**Abstract**

The structure of apatites allows large variations of composition given by the generic formula (M10(XO4)6Z2) including partial or complete substitution of both the cationic as well as the anionic sites, formation of nonstoichiometric forms and solid solutions. More than half of naturally occurring elements can be accommodated by apatite structure in a significant extend. The sixth chapter of this book is divided into five sections. The first, second and the third part deals with many examples of substitution including cationic substitution of M sites, anionic substitution of X-site and anionic substitution of Z-site, respectively. The remaining two sections continue with solid solution of apatites and ends with description of trace elements and their isotopes in the structure of apatite, respectively.

**Keywords:** Apatite, Substitution, Solid solution, Trace elements, Isotopes, Complexa‐ tion of Metal Cations, Diffusion

As was already said in **Chapter 1**, the generic formula of apatite (M10(XO4)6Z2) enables partial or complete substitution for cationic as well as anionic sites [1],[2]:


where □ represents the vacancy cluster [1].

Besides the monoionic substitution, the co-substitution and mutual combinations of substitu‐ tions in anionic and cationic sites (multi-ionic substitution) were also often reported [3],[4],[5], [6]. Mutual substitutions of trace elements into apatite structure brought new physicochemi‐ cal, mechanical and biological properties in comparison with pure apatite or monoionic substituted apatite materials, e.g. hydroxylapatite [3].

Some substitutions can proceed only at the synthesis stage, while a limited ion exchange between solid apatite and surrounding solution can also occur. Due to their high chemical diversity and ion-exchange capabilities, apatites are considered as materials for toxic waste storage and for wastewater purification. The ion exchange in apatitic structures in human organism also presents an interest for medicine [7].

Recent studies have shown that a number of alkaline-earth-rare-earth silicates and germa‐ nates also have the apatite structure, and these have the cell sizes which span the division between the "apatites" and the "pyromorphites". Some, particularly barium and lanthanum apatites, have the lattice parameters comparable with the members of the pyromorphite group. Thus, Ba2La8(SiO4)6O2 has the cell parameters *a* = 9.76 Å and *c* = 7.30 Å and Pb10(PO4)6F2 shows *a* = 9.76 and *c* = 7.29 Å, while Ba3La7(GeO4)6O1.5 has *a* = 9.99 Å and *c* = 7.39 Å and Pb10(AsO4)6F2 has *a* = 10.07 Å and *c* = 7.42 Å. During synthetic studies, however, it became apparent that the prediction of the composition of compounds with apatite-type structures could not be made solely on the basis of satisfying the valence considerations, since the occurrence of the apatitetype structure also appears to be determined by the ratio of the mean size of "A" ions (i.e. Ca ions in fluorapatite) to the mean size of *"X"* ions in XO4 [8],[9].

**Fig. 1.** The ionic radius of elements that can be accommodated instead of M in the lattice of apatite (M5(XO4)3Zq).

The structure of hydroxyapatite allows large variations from its theoretical composition as well as the formation of nonstoichiometric forms and ionic substitutions. More than half of naturally occurring elements are known to be accommodated in the apatite lattice to significant extent. Ca2+ cation can be substituted by Na+ , K+ , Mg2+, Sr2+, Pb2+, Mn2+ (**Fig. 1**(**a**)) or rare-earth elements1 (REE, **Fig. 1**(**b**)) and PO4 3− anions by AsO4 3−, SO4 2− or CO3 2− without destroying the apatite structure. The changes in lattice parameters must be indicative of the type of substitution occurring. For example, Cl<sup>−</sup> interchange for OH<sup>−</sup> ions causes a change to lattice parameters from *a =* 9.4214 Å and *c* = 6.8814 Å to 6.628 Å and 6.764 Å, respectively. Another example is the Sr2+ substitution for Ca2+, which causes lengthening of *a*- and *c*-axes from 9.418 Å and 6.884 Å to 9.76 Å and 7.27 Å, respectively [8],[12],[13],[14],[15].

Besides the monoionic substitution, the co-substitution and mutual combinations of substitu‐ tions in anionic and cationic sites (multi-ionic substitution) were also often reported [3],[4],[5], [6]. Mutual substitutions of trace elements into apatite structure brought new physicochemi‐ cal, mechanical and biological properties in comparison with pure apatite or monoionic

Some substitutions can proceed only at the synthesis stage, while a limited ion exchange between solid apatite and surrounding solution can also occur. Due to their high chemical diversity and ion-exchange capabilities, apatites are considered as materials for toxic waste storage and for wastewater purification. The ion exchange in apatitic structures in human

Recent studies have shown that a number of alkaline-earth-rare-earth silicates and germa‐ nates also have the apatite structure, and these have the cell sizes which span the division between the "apatites" and the "pyromorphites". Some, particularly barium and lanthanum apatites, have the lattice parameters comparable with the members of the pyromorphite group. Thus, Ba2La8(SiO4)6O2 has the cell parameters *a* = 9.76 Å and *c* = 7.30 Å and Pb10(PO4)6F2 shows *a* = 9.76 and *c* = 7.29 Å, while Ba3La7(GeO4)6O1.5 has *a* = 9.99 Å and *c* = 7.39 Å and Pb10(AsO4)6F2 has *a* = 10.07 Å and *c* = 7.42 Å. During synthetic studies, however, it became apparent that the prediction of the composition of compounds with apatite-type structures could not be made solely on the basis of satisfying the valence considerations, since the occurrence of the apatitetype structure also appears to be determined by the ratio of the mean size of "A" ions (i.e. Ca

**Fig. 1.** The ionic radius of elements that can be accommodated instead of M in the lattice of apatite (M5(XO4)3Zq).

, K+

3− anions by AsO4

The structure of hydroxyapatite allows large variations from its theoretical composition as well as the formation of nonstoichiometric forms and ionic substitutions. More than half of naturally occurring elements are known to be accommodated in the apatite lattice to significant extent.

3−, SO4

structure. The changes in lattice parameters must be indicative of the type of substitution

2− or CO3

, Mg2+, Sr2+, Pb2+, Mn2+ (**Fig. 1**(**a**)) or rare-earth elements1

2− without destroying the apatite

substituted apatite materials, e.g. hydroxylapatite [3].

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

organism also presents an interest for medicine [7].

ions in fluorapatite) to the mean size of *"X"* ions in XO4 [8],[9].

Ca2+ cation can be substituted by Na+

(REE, **Fig. 1**(**b**)) and PO4

The substitutions at Z site play a very important role in the crystallography of specific species. The Z site lies in the channel formed by the X sites in fluorapatite and is of just the right size to fit between X atoms, and it lies on (001) mirror planes to yield the space group P63/M. When Cl substitutes for F, Cl is too large to fit on the mirror plane, so it is displaced along the c-axis and the space group becomes P63. The OH substitution is even more complex. OH anions are not spherically symmetric due to H+ (proton) present in the charge cloud of O atoms. H causes a displacement of O off the mirror plane, the O-H orientation tends to align in a given channel, but adjacent channels may have different displacements and orientations. The result is that well-crystallized hydroxylapatites are usually monoclinic with the space group P21/M or P21 [12].

Some of the various families of substitutions that were experimentally established in apa‐ tites are summarized in **Table 1**. In general, the ions that substitute for Ca in the A position have the valences from 1 to 3 and the coordination numbers of VII at Ca(2) (6*h*) site and IX at Ca(1) (4*f*) site. **Table 2** introduces the cation radii of possible apatite substituents at M-site [2].


**Table 1.** Structural formulas of apatites: M(1)4M(2)6(XO4)6Z2 [2].

<sup>1</sup> The minerals with essential rare-earth elements (REE or rare-earth metals, REM) or chemically related elements Y or Sc are termed as rare-earth minerals. They must be named with suffix (Levinson modifier [10],[11]), indicating the dominant rare-earth element (some examples can be found in **Chapter 1** (**Table 3**)). Please see also note **2**.


(E) and (?) denote interpolated and doubtful values, respectively.

**Table 2.** Cation radii of possible apatite substituents at M10-site of M10(XO4)6Z2 unit [2].

An example of charge compensating substitution for phosphorus by two cations is the substitution during the synthesis of apatite species of the composition of Ca10(SiO4)3(SO4)3F2 (CSSF, fluorellestadite [16]) [2],[17],[18]:

$$\mathbf{2}\ \mathbf{P}^{\mathbb{S}^{\ast}} \longleftrightarrow \mathbf{S} \mathbf{i}^{\ast \ast} + \mathbf{S}^{\mathbb{6} \ast} \tag{1}$$

These synthetic phases have mineral equivalents in the minerals from the ellestadite group, which are listed in **Table 3**. Since the mineral with ideal end-member formula Ca5(SiO4)1.5(SO4)1.5Cl is assumed not to exist, the name ellestadite-(Cl) is discredited [19].



**Substituents Coordination number**

**Arens Shannon and Prewitt VI VI VII VIII IX**

Pb 1.20 1.18 — 1.29 1.33 Eu — 1.17 — 1.25 — Sn 0.93 — — 1.22 — Sr 1.12 1.16 1.21 1.25 — Ca 0.99 1.00 1.07 1.12 1.18 Cd 0.97 0.95 1.00 1.07 — Mn — 0.83 — 0.93 — Zn 0.74 0.745 — — 0.90 (E) Co 0.72 0.735 — — — Cu 0.72 0.73 — — — Mg 0.66 0.72 — 0.89 — Ni 0.69 0.69 — — —

M2+ Ba 1.34 1.36 1.39 — 1.47

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

M+ K 1.33 1.38 1.46 (?) 1.51 (?) 1.55 (?, E)

(E) and (?) denote interpolated and doubtful values, respectively.

(CSSF, fluorellestadite [16]) [2],[17],[18]:

**Descriptor Brief description**

*c*:*a* Variable axial ratio

*b* [Å]

*a* [Å] Lattice constant of hexagonal unit cell

*r*MI [Å] Shannon's ionic radii of M(I)-site ion (nine-coordination)

**Table 2.** Cation radii of possible apatite substituents at M10-site of M10(XO4)6Z2 unit [2].

Na 0.97 1.02 1.13 (?) 1.16 1.32 (?, E)

An example of charge compensating substitution for phosphorus by two cations is the substitution during the synthesis of apatite species of the composition of Ca10(SiO4)3(SO4)3F2

These synthetic phases have mineral equivalents in the minerals from the ellestadite group, which are listed in **Table 3**. Since the mineral with ideal end-member formula Ca5(SiO4)1.5(SO4)1.5Cl is assumed not to exist, the name ellestadite-(Cl) is discredited [19].

5 46 2 P Si S + ++ ÜÞ + (1)

**Table 3.** The list of 29 discrete descriptors of electronic and crystal structure parameters [23].

The fluorellestadite apatite and its solid solutions are minor components of many fluorinemineralized clinkers. It is stable to liquidus temperature of 1240°C at which it incongruently melts to dicalcium silicate (2CaO·SiO2) and liquid [16]. The solid-state synthesis and the luminescence properties of europium-doped fluorellestadite (CSSF:Eu2+) cyan-emitting phosphor were described by QUE et al [20]. Ellestadite apatites and their solid solutions are promising materials for the immobilization of toxic metals or hazardous fly ash [21],[22].

The general composition of silico-sulfate apatites, i.e. **ellestadites**, is Ca10(SiO4)3−x/ 2(PO4)x(SO4)3−x/2(F,Cl,OH)2 and their structures conform to P63/<sup>M</sup> hexagonal symmetry where F − is located at the 2a (0, 0, ¼) position, while Cl<sup>−</sup> is displaced out of the 6h Ca(2) triangle plane and occupies 4e (0, 0, z) split positions with z ranging from 0.336(3) to 0.4315(3). Si/S random‐ ly occupies the 6h tetrahedral site [19],[21].

The syntheses of Sr and Pb analogues of CSSF are also reported [18]. Strontium silico-sulfate apatite is not stable and decomposes to the mixture of strontium silicate and sulfate when heated to 1130°C for 30 min. Since high temperatures must be avoided, several attempts to prepare cadmium and barium silico-sulfate apatites were unsuccessful and the silicocarno‐ tite-like phase was obtained from a mixture of the composition of Ca10(GeO4)3(SO4)8F2 rather than apatite [17].

Since there is a huge potential for the substitution in apatite structure (M(1)4M(2)6(XO4)6Z2 and for the formation of solid solution as well, the classification method enables to identify the key crystallographic parameters which can serve as strong classifiers of crystal chemistries. The structure maps for apatite compounds via data mining were reported by BALACHANDRAN and RAJAN [23]. The selection of the pair of key parameters from a large set of potential classifiers is accomplished through the linear data dimensionality reduction method. This structure can be represented as a 29-dimensional vector, where the vector components are discrete scalar descriptors (**Table 3**) of electronic and crystal structure attributes utilized for the construc‐ tion of the map of apatite compounds.

Basically, the structure map approach involves the visualization of the data of known compounds with known crystal structures in a two-dimensional space using two scalar descriptors (normally heuristically chosen), which are associated with physical/chemical properties, crystal chemistry or electronic structure. The objective is to map out the relative geometric position of each structure type from which one tries to discern qualitatively if there are strong associations of certain structure types to certain bivariate combinations of param‐ eters [23].

**Fig. 2.** Bond-distortion angle applied for the construction of structure map [23].

The general composition of silico-sulfate apatites, i.e. **ellestadites**, is Ca10(SiO4)3−x/ 2(PO4)x(SO4)3−x/2(F,Cl,OH)2 and their structures conform to P63/<sup>M</sup> hexagonal symmetry where F

and occupies 4e (0, 0, z) split positions with z ranging from 0.336(3) to 0.4315(3). Si/S random‐

The syntheses of Sr and Pb analogues of CSSF are also reported [18]. Strontium silico-sulfate apatite is not stable and decomposes to the mixture of strontium silicate and sulfate when heated to 1130°C for 30 min. Since high temperatures must be avoided, several attempts to prepare cadmium and barium silico-sulfate apatites were unsuccessful and the silicocarno‐ tite-like phase was obtained from a mixture of the composition of Ca10(GeO4)3(SO4)8F2 rather

Since there is a huge potential for the substitution in apatite structure (M(1)4M(2)6(XO4)6Z2 and for the formation of solid solution as well, the classification method enables to identify the key crystallographic parameters which can serve as strong classifiers of crystal chemistries. The structure maps for apatite compounds via data mining were reported by BALACHANDRAN and RAJAN [23]. The selection of the pair of key parameters from a large set of potential classifiers is accomplished through the linear data dimensionality reduction method. This structure can be represented as a 29-dimensional vector, where the vector components are discrete scalar descriptors (**Table 3**) of electronic and crystal structure attributes utilized for the construc‐

Basically, the structure map approach involves the visualization of the data of known compounds with known crystal structures in a two-dimensional space using two scalar descriptors (normally heuristically chosen), which are associated with physical/chemical properties, crystal chemistry or electronic structure. The objective is to map out the relative geometric position of each structure type from which one tries to discern qualitatively if there are strong associations of certain structure types to certain bivariate combinations of param‐

is displaced out of the 6h Ca(2) triangle plane

−

than apatite [17].

eters [23].

is located at the 2a (0, 0, ¼) position, while Cl<sup>−</sup>

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

ly occupies the 6h tetrahedral site [19],[21].

tion of the map of apatite compounds.

A new structure map, defined using the two distortion angles (**Fig. 3**) [23]:


That enables to classify the apatite crystal chemistries based on the site occupancy at M, X and Z sites and this classification is accomplished using the K-means clustering analysis (**Fig. 3**).

**Fig. 3.** Structure map for the classification of apatite chemistries based on the site occupancy (**Table 4**) at M, X and Z sites [23].

For example, clusters 1 and 2 (*k* = 1 and *k* = 2) correspond to F-apatites (fluorapatites). They are well localized in the structure map and are characterized by relatively low αMII and *ΨMI* <sup>−</sup>*O*<sup>1</sup> *MIz*=0 . Two F-apatites which do not belong to the clusters *k* = 1 and *k* = 2 are Hg5(PO4)3F (in *k* = 4) and Zn5(PO4)3F (in *k* = 7). While the existence of fully stoichiometric Zn5(PO4)3F apatite com‐ pound is uncertain due to relatively small ionic size of Zn2+ cations, the relative position of Hg5(PO4)3F suggests some peculiar characteristics [23].



**Table 4.** The relationship linking various clusters shown in **Fig. 3** with the site occupancy in the apatite unit [23].

Even though Ca2+ and Hg2+ cations have roughly the same ionic size (1.18 and 1.23 Å at M(I) site), their electronegativity data indicates that Hg atoms (electronegativity value of 2 in Pauling scale) are relatively highly covalent compared to Ca atoms (electronegativity value of 1 in Pauling scale). In the structure map, this covalent character is predicted to be manifest‐ ed in the bond distortion angle *ΨMI* <sup>−</sup>*O*<sup>1</sup> *MIz*=0 [23].
