**1.2. The crystal structure of apatite minerals**

The stoichiometric end-member formula for phosphate-bearing apatites is M10(PO4)6Z2 (Z = 2) (reduced formula M5(PO4)3Z (Z = 2) can be used [45]), where *M* and *Z* represent divalent cations and monovalent anion, respectively. In the case of oxyapatites (M10(PO4)6O), 2Z<sup>−</sup> ions are replaced by O2− [37]. Various representations of orthophosphate ion are introduced in **Fig. 5**.

**Fig. 5.** Representation used for orthophosphate anion [106].

The PO4 unit in the apatite structure can be partially substituted by AsO4 (e.g. hedyphane (Ca2Pb3(AsO4)3Cl) [102] and minerals from the group of pyromorphite (Pb5(PO4)3Cl [17],[52], etc.), SiO4, SO4, VO4 (vanadinite (Pb5(VO4)3Cl) [103] and CO3 29 [104],[105]. **Table 4** compares the properties of orthophosphate anion with other isoelectronic ortho-oxyanions [106].

<sup>27</sup> Breccias are among the most common features in ore deposits. They are associated with numerous types of ores, of either endogenic or supergenic origin, and in both subsurface and submarine environments. Breccia is a rock composed of angular fragments of preexisting rocks embedded in fine-grained matrix cement [101].

<sup>28</sup> The Commission on New Minerals, Nomenclature and Classification (CNMNC) of the International Mineralogical Association (IMA) was formed in July 2006 by a merger between the Commission on New Minerals and Mineral Names (CNMMN) and the Commission on Classification of Minerals, at the request of both commissions.

<sup>29</sup> Please see the discussion dedicated to the nomenclature of other minerals with the structure of apatite in **Section 1.1**.


**Table 4.** The comparison of properties of isoelectric ortho-oxyanions [106].

**• Saamite**: a rare earth element–strontian or calcium variety of fluorapatite of the composi‐ tion of (Ca,Sr,REE)5(PO4)3(F,O) [40],[94]. According to VOLKOVA AND MELENTIEV [95 ], it is a saamite variety of apatite containing 5.58–11.42% SrO. Currently, the mineral name saamite refers to IMA approved mineral of the composition of Ba□Na3Ti2Nb(Si2O7)2O2(OH)2·2H2O from the Kirovskii mine, Mount Kukisvumchorr, Khibiny alkaline massif, Kola Peninsula,

**• Collophane**: a varietal name for massive cryptocrystalline carbonate-rich apatite23 (Ca5(PO4,CO3,OH)3(F,OH) [97]). It is often used when the specific phase of apatite cannot be identified. The deposits of collophane are often associated with fossilized bone or copro‐ lites. The term is sometimes used also in the context of bone composition and structure [98], [99]. Most of the collophane occurs as pelletal phosphorite, but some occurs as a collo‐

The list of calcium phosphate species accepted by Commission on New Minerals and Mineral

The stoichiometric end-member formula for phosphate-bearing apatites is M10(PO4)6Z2 (Z = 2) (reduced formula M5(PO4)3Z (Z = 2) can be used [45]), where *M* and *Z* represent divalent cations

replaced by O2− [37]. Various representations of orthophosphate ion are introduced in **Fig. 5**.

Short Valence bond Resonance Polarized Electronic Ionic Tetrahedron

The PO4 unit in the apatite structure can be partially substituted by AsO4 (e.g. hedyphane (Ca2Pb3(AsO4)3Cl) [102] and minerals from the group of pyromorphite (Pb5(PO4)3Cl [17],[52],

27 Breccias are among the most common features in ore deposits. They are associated with numerous types of ores, of either endogenic or supergenic origin, and in both subsurface and submarine environments. Breccia is a rock composed

28 The Commission on New Minerals, Nomenclature and Classification (CNMNC) of the International Mineralogical Association (IMA) was formed in July 2006 by a merger between the Commission on New Minerals and Mineral Names

29 Please see the discussion dedicated to the nomenclature of other minerals with the structure of apatite in **Section 1.1**.

properties of orthophosphate anion with other isoelectronic ortho-oxyanions [106].

and monovalent anion, respectively. In the case of oxyapatites (M10(PO4)6O), 2Z<sup>−</sup>

O- O- O-

O O O

O

etc.), SiO4, SO4, VO4 (vanadinite (Pb5(VO4)3Cl) [103] and CO3

of angular fragments of preexisting rocks embedded in fine-grained matrix cement [101].

(CNMMN) and the Commission on Classification of Minerals, at the request of both commissions.

3-

P5+ O2 O- PO4

P P P O P

[100],[101].

ions are

O2-

[104],[105]. **Table 4** compares the

O2-

of International Mineralogical Association (IMA) [67] is given in **Table 3**.

O- O2-

29

O O O

phane mudstone and as cement in sedimentary breccia27

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

**1.2. The crystal structure of apatite minerals**

O

**Fig. 5.** Representation used for orthophosphate anion [106].

Russia [96].

Names (CNMMN)28

O-

O

3-

The crystal structure of apatite (*sensu stricto* fluorapatite) was first independently solved in 1930 by MEHMEL [107] and NÁRAY-SZABÓ [108]. The archetype crystalline30 structure of apatite is hexagonal with the space group P63/M and the unit-cell parameters *a* = 9.3–9.6 and *c* = 6.7–6.9 Å. The above-mentioned generic crystal-chemical formula can be also written as follows [45], [109],[148]:

> () ( ) () ( ) ( ) VII IX IV 4 6 <sup>2</sup> <sup>2</sup> <sup>6</sup> M 1 M 2 XO 1 O 2 O 3 Z ; é ù ë û

<sup>30</sup> The term crystalline means atomic ordering on the scale that can produce an "idexable" (i.e. with Mille indices) diffraction pattern when the substance is traversed by a wave with suitable wavelength (X-ray, electrons, neutrons, etc.). However, some amorphous substances (e.g. georgeite, calciouranoite) were also accepted as minerals by the CNMMN.

**Fig. 6.** Vertical symmetry elements of the space group P63/M (a) [38] and the crystal structure of apatite as seen along *c*axis (b) [45].

where left superscripts indicate ideal coordination numbers. **M** represents large cations, **X** represents metal or metalloids and **Z<sup>−</sup>** represents anion (sometimes termed as column anion) [109].

Minerals from apatite group belong to the hexagonal–dipyramidal crystal system with the space group P63/M (fluorapatite, hydroxylapatite and chlorapatite [45]), to trigonal–pyrami‐ dal system with the space group P3 (belovite–Ce [110]), also to trigonal–rhomobohedral system with the space group *P*3 ¯ (belovite–La [45],[111]) and to hexagonal–pyramidal system with the space group P63 (fluorcaphite [45],[112],[113]).

Fluorapatite (Ca10(PO4)6F2, FA), chlorapatite (Ca10(PO4)6Cl2, ClA) and hydroxylapatite (Ca10(PO4)6OH2, HA) are the most important end members of apatite groups of minerals (**Table 7**). The hexagonal (P63/M) and monoclinic (P21/B) polymorphs31 of apatite were described in literature [45],[104],[114].

The P63/M space group **Fig. 6**(**a**) has three kinds of vertical symmetry elements [37]:


There are also mirror planes perpendicular to the *c*-axis and *z* = ¼, *z* = ¾ and numerous centers of symmetry.

<sup>31</sup> Polymorphic minerals are those that have essentially the same chemical composition but different crystal structures. The polymorphic forms of minerals are considered as different species if their structures are topologically different. For example, graphite and carbon are polymorphs of crystalline carbon; both have the same composition, but their structures are topologically different and therefore the minerals such as these are considered as separate species [4].

**Fig. 7.** The nearest neighbor of Ca(1)O9 and Ca(2)O5Z(O) cationic polyhedral sites in the apatite structure (a) [115] and in the structure of [PO4] 3− tetrahedra (b) [33].

The P63/M structure of calcium apatites **Fig. 6**(**b**) consists of isolated PO4 (in general XO4) tetrahedra centered at *z* = ¼ and ¾ are linked by **Ca(1)** (**M**(1)) in ninefold (6+3, 3 × O1, 3 × O2 and 3 × O3 atoms) coordinated cation polyhedron (**M**(1)O9) with a **Ch** site symmetry and **Ca(2)** (**M**(**2**)) in irregular sevenfold (6+1, O1, O2 and 4 × O3 + **Z**) coordinated polyhedron (**M**(2)O5**Z**(O) with **Cs** site symmetry (**Fig. 7**). The **M**(1)O9 polyhedra share (0001) pinacoid10 faces to form channel parallel to *c-*axis. In some cases, the **M**(**1**) sites are split into pairs of nonequivalent sites, which correspond to lowering of space group symmetry. The **M**(**2**) sites may be more irregular and the central cation may be considered to be eightfold (**M**(2)O5**Z**) or ninefold (**M**(2)O5**Z**(O)) coordinated. A prominent feature of the structure is large *c*-axis channels (apatitic channels [105] or anionic columns), which accommodate **Z** anion (**Fig. 8**). In other words, the **M**(1)4(**X**O4)6 framework creates tunnels with the diameter adjusted to filling characteristics of **M**(2)O5**Z**(O) components [33],[109],[115],[116].

where left superscripts indicate ideal coordination numbers. **M** represents large cations, **X**

**Fig. 6.** Vertical symmetry elements of the space group P63/M (a) [38] and the crystal structure of apatite as seen along *c*-

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

Minerals from apatite group belong to the hexagonal–dipyramidal crystal system with the space group P63/M (fluorapatite, hydroxylapatite and chlorapatite [45]), to trigonal–pyrami‐ dal system with the space group P3 (belovite–Ce [110]), also to trigonal–rhomobohedral system

Fluorapatite (Ca10(PO4)6F2, FA), chlorapatite (Ca10(PO4)6Cl2, ClA) and hydroxylapatite (Ca10(PO4)6OH2, HA) are the most important end members of apatite groups of minerals

**1.** Sixfold screw axes passing through the corners of the unit cells. These symmetry elements are equivalent to a threefold rotation axis with a superimposed twofold screw axis.

There are also mirror planes perpendicular to the *c*-axis and *z* = ¼, *z* = ¾ and numerous centers

<sup>31</sup> Polymorphic minerals are those that have essentially the same chemical composition but different crystal structures. The polymorphic forms of minerals are considered as different species if their structures are topologically different. For example, graphite and carbon are polymorphs of crystalline carbon; both have the same composition, but their structures

are topologically different and therefore the minerals such as these are considered as separate species [4].

(**Table 7**). The hexagonal (P63/M) and monoclinic (P21/B) polymorphs31

**2.** Threefold rotation axes passing through 2/3, 1/3, 0 and 1/3, 2/3, 0.

The P63/M space group **Fig. 6**(**a**) has three kinds of vertical symmetry elements [37]:

**3.** Twofold screw axes passing through the midpoints of the cell edges and its center.

represents anion (sometimes termed as column anion)

of apatite were

¯ (belovite–La [45],[111]) and to hexagonal–pyramidal system with the

represents metal or metalloids and **Z<sup>−</sup>**

space group P63 (fluorcaphite [45],[112],[113]).

described in literature [45],[104],[114].

with the space group *P*3

of symmetry.

[109].

axis (b) [45].

**Fig. 8.** Anion column in the hexagonal structure of fluor-, hydroxyl- and chlorapatite (a) [33] and depiction of triangle formed by Ca(2) atoms: Z′ and Z″, which denotes atoms disordered above and below the mirror plane (b) [116].

Adjacent Ca(l) and Ca(2) polyhedra are linked through oxygen atoms shared with PO4 tetrahedra. The relationships among ionic sites and multiplicity and Wyckoff positions in all known space groups of apatite supergroup mineral are shown in **Table 5** [33],[38],[45], [66], [104],[117],[118].


**Table 5.** Structure site multiplicities and Wyckoff positions for all known space groups of apatite supergroup minerals [45].

The anion column in fluorapatite **Fig. 8**(F) shows fluoride anion located on the mirror plane at *z* = ¼ and ¾ in successive unit cells. Three successive hydroxyls in hydroxylapatite (column **OH**) are disordered 0.35 Å above the mirror planes and three successive hydroxyls are below the mirror planes, with the sense of disordering reversed by an impurity of fluoride anion (stippled circle at the position *z* = 1¾). In the column "**Cl**" of chlorapatite, there are three successive anions disordered about 1.2 Å above and three below the mirror planes. The vacancy (□) at *z* = 1¾ in chlorapatite must exist in order to reverse the sense of ordering, as F and OH species are prohibited [33],[116].

Each F is bonded to three Ca(2) atoms, which form a triangle within the mirror plane **Fig. 8**(**b**) and **Fig. 16**(**b**). Because of its larger size and longer Ca–Cl bond length as compared to Ca–OH and Ca–F, Cl anions in chlorapatite are displaced from the (0,0,¼) special position on the mirror plane to two equivalent half-occupied positions at (0,0,0.4323) and (0,0,0.0677). In chlorapa‐ tite, Cl anion is displaced so far from the mirror plane (1.2 Å) that a weak bond (0.09 valence units) forms between Ca(2) and the second Cl anion, Cl′, located one-half unit cell away along *c* (Ca(2)-Cl′ bond distance is 3.27 Å). Slight overbonding of Ca(2) because of this weak Ca(2)- Cl′ interaction is balanced through reduced bonding between Ca(2) and, O(l) in chlorapatite [33].

The species-forming substitutions at the **Z** anionic site are limited to the monovalent anions F − , Cl<sup>−</sup> and OH<sup>−</sup> . This implies 50 negative charges per unit cell (i.e. 24 O2− + (F,Cl,OH)<sup>−</sup> ) for all known apatite minerals. In addition, many studies of synthetic compounds with the apatite structure show that Z site is occupied by O2−, which increases total negative charges, vacan‐ cies and water molecules. The M site can be occupied by Cd, Co, K and by almost all REE. The X site can be occupied by Be, Cr, Ge and Mn [45].

<sup>32</sup> Consists of Wyckoff letter (f) and multiplicity (4). The multiplicity of the Wyckoff position is equal to the number of equivalent points per unit cell.

**Fig. 9.** Correlation between P63/m and P21/b sites in ternary apatites [116].

known space groups of apatite supergroup mineral are shown in **Table 5** [33],[38],[45], [66],

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

**¯** *P***3**

M(1) 4f32 2 × 2b 2i, 2h 2 × 2d 2 × 1b, 2 × 1c 4f 2 × 2a M(2) 6h 6c 3k, 3j 6g 2 × 3d 2a, 2 × 2e 3 × 2a X 6h 6c 3k, 3j 6g 2 × 3d 3 × 2e 3 × 2a O 2 × 6h, 12i 4 × 4c 2 × 3k, 2 × 3j, 2 × 6l 4 × 6g 8 × 3d 6 × 2e, 3 × 4f 12 × 2a Z 2a or 2b or 4e (×0.5) 2a 1a, 1b or 2g 1a, 1b 2 × 1a 2a or 2e 2a

**Table 5.** Structure site multiplicities and Wyckoff positions for all known space groups of apatite supergroup minerals

The anion column in fluorapatite **Fig. 8**(F) shows fluoride anion located on the mirror plane at *z* = ¼ and ¾ in successive unit cells. Three successive hydroxyls in hydroxylapatite (column **OH**) are disordered 0.35 Å above the mirror planes and three successive hydroxyls are below the mirror planes, with the sense of disordering reversed by an impurity of fluoride anion (stippled circle at the position *z* = 1¾). In the column "**Cl**" of chlorapatite, there are three successive anions disordered about 1.2 Å above and three below the mirror planes. The vacancy (□) at *z* = 1¾ in chlorapatite must exist in order to reverse the sense of ordering, as F

Each F is bonded to three Ca(2) atoms, which form a triangle within the mirror plane **Fig. 8**(**b**) and **Fig. 16**(**b**). Because of its larger size and longer Ca–Cl bond length as compared to Ca–OH and Ca–F, Cl anions in chlorapatite are displaced from the (0,0,¼) special position on the mirror plane to two equivalent half-occupied positions at (0,0,0.4323) and (0,0,0.0677). In chlorapa‐ tite, Cl anion is displaced so far from the mirror plane (1.2 Å) that a weak bond (0.09 valence units) forms between Ca(2) and the second Cl anion, Cl′, located one-half unit cell away along *c* (Ca(2)-Cl′ bond distance is 3.27 Å). Slight overbonding of Ca(2) because of this weak Ca(2)- Cl′ interaction is balanced through reduced bonding between Ca(2) and, O(l) in chlorapatite

The species-forming substitutions at the **Z** anionic site are limited to the monovalent anions F

known apatite minerals. In addition, many studies of synthetic compounds with the apatite structure show that Z site is occupied by O2−, which increases total negative charges, vacan‐ cies and water molecules. The M site can be occupied by Cd, Co, K and by almost all REE. The

32 Consists of Wyckoff letter (f) and multiplicity (4). The multiplicity of the Wyckoff position is equal to the number of

. This implies 50 negative charges per unit cell (i.e. 24 O2− + (F,Cl,OH)<sup>−</sup>

**¯ P3 P21/m P21**

) for all

[104],[117],[118].

[45].

[33].

and OH<sup>−</sup>

equivalent points per unit cell.

− , Cl<sup>−</sup>

**Site P63/m P63** *P***6**

and OH species are prohibited [33],[116].

X site can be occupied by Be, Cr, Ge and Mn [45].

The difference between hexagonal and monoclinic polymorphs (e.g. apatite–(CaOH) and apatite–(CaOH)–M, see **Table 3**) lies in the position of **Z**<sup>−</sup> anions along large *c*-axis channels33 (apatitic channels or anionic columns). This gives the rise (or not) to a mirror plane but does not correspond to a large ion rearrangement [37]. As the average ionic radii increases, i.e. the size of the tunnel ion increases through the series F > OH > Cl > Br, the metaprism untwists to accommodate larger anion [45],[119]. The correlation between the column-anion sites is introduced in **Fig. 9**.

Monoclinic symmetry of mineral with the space group **P21/b** named as clinohydroxylapatite [120] and subsequently renamed as apatite–(CaOH)–M [49] has typical axial setting of apatites resulting from the orientation ordering of OH<sup>−</sup> anions within [00z] anionic columns, with consequent doubling periodicity along [010] (*b*-axis). The following unit-cell parameters are given: *a* = 9.445 Å, *b* = 18.853 Å, *c* = 6.8783 Å and *γ* = 120° [33],[45],[116].

The structure of minerals from the family of apatite allows to formulate seven requirements, including the following [109]:


<sup>33</sup> The positions of noncolumn atoms in P21/B ternary apatite are similar to those in P63/M ternary apatite [116].

