O13)3(XO4)3Z5δ M25X15O51Z5δ …*β*(*ααααβ*)*α*… M25(X3O10)3(X2O7)3Z5δ …*β*(*αααββ*)*α*… 6 M30(X5O15)3(XO4)3Z6δ M30X18O60Z6δ …*β*(*αααααα*)*α*… M30(X4O13)3(X2O7)3Z6δ …*β*(*ααααββ*)*α*… M30(X3O10)6Z6δ …*β*(*αααβββ*)*α*… 7 M35(X6O19)3(XO4)3Z7δ M35X21O69Z7δ …*β*(*ααααααβ*)*α*… M35(X5O16)3(X2O7)3Z7δ …*β*(*αααααββ*)*α*… M35(X4O13)3(X4O10)3Z7δ …*β*(*ααααβββ*)*α*… 8 M40(X7O22)3(XO4)3Z8δ M40X24O78Z8δ …*β*(*ααααααββ*)*α*… M40(X5O16)3(X3O10)3Z8δ …*β*(*αααααβββ*)*α*… M40(X4O13)6X6δ …*β*(*ααααββββ*)*α*…

(Ca4Pb6(Si2O7)3Cl2 [124]) [109],[125],[126]. The concept of polysomatism was

(Pb3Ca2(SiO4)(Si2O7) [121],[122],[123]) and

limit of the metaprism twist angle and to the change in symmetry.

changes ionic sizes to drive the framework tuning.

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

disordered sequences [109].

Less known polysomes of apatite are **ganomalite**<sup>34</sup>

which are encountered in superionic conductivity [109].

34 Greek name reflecting luster appearance of mineral.

35 Mineral is named according to American geologist LEWIS NASON.

**1.3 Polysomatic apatites**

**nasonite**<sup>35</sup>

Certain complex structures are logically considered as intergrowths of chemically or topolog‐ ically discrete modules. When the proportions of these components vary systematically, a polysomatic series is created. Certain complex structures are logically considered as inter‐ growths of chemically or topologically discrete modules. When the proportions of these components vary systematically a polysomatic series is created, the creation of which provides a basis for understanding the defects, the symmetry alternation and the trends in physical properties. The composition of polysomic family, which is formed by the condensation of *N*modules of apatite (where *N* is the number of modules in the crystallographic repeat, **Table 6**) units of M5X3O18Xδ, can be described by the formula [109]:

$$\mathbf{M\_{8N}} \\ \mathbf{X\_{3N}} \\ \mathbf{O\_{9N\*6}} \\ \mathbf{X\_N} \dots$$

The apatite modules condense in a configuration to create B*n*O3*n*+1, where the values of *n* vary in range: 1 ≤ *n* ≤ ∞. For *N* = 2, the composition of polysome corresponds to the hydroxylapa‐ tite, e.g. Ca10(PO4)6(OH)2 if **M** = Ca, **X** = P and **Z** = OH.

Based on the value of parameter *N*, the following polysomes of apatite are recognized [109]:


The *Z* site could be vacant or partially occupied as required from the charge balance, and the **M:X** ratio must be maintained 5:3 (**Table 7**).

The apatite modules, while topologically identical, are often compositionally or symmetrical‐ ly distinct and an infinite number of polysomes are feasible. The end members are the *N* = 2 polysome with all tetrahedra separated, and *N* = ∞ polysome, in which the hypothetical compound M5X3O9Z contains infinite, corner connected tetrahedral strings [109].

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

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].

which can be broken through the introduction of a rotated layer. The case when the modules are placed directly upon one another in the sequence …*α*(*α*)*α*… (**Fig. 10**(**b**)), of the composi‐ tion that corresponds to the hypothetical compounds**M**(1)2**M**(2)3**X**3O9**Z** with continuous chains of corner connected tetrahedral is created. Alternatively, if every module is rotated by 60° (rotationally twined) with respect to the order …*β*(*αβ*)*β*…, six oxygens per layer pair are duplicated in the trigonal prisms and overall composition of polysome is M(1)4M(2)6X6O24Z2. This motive can be found in the mineral mattheddleite (Pb(1)4Pb(2)6[Si/SO4]6(Cl,OH)2) [109].

The prism of expanded apatite space (**Fig. 11**) enables to formulate new derivatives via the creation of M(1)4M(2)6(XO3/XO4/XO5)6Z2 hybrids, which may display the polysomatic charac‐ ter [109].
