**6.4. Solid solutions of apatites**

Crystalline solid solutions7 [92] of apatites are frequently encountered where the possibility and type depend on the condition of formation or preparation, thermal history after forma‐ tion and the end-members of the series [2]. The structure of ternary solid solution of hexago‐ nal (P63/M, Ca5(PO4)3(F0.39Cl0.33OH0.28)) and monoclinic (P21/B, Ca5(PO4)3(F0.29Cl0.47OH0.24)) F-OH-Cl apatite was resolved by HUGHES et al [93]. Phosphate tetrahedra and Ca(l) polyhedra of both structures are generally very similar to analogous polyhedra in the end-member fluor-, chlorand hydroxylapatite structures. Ca(2) polyhedron, which includes the column anions among its ligands, exhibits significant but regular variations in interatomic distances that can be directly correlated to Cl content.

The solid solution in hexagonal ternary apatite is achieved by a 0.4 Å shift along the c-axis of Cl atom relating to its position in end-member chlorapatite. This adjustment affects the Markovian sequence8 [94] of anions in the (0,0,z) anion columns by providing a structural environment that includes column OH species at the distance of 2.96 Å from Cl. The shift of Cl atom is accompanied by splitting of Ca(2) atoms into two distinct positions as a function of the kind of anion neighbor (F or OH vs. Cl). Additional nonequivalent Cl site, similar to that in end-member chlorapatite, is also present. Those Cl atoms with adjacent OH occupy a site different from Cl atoms adjacent to vacancies in the anion column [93].

Reduction of symmetry in monoclinic ternary apatite results from the ordering of Cl and OH within the anion columns. The atomic positions of Cl and OH in the anion column are equivalent to those in hexagonal ternary apatite, but each is ordered into only one of the two hexagonal symmetry-equivalent sites [93].

The apatite supergroup minerals of the solid solution [95]:

<sup>7</sup> For the purposes of nomenclature, a complete solid-solution series without structural order of ions defining the endmembers is arbitrarily divided at 50 mol.% ("50% rule") to two portions with different names. Analogously, the 50% rule applied to members of ternary solid-solution series implies that the mineral names should be given only to the three endmembers. Each name should be applied to the compositional range from the end-member to the nearest right bisector of the sides of the composition triangle. For example, the apatite series Ca5(PO4)3(F,OH,Cl) is represented by three compositional fields of fluorapatite (A), hydroxylapatite (B) and chlorapatite (C) [92].

<sup>8</sup> Statistical model where a random sequence *k*, the probability distribution *p*(*k*) of which satisfies the equation [94]: (a) *p*(*k* ¯)= *<sup>p</sup>*(*k*1) *<sup>p</sup>*(*k*<sup>0</sup> *i*−1 |*ki* ) *p*(*ki*+1 *<sup>n</sup>* <sup>|</sup>*ki* ) ;

is referred to as the Markovian sequence or the Markovian chain.

$$\mathrm{Ca}\_{\mathrm{y}}\big[\big(PO\_{4}\big)\_{\mathfrak{z}\to\mathfrak{x}}\big(A\mathrm{s}O\_{4}\big)\_{\mathfrak{x}}\big]\_{\mathfrak{z}\to\mathfrak{z}\_{\mathfrak{y}}}\big(SO\_{4}\big)\_{\mathfrak{y}}\big(\mathrm{SiO}\_{4}\big)\_{\mathfrak{y}}\big]\_{\mathfrak{z}\_{\mathfrak{y}}}\big(OH,F,\mathrm{Cl}\big)$$

where *x* = 0 – 3 and *y* = 0 – 1.5 were found in altered calcareous xenoliths within the ignim‐ brite of the Upper Chegem caldera, Northern Caucasus, Russia. These minerals belonging to the apatite supergroup occur in all zones of skarn from the core to the contact with ignim‐ brite as follows: brucite-marble, spurrite (Ca5(SiO4)2CO3 [96]), humite (Mg7(SiO4)3(F,OH)2 [97]) and larnite9 (Ca2SiO4 [98],[99],[100],[101]) zones. They are associated with both high-tempera‐ ture minerals: reinhardbraunsite (Ca5(SiO4)2(OH)2 [102]), chegemite (Ca7(SiO4)3(OH)2 [103]), wadalite (Ca6Al5Si2O16Cl3 [104]), rondorfite (Ca8Mg(SiO4)4Cl2 [105]), cuspidine (Ca4(Si2O7)F2 [106]), lakargiite (CaZrO3 [107]) and srebrodolskite (Ca2Fe3+ 2O5 [108]), corresponding to the sanidinite metamorphic facies,10 and secondary low-temperature minerals: calcium hydrosili‐ cates (hillebrandite [113], awfillite [114], bultfonteinite [115]), hydrogarnets [116] and miner‐ als of the ettringite group [117].

The minerals of the apatite supergroup often form elongated cracked hexagonal or pseudohexagonal crystals up to 250 μm in size as well as grain aggregates. A new solid-solution series was found between ellestadite and svabite-johnbaumite (±apatite) with the ellestadite type isomorphic substitution according the following scheme [95]:

$$2\left[\text{RO}\_4\right]^{\text{J}^-} \rightarrow \left[\text{SO}\_4\right]^{\text{J}^-} + \left[\text{SiO}\_4\right]^{\text{J}^-} \tag{30}$$

where *R* = As5+ and P5+. The As content in investigated minerals decreases from the contact skarn zone with the ignimbrite towards the core of altered xenoliths (from 2.11 As pfu11 to 0), for example [95]:

**i.** Svabite:

**6.4. Solid solutions of apatites**

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

[92] of apatites are frequently encountered where the possibility

[94] of anions in the (0,0,z) anion columns by providing a structural

and type depend on the condition of formation or preparation, thermal history after forma‐ tion and the end-members of the series [2]. The structure of ternary solid solution of hexago‐ nal (P63/M, Ca5(PO4)3(F0.39Cl0.33OH0.28)) and monoclinic (P21/B, Ca5(PO4)3(F0.29Cl0.47OH0.24)) F-OH-Cl apatite was resolved by HUGHES et al [93]. Phosphate tetrahedra and Ca(l) polyhedra of both structures are generally very similar to analogous polyhedra in the end-member fluor-, chlorand hydroxylapatite structures. Ca(2) polyhedron, which includes the column anions among its ligands, exhibits significant but regular variations in interatomic distances that can be

The solid solution in hexagonal ternary apatite is achieved by a 0.4 Å shift along the c-axis of Cl atom relating to its position in end-member chlorapatite. This adjustment affects the

environment that includes column OH species at the distance of 2.96 Å from Cl. The shift of Cl atom is accompanied by splitting of Ca(2) atoms into two distinct positions as a function of the kind of anion neighbor (F or OH vs. Cl). Additional nonequivalent Cl site, similar to that in end-member chlorapatite, is also present. Those Cl atoms with adjacent OH occupy a site

Reduction of symmetry in monoclinic ternary apatite results from the ordering of Cl and OH within the anion columns. The atomic positions of Cl and OH in the anion column are equivalent to those in hexagonal ternary apatite, but each is ordered into only one of the two

 For the purposes of nomenclature, a complete solid-solution series without structural order of ions defining the endmembers is arbitrarily divided at 50 mol.% ("50% rule") to two portions with different names. Analogously, the 50% rule applied to members of ternary solid-solution series implies that the mineral names should be given only to the three endmembers. Each name should be applied to the compositional range from the end-member to the nearest right bisector of the sides of the composition triangle. For example, the apatite series Ca5(PO4)3(F,OH,Cl) is represented by three

A

B C

Statistical model where a random sequence *k*, the probability distribution *p*(*k*) of which satisfies the equation [94]:

different from Cl atoms adjacent to vacancies in the anion column [93].

Crystalline solid solutions7

directly correlated to Cl content.

hexagonal symmetry-equivalent sites [93].

The apatite supergroup minerals of the solid solution [95]:

compositional fields of fluorapatite (A), hydroxylapatite (B) and chlorapatite (C) [92].

Markovian sequence8

7

8

(a) *p*(*k*

¯)= *<sup>p</sup>*(*k*1) *<sup>p</sup>*(*k*<sup>0</sup>

*i*−1 |*ki* ) *p*(*ki*+1 *<sup>n</sup>* <sup>|</sup>*ki* ) ;

is referred to as the Markovian sequence or the Markovian chain.

Ca5[(AsO4)2.01(PO4)0.33(SiO4)0.33(SO4)0.33]3[F0.58(OH)0.30Cl0.12]̅1;

**ii.** As-bearing fluorapatite:

Ca5[(PO4)1.56(AsO4)1.06(SiO4)0.19(SO4)0.19]3[F0.59(OH)0.35Cl0.06]̅1;

**iii.** As-bearing hydroxylellestadite:

Ca5[(SiO4)1.25(SO4)1.25(AsO4)0.43(PO4)0.07]3[(OH)0.70Cl0.20F0.10]̅1;

**iv.** Si, S-bearing hydroxylapatite:

Ca5[(PO4)0.95(SO4)0.93(SiO4)0.93(AsO4)0.19]3[(OH)0.67Cl0.18F0.15]̅1;

<sup>9</sup> The name is also often used for synthetic phase of the same composition (dicalcium silicate, Ca2SiO4, C2S), which is the main component of belite in Portland cement [99],[100],[101].

<sup>10</sup> Since sanidinite facies are formed under conditions of intensive contact metamorphosis at high temperatures and low pressure, volatiles such as carbon dioxide and water are removed from the rock. The components characteristic for the sanidinite facies are sanidine (feldspar, KAlSi3O8 [109]), corundum (oxide, Al2O3 [110]), cordierite (cyclosilicate, Mg2Al4Si5O18 [111]), sillimanite (nesosilicate, Al2OSiO4 [112]) and glass formed as the product of partial fusion.

<sup>11</sup> The abbreviation for per formula unit (pfu), see also **Footnote 36** in **Chapter 1**.

**v.** Hydroxylellestadite:

Ca5[(SO4)1.49(SiO4)1.49(PO4)0.02]3[(OH)0.74F0.13Cl0.13]̅1.

The crystals of As-bearing phases belonging to the investigated solid solution are heteroge‐ neous and small in size. Therefore, X-ray single-crystal data were obtained for only Si, S, Asbearing hydroxylapatite (see the formula above): P63/M, *a* = 9.5193 Å, *c* = 6.9052 Å, *V* = 541.90 Å3 and *Z* = 4. The Raman spectroscopy also confirms that the investigated samples belong to the arsenate phosphate-silicate-sulfate multiple solid solution [95].

The hydrothermal synthesis of vanadate/phosphate hydroxyapatite solid solutions of the composition of Ca10(VO4)x(PO4)6−x(OH)2, where x = 0, 1, 2, 3, 4, 5 and 6, was firstly reported by ONDA et al [118]. The lattice parameters increased linearly with increasing content of vanadi‐ um according to Vegard's law. The apatite crystals were precipitated in the form of column crystals with the length of about 40 – 100 nm and the width of about 25 – 40 nm. The sizes of the nanoparticle solid solutions increased with increasing vanadium content, whereas the morphology was independent of the vanadate/phosphate ratio. Calcium hydroxyapatites substituted with vanadate were also prepared by SUGIYAMA et al [119] and used as catalysts in oxidative dehydrogenation of propane. The catalytic activity12 of vanadate-substituted calcium hydroxyapatites was evidently greater than that of magnesium pyrovanadate, which is one of the most active catalysts for this oxidation.

The crystal structure of 11 samples of synthetic Na-Ca-sulfate apatite systems of the compo‐ sition of Na6.45Ca3.55(SO4)6(FxCl1−x)1.55, where *x* = 0 – 1, was refined by PIOTROWSKI et al [120] in the P63/M space group (*Z* = 1). The sulfate tetrahedra and the two symmetrically independ‐ ent cation polyhedra around M(1) and M(2) (occupied by Na and Ca, respectively) are generally very similar to analogous polyhedra in phosphate apatites. A common structural feature of all members of the solid-solution series is the deficiency in total Cl<sup>−</sup> and F<sup>−</sup> content compared to phosphate apatites. The mean value of (Cl + F) forthe solid solution equals 1.55(6) atoms per unit cell compared to the ideal value of 2 atoms per unit cell observed in phos‐ phate apatites. The solid-solution series Na6.45Ca3.55(SO4)6Cl1.55 + Na6.45Ca3.55(SO4)6F1.55 shows a gap towards the side of fluoride-rich compounds. Under ambient pressure, the gap exists between 0 < *n*Cl/*n*Cl + *n*F < 0.33, where *n*Cl and *n*F represent the numbers of Cl- and F-atoms per unit cell, respectively.

Lead apatites form a family of isomorphous compounds, and well-known members of the group are mimetite (Pb5(AsO4)3Cl, **Section 1.6.7**) and pyromorphite (Pb5(PO4)3Cl, **Sec‐ tion 1.6.4**). Isostructural with vanadinite Pb5(VO4)3Cl, these three constituents form a ternary system within the apatite group of P63/M symmetry (hexagonal bipyramid). The mimetite and pyromorphite structures can incorporate numerous admixtures, mainly Ca, Ba, As, V, P and others. The most common substitution is the isovalent replacement of part of Pb with Ca and As with P and V. Extensive substitution of (AsO4) 3− group by tetrahedrally coordinated and isovalent (PO4) 3− ion is well established by the existence of a complete solid solution between mimetite and pyromorphite [121].

<sup>12</sup> The utilization of apatites as catalysts is described in **Section 10.7.**

A number of compounds of the mimetite Pb5(AsO4)3Cl-pyromorphite Pb5(PO4)3Cl solidsolution series were synthesized at room temperature by BAJDA et al [121] and investigated with Raman and infrared spectroscopy. The peak positions of the dominant antisymmetric stretching (*ν*3) and bending (*ν*4) vibrations in the 720 – 1040 cm−1 and 400 – 580 cm−1 regions of the Raman and IR spectra of minerals from the mimetite-pyromorphite series vary primarily as a function of the As/(As + P) ratio in the solids' structure. It is due to the effect of the atomic mass and bond forces on the banding energies of the substituting tetrahedra. The observed correlation between the band positions and the extent of the anionic substitution among the series can be used to estimate the As and P content in mimetite-pyromorphite solid solu‐ tions [121].

Solid solutions of Pb8M2(XO4)6 lead alkali apatites were studied by MAYER et al [122]. The Pb8Na2−xKx(PO4)6, Pb8Na2−xKx(AsO4)6, Pb8Na2−xRbx(PO4)6 and Pb8K2−xRbx(PO4)6 compounds crystallize at all compositions in the P63/M hexagonal apatite structure and form true solid solutions.

Some other examples of apatite solid solutions are listed below [2]:

**•** Ca2Y8(SiO4)6O2 – Ca8Y2(PO4)6O2;

**v.** Hydroxylellestadite:

Å3

Ca5[(SO4)1.49(SiO4)1.49(PO4)0.02]3[(OH)0.74F0.13Cl0.13]̅1.

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

the arsenate phosphate-silicate-sulfate multiple solid solution [95].

oxidative dehydrogenation of propane. The catalytic activity12

the most active catalysts for this oxidation.

As with P and V. Extensive substitution of (AsO4)

12 The utilization of apatites as catalysts is described in **Section 10.7.**

mimetite and pyromorphite [121].

unit cell, respectively.

isovalent (PO4)

The crystals of As-bearing phases belonging to the investigated solid solution are heteroge‐ neous and small in size. Therefore, X-ray single-crystal data were obtained for only Si, S, Asbearing hydroxylapatite (see the formula above): P63/M, *a* = 9.5193 Å, *c* = 6.9052 Å, *V* = 541.90

and *Z* = 4. The Raman spectroscopy also confirms that the investigated samples belong to

The hydrothermal synthesis of vanadate/phosphate hydroxyapatite solid solutions of the composition of Ca10(VO4)x(PO4)6−x(OH)2, where x = 0, 1, 2, 3, 4, 5 and 6, was firstly reported by ONDA et al [118]. The lattice parameters increased linearly with increasing content of vanadi‐ um according to Vegard's law. The apatite crystals were precipitated in the form of column crystals with the length of about 40 – 100 nm and the width of about 25 – 40 nm. The sizes of the nanoparticle solid solutions increased with increasing vanadium content, whereas the morphology was independent of the vanadate/phosphate ratio. Calcium hydroxyapatites substituted with vanadate were also prepared by SUGIYAMA et al [119] and used as catalysts in

hydroxyapatites was evidently greater than that of magnesium pyrovanadate, which is one of

The crystal structure of 11 samples of synthetic Na-Ca-sulfate apatite systems of the compo‐ sition of Na6.45Ca3.55(SO4)6(FxCl1−x)1.55, where *x* = 0 – 1, was refined by PIOTROWSKI et al [120] in the P63/M space group (*Z* = 1). The sulfate tetrahedra and the two symmetrically independ‐ ent cation polyhedra around M(1) and M(2) (occupied by Na and Ca, respectively) are generally very similar to analogous polyhedra in phosphate apatites. A common structural

compared to phosphate apatites. The mean value of (Cl + F) forthe solid solution equals 1.55(6) atoms per unit cell compared to the ideal value of 2 atoms per unit cell observed in phos‐ phate apatites. The solid-solution series Na6.45Ca3.55(SO4)6Cl1.55 + Na6.45Ca3.55(SO4)6F1.55 shows a gap towards the side of fluoride-rich compounds. Under ambient pressure, the gap exists between 0 < *n*Cl/*n*Cl + *n*F < 0.33, where *n*Cl and *n*F represent the numbers of Cl- and F-atoms per

Lead apatites form a family of isomorphous compounds, and well-known members of the group are mimetite (Pb5(AsO4)3Cl, **Section 1.6.7**) and pyromorphite (Pb5(PO4)3Cl, **Sec‐ tion 1.6.4**). Isostructural with vanadinite Pb5(VO4)3Cl, these three constituents form a ternary system within the apatite group of P63/M symmetry (hexagonal bipyramid). The mimetite and pyromorphite structures can incorporate numerous admixtures, mainly Ca, Ba, As, V, P and others. The most common substitution is the isovalent replacement of part of Pb with Ca and

3− ion is well established by the existence of a complete solid solution between

feature of all members of the solid-solution series is the deficiency in total Cl<sup>−</sup>

of vanadate-substituted calcium

and F<sup>−</sup>

3− group by tetrahedrally coordinated and

content

