Open access peer-reviewed chapter

Substituents and Dopants in the Structure of Apatite

By Petr Ptáček

Reviewed: January 8th 2016Published: April 13th 2016

DOI: 10.5772/62213

Downloaded: 1476

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
  • Complexation 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]:

  1. Cation substitution, where M = Ca2+, Pb2+, Sr2+, Mg2+, Fe2+, Mn2+, Cd2+, Ba2+, Co2+, Ni2+, Cu2+, Zn2+, Sn2+, Eu2+, Na+, K+, Li+, Rb+, NH4+, La3+, Ce3+, Sm3+, Eu3+, Y3+, Cr3+, Th4+, U4+, U6+ and □.

  2. Substitution for phosphorus by one or two cations, where X = PO43−, AsO43−, SiO43−, VO43−, CrO43−, CrO42−, MnO43−, SO42−, SeO42−, BeF42−, GeO44−, ReO53−, SbO3F4−, SiO3N5−, BO45−, BO33− and CO32−.

  3. Z-site substation, where Z = F, OH, Cl, O2, O3, NCO, BO2, Br, I, NO2, CO32−, O22−, O2−, S2−, NCN2−, NO22− and □.

where □ represents the vacancy cluster [1].

Besides the monoionic substitution, the co-substitution and mutual combinations of substitutions 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 physicochemical, 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 germanates 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 apatite-type 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 elements[1] - (REE, Fig. 1(b)) and PO43− anions by AsO43−, SO42− or CO32− without destroying the apatite structure. The changes in lattice parameters must be indicative of the type of substitution occurring. For example, Cl interchange for OH 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].

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/mor P21 [12].

Some of the various families of substitutions that were experimentally established in apatites 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) (6h) site and IX at Ca(1) (4f) site. Table 2 introduces the cation radii of possible apatite substituents at M-site [2].

M10X6O24Z2Designation
M(1)4M(2)6O12O6O6
Ca10P6O24(OH)2HAP
C4Ln6Si6
Sr10S3Si3F2FAP
Ca2Ln8Si6O2Oxyapatite
SrCa9P6Z-site vacancies
Nd4Ca6Ge62
Sr10P4Si22
Na2Ca8P62
2La2Ca4La22M-, Z-site vacancy
2La2La2Ge6(OH)2M-site vacancies (?)

Table 1.

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

SubstituentsCoordination number
ArensShannon and Prewitt
VIVIVIIVIIIIX
M2+Ba1.341.361.391.47
Pb1.201.181.291.33
Eu1.171.25
Sn0.931.22
Sr1.121.161.211.25
Ca0.991.001.071.121.18
Cd0.970.951.001.07
Mn0.830.93
Zn0.740.7450.90 (E)
Co0.720.735
Cu0.720.73
Mg0.660.720.89
Ni0.690.69
M+K1.331.381.46 (?)1.51 (?)1.55 (?, E)
Na0.971.021.13 (?)1.161.32 (?, E)

Table 2.

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

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

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]:

2P5+Si4++S6+E1

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].

DescriptorBrief description
a [Å]Lattice constant of hexagonal unit cell
b [Å]
c:aVariable axial ratio
rMI [Å]Shannon’s ionic radii of M(I)-site ion (nine-coordination)
rX [Å]Shannon’s ionic radii of X-site ion
rMII [Å]Shannon’s ionic radii of M(II)-site ion (seven-coordination for X = F, eight-coordination for X = Cl and Br)
RZ [Å]Shannon’s ionic radii of Z-site ion
Av CR [Å]Average crystal radius = [(rM(I)x4) + (rM(II)x6) + (rXx6) + (rOx24) + (rZx2))]/42
MEN - OENElectronegativity difference between M and O atom
XEN - OENElectronegativity difference between X and O atom
MEN - ZENElectronegativity difference between M atom at M(II) site and Z atom
MEN - XENElectronegativity difference between M atom at M(I) site and X atom
M(I) – O(1) [Å]Distance between M(I) atom and O(1) atom
M(I) – O(1)M(I)z = 0 [Å]Distance between M(I) atom and O(1) atom with the constraint z = 0 at M(I)
ΔM(I)−O [Å]Difference in the lengths M(I) – O(1) and M(I) – O(2).
ΔMIOMIz=0Difference in the lengths M(I) – O(1) and M(I) – O(2) with the constraint z = 0 at M(I)
ΨM(I)−O [°]Angle that M(I)-O(1) bond makes with respect to c
ΨMIOMIz=0[°]Angle that M(I)-O(1) bond makes with respect to c with the constraint z = 0 at M(I)
δM(I) [°]Counter-rotation angle of M(I)O6 structural unit
ϕ M(I) [°]Metaprism twist angle (π/3 – 2δM(I))
αM(I) [°]Orientation of M(I)6 unit with respect to a
<X-O> [Å]Average X-O bond length
<τO−X−O> [°]Average O-X-O bond-bending angle
ρM(II) [Å]M(II)-M(II) triangular side length
M(II) – Z [Å]Orientation of M(II)-M(II)-M(II) triangles with respect to a
M(II) – O(3) [Å]Distance between M(II) and O3 atoms
φO(3)−M(II)−O(3) [°]O(3) – M(II) – O(3) angle
Etotal [eV]Total energy calculated from ab initio calculations

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 fluorine-mineralized 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 byQueet 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/mhexagonal symmetry where F is located at the 2a (0, 0, ¼) position, while Cl 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 randomly 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 silicocarnotite-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 byBalachandranandRajan[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 construction 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 parameters [23].

Fig. 2.

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

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

  1. 1.The αMII (rotation angle of MII-MII-MII triangular units);

  2. The ΨMIO1MIz=0(angle that M(I) – O1 bond makes with the c axis when z = 0 for the M(I) site).

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 ΨMIO1MIz=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 compound is uncertain due to relatively small ionic size of Zn2+ cations, the relative position of Hg5(PO4)3F suggests some peculiar characteristics [23].

ClusterSite occupancy
k = 1 and k = 2SiteMBa, Pb, Sr, Ca
XP, V, Mn
ZF
k = 3SiteMBa
XP
ZCl, Br
k = 4SiteMSr, Hg
XP
ZCl, Br
k = 5SiteMCa, Cd, Pb
XV, Cr, As
ZCl
k = 6SiteMCa, Pb
XP
ZCl, Br
k = 7SiteMZn
XP
ZZZF, Cl

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 manifested in the bond distortion angle ΨMIO1MIz=0[23].

6.1. Cationic substitution at M(1) and M(2) sites

6.1.1. Strontium-substituted apatites

Sr2+ ion, which is larger than Ca2+, is ordered almost completely into the smaller Ca(2) site in the apatite structure (Fig. 4). The bond valence sums of Sr ions at two sites demonstrate that Sr is severely overbonded at apatite Ca site but less at Ca(2) site. Complete ordering of Sr into Ca(2) sites has important implications for the diffusion of that element in the apatite structure. It is the subject of several recent studies. The diffusion of Sr in (001) was shown to be as rapid or even more rapid than the diffusion parallel to [001]. As there are neither sites available for Sr, which are linked in (001), nor any interstitial sites, which can contain Sr2+ ion, the diffusion mechanism involving the vacancies or defects or both is indicated [24].

A series of Sr-substituted hydroxyapatites, (SrxCa1−x)5(PO4)3OH, where x = 0.00, 0.25, 0.50, 0.75 and 1.00, was investigated byO’Donnellet al [25]. The lattice parameters (a and c), the unit cell volume and the density were shown to increase linearly with strontium addition and were consistent with the addition of slightly larger and heavier ion (Sr) instead of Ca. There was a slight preference for strontium to enter Ca(2) site in mixed apatites.

Fig. 4.

The structure of natural Sr-bearing apatite refined by Hughes et al [24] and viewed along the c-axis.

Strontium is often substituted for calcium in order to confer the radio-opacity in glasses used for dental cements, biocomposites and bioglass-ceramics. It can be concluded that strontium substitutes for calcium with little change in the glass structure as a result of their similar charge to size ratio. Glasses with low content of strontium nucleate in the bulk to form calcium apatite phase. Glasses with medium strontium content nucleate to mixed calcium-strontium apatite at the surface and glass fully substituted by strontium to strontium fluorapatite [26].

6.1.2. Magnesium-substituted apatite

Magnesium-substituted hydroxyapatite (MgHAP) powders with different crystallinity levels, prepared at room temperature via a heterogeneous reaction between Mg(OH)2/Ca(OH)2 powders and (NH4)2HPO4 solution using the mechanochemical- hydrothermal route, were reported bySuchaneket al [27]. The as-prepared products contained unreacted Mg(OH)2 and therefore had to undergo the purification in ammonium citrate aqueous solutions at room temperature. MgHAP contained 0.24 - 28.4 wt.% of Mg and the concentration of Mg was slightly lower near the surface than that in the bulk.

Two effects of different magnesium sources (magnesium nitrate and magnesium stearate) on the synthesis of Mg-substituted hydroxyapatite (Mg-n-HAP) nanoparticles by the co-precipitation method were investigated byLijuanet al [28]. There was no obvious difference of morphology, nanoparticle size and thermal stability between those two Mg-n-HAPs. However, Mg-n-HAP synthesized by magnesium stearate had lower crystallinity and better dispersibility, suggesting that magnesium stearate was a novel magnesium source to synthesize Mg-n-HAP, which can effectively reduce the powder crystallinity and prevent the aggregation of Mg-n-HAP nanoparticles, owing to the introduction of organic magnesium source, so as to obtain a promising candidate material to prepare Mg-n-HAP/polymer composite used in a variety of bone applications.

6.1.3. Copper-substituted apatites

Copper-substituted hydroxyapatite (Ca10−xCux(PO4)6(OH)2 (where x = 0.05 – 2.0) and fluorapatite Ca10−xCux(PO4)6F2 (x = 0.05 – 2.0) were synthesized byShanmugamandGopal[29] via the co-precipitation method and subsequent thermal treatment to 700°C for 30 min. Due to its antimicrobial activity, the copper-substituted fluorapatite could be applied as an antimicrobial biomaterial for various purposes like orthopedic and dental implantations.

6.1.4. Nickel-substituted apatites

According toMobasherpouet al [30], the reaction mechanism corresponding to equimolar exchange of nickel and calcium and yielding to Ca10−xNix(PO4)6(OH)2, where x varies from 0 to 10, could be described by the following equation:

Ca10PO46OH2+xNiCa10xNixPO46OH2+xCa2+E2

In this process, Ni2+ ions are first adsorbed onto the surface of hydroxyapatite (surface complexation, Section 6.5.2) and then the substitution of Ca2+ for Ni2+ ions takes place.

6.1.5. Zinc-substituted apatites

Zinc is a common bioelement. The zinc content in human bones ranges from 0.0126% to 0.0217% by weight [7]. Zinc as a cationic substituent in hydroxyapatite provides the option to counteract the effects of osteoporosis [31]. The incorporation of zinc into the HAP structure (Zn-HAP) was abundantly studied, owing to the key effect of Zn2+ cations in several metabolic processes that makes zinc eligible for use in many biomedical applications and to its possible antimicrobial activity [3].

The results of structure analysis indicated that Zn ions substituted partially for Ca ions in the apatite structure and the upper limit of Zn substitution for Ca in HA was about 20 mol.%. In general, the HAP lattice parameters, a and c, decreased with Zn addition [32].

Zn-substituted apatite was synthesized by the precipitation method as follows [33]:

10xCa2++101xZn2++6PO43+2OHCa10xZn101xPO46OH2E3

where 0 ≤ x ≤ 1. The pH of the solution was adjusted to 8 by aqueous solution of NH3, and the reaction mixture was kept at 90°C for 5 h with stirring. The resulting suspension was then subjected to suction filtration, and the powdery product was dried at 100°C for 10 h. It is known that the usage of chloride or nitrate of calcium as a starting reagent may cause the incorporation of Cl or NO3 into the structure of apatite. This can be avoided by the utilization of acetate salts, because acetate ions are not incorporated into the apatite, i.e. they would not affect the apatite structure.

6.1.6. Iron-substituted apatites

The synthesis and the characterization of iron-substituted hydroxyapatite via a simple ion-exchange procedure were described byKrameret al [34]. Using a ferric chloride solution and a simple soaking procedure, FeHAP can be prepared with no apparent formation of the second phase. The substitution of Fe3+ into the HAP lattice results in FeHAP powders with magnetic properties. This novel simplified room temperature soaking procedure can be applied in the future to synthesize magnetic apatite-based nanoparticles for biomedical applications.

6.1.7. Cobalt-substituted apatites

The synthesis and the characterization of cobalt-substituted hydroxyapatite (Co-HAP) powders via the precipitation method were described byKrameret al [35]. Using a cobalt chloride solution and a simple soaking procedure, it is possible to prepare CoHAP with no apparent formation of second phases. Cobalt-substituted samples displayed paramagnetic properties as opposed to the diamagnetism of pure HA. The degradation studies showed that Co-HAP did not display markedly different degradation behavior from pure HAP, and the amount of cobalt released over the course of a month was extremely low, alleviating the toxicity concerns. Cobalt-substituted hydroxyapatite nanoparticles, the biomaterial with magnetic properties, could be a promising material to be used in a variety of biomedical applications, including the magnetic imaging, drug delivery or hyperthermia-based cancer treatments.

Single crystals of chlorapatite [Ca5(PO4)3Cl] with the substitution of approximately 20% of Ca2+ by Co2+ (space group P63/m, a = 9.625(3) and c = 6.747(1) Å, V = 541.3 Å3) were prepared byAndersonandKostiner[36] via the flux techniques. Co ion is present at available six-coordinated cation site.

6.1.8. Manganese-substituted apatites

Naturally occurring manganese-substituted apatite is known as manganese-bearing apatite (Mn,Ca5(PO4)3F, Section 1.1). According to the findings ofHugheset al [24], the symmetry of Mn-bearing apatite does not degenerate from P63/mto P6 or P3 with Mn substitution, nor degenerates the symmetry limit of Mn substitution to one atom/unit cell. Mn2+ substituent, which is smaller than Ca2+, preferentially occupies larger apatite Ca(l) site although not completely. Mn atom is underbonded at Ca site, less so at larger Ca(l) site; nine O atoms coordinating that site satisfy more effectively the Mn bond valence than seven ligands coordinating Ca(2) site. The M-O bond lengths of Mn-substituted sites reflect the substitution of the smaller Mn ion.

Fig. 5.

The structure of natural Mn-bearing apatite refined by Hughes et al [24] and viewed along the c-axis.

It is interesting to note that apatite acts effectively as a geochemical sieve that traps Mn2+ and excludes Fe2+ elements, which are virtually inseparable in most geochemical systems. The bond valence sums for Fe2+ at apatite Ca sites yield 1.26 and 1.19 valence units for Ca(1) and Ca(2) sites, respectively; large discrepancy from the formal valence prohibits extensive substitution of Fe2+ in the apatite structure (Fig. 5) [24].

The crystal structure of pale blue transparent Mn-rich fluorapatite (9.79 wt.% of MnO) with optimized formula (Ca8.56M2+1.41Fe2+0.01)P6O24F2 was resolved byHugheset al [24] to be of the space group of P63/mwith the cell parameters a = 9.3429 Å, c = 6.8110 Å and Z = 2. Mn is strongly ordered at Ca(1) site (Ca(1)0.72Mn0.28, Ca(2)0.96Mn0.04). The apatite structure also contains Mn5+ at X-site (P5.96Mn5+ 0.04).

6.1.9. Substitution of REEs in apatite

Crystals of La-, Gd- and Dy-bearing fluorapatite [La-FAP, Gd-FAP, Dy-FAP, Ca10−x−2y NayREEx+y(P1−ySixO4)Z2, where x = 0.24 – 0.29 and y = 0.32 – 0.36] were synthesized by hydrothermal route byFleetandPan[37]. The substitution of trivalent REE in apatite is principally compensated as follows:

REE3++Si4+Ca2+P5+Ca10xREExP1xSixO46Z2E4
REE3++Na+2Ca2Ca102yNayREEyPO46Z2E5
REE3++O2Ca2+ZCa102zREEzPO46Z2zOzE6
2REE3++V3Ca2+Ca103wREE2wVwPO46Z2E7

The structure of some REE-bearing apatites [37],[38] is shown in Fig. 6.

Fig. 6.

Rare-earth-element ordering and structural variations in natural rare-earth-bearing fluorapatites (a), LaFAP (b), NdFAP (c), GdFAP (d) and DyFAP (e) [37],[38].

The partitioning of REE between two Ca positions in apatite contradicts usual first-order dependence on spatial accommodation, with LREE[1] - [39],[40],[41],[42],[43], in particular, favoring the smaller Ca(2) position. This behavior was variously ascribed to the control via [37]:

  1. Substitution mechanism;

  2. Electronegativity difference;

  3. Bond valence.

The preference of individual REE among multiple Ca positions in minerals (the site occupancy of individual REE) was not extensively studied because of the inability of conventional diffraction methods to distinguish among individual elements at multiply-occupied sites. The site preference for individual LREE from theoretical bond-valence sums was estimated byHugheset al [38], reasoning that La → Pr should preferentially substitute into Ca(2), whereas Pm → Sm should selectively substitute into Ca(1).

The isomorphic substitutions of neodymium for strontium in the structure of synthetic Sr5(VO4)3OH apatite structure type (P63/m) were reported byGet’manet al [44]. The synthesis of apatite specimen was performed via the solution thermolysis on the assumption of the following reaction:

5xSrNO32+x2Nd2O3+3NH4VO3Sr5xNdxVO43OH1xOx+E8

where x = 0, 0.02, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18 and 0.20. The substitution scheme can be expressed as:

Sr2++OHNd3++O2E9

The procedure includes three stages:

  1. Preparation of solution;

  2. Thermolysis;

  3. Treatment of the dry residue.

The solutions for the thermolysis were prepared by dissolving Sr(NO3)2 in water; Nd2O3 was dissolved in water with nitric acid added; NH4VO3 was dissolved in water with hydrogen peroxide added. Dry residues after concentrating the solutions were pestled in an agate mortar and calcined with the temperature steadily raised from 600 to 800°C and intermittent grindings [44].

6.1.10. Actinides-bearing apatites

Thorium and uranium (actinides [45],[46][1] -)-bearing apatites were synthesized byLuoet al [47] from doped phosphate-halide-rich melts. The structure refinements (Fig. 7) of U-doped fluorapatites indicate that U substitutes almost exclusively into Ca(2) site with the site occupancy ratios UCa(2)/UCa(1), which range from 5.00 to 9.33. Similarly, the structure refinements of Th-doped fluorapatites indicate that Th substitutes dominantly into Ca(2) site with ThCa(2)/ThCa(1) values, which range from 4.33 to 8.67.

Fig. 7.

The structure of UFAP (a), ThFAP (b), UClAP (c), ThClAP (d), ThSrFAP (e) and ThSrClAP (f) [47] viewed along the c-axis.

The structure refinements of U-doped chlorapatites show that U is essentially distributed equally between the two Ca sites with UCa(2)/UCa(1) values, which range from 0.89 to 1.17. The results of Th-doped chlorapatites show that Th substitutes into both Ca(1) and Ca(2) sites with ThCa(2)/ThCa(1) values, which range from 0.61 to 0.67. In Th-doped strontium apatites with F and Cl end-members, Th is incorporated into both Ca(1) and Ca(2) sites. The range of ThCa(2)/ThCa(1) values is 0.56 to 1.00 for the F end-member and 0.39 to 0.94 for the Cl end-member. U-doped samples indicate that U in fluorapatite is tetravalent, whereas, in chlorapatite, it is heterovalent but dominantly hexavalent [47].

Based on the chemical analyses of U-, Th-doped fluor-, chlor- and strontiumapatite specimens in this study, local charge compensation may be maintained by the following coupled substitutions (M represents U or Th and [] represents the vacancy) [47]:

M4++2Ca2+E10
M6++23Ca2+E11
M4++2Na+3Ca2+E12
M6++4Na+5Ca2+E13
M4++2Si4+Ca2++2P5+E14
M6++2Si4+Ca2++4P5+E15

The incorporation of U and Th into fluorapatite results in a decrease of the size of both Ca polyhedra, but the incorporation of U and Th into chlorapatite gives rise to an increase in the volume of both Ca polyhedra. The decrease of both Ca polyhedral volumes in fluorapatite caused by the substitution of U and Th can be explained by the decrease of ionic radius from Ca to U and Th. However, the increase in the volume of both Ca polyhedra in chlorapatite is hard to understand. Because of the effect on Ca(2) polyhedron caused by the replacement of F by Cl, it can be explained by the structural distortion of Ca(2) polyhedron [47].

Uranium-doped oxy-silicophosphates (britholites) of the composition of CaxLay(SiO4)6−u (PO4)uOt:U4+ were synthesized byRiadhet al [48] via the high-temperature solid-state reaction. The uranium solubility limit was found to be comprised between 4.6 and 4.8 mol.%. The investigation of uranium heated to 1200°C led to the uranium diffusion coefficient of 2.14·10−14 m2·s−1. The synthesis and the characterization of uranium- (Ca9Nd1−xUx(PO4)5−x(SiO4)1+xF2) and thorium-bearing britholites (Ca9Nd1−xThx(PO4)5−x(SiO4)1+xF2) were also reported byTerraet al [49],[50]:

14Nd2O3+94Ca2P2O7+72CaCO3+CaF2+32SiO2+12An4+O2Ca9Nd0.5An0.54+PO44.5SiO41.5F2+72CO2gE16

or

14Nd2O3+74Ca2P2O7+92CaCO3+CaF2+32SiO2+12An4+P2O7αCa9Nd0.5An0.54+PO44.5SiO41.5F2+92CO2gE17

where An4+ substitutes for tetravalent U4+ and Th4+.

The incorporation of thorium in the structure is probably possible due to small differences of ionic radius between calcium (1.06 Å), neodymium (1.05 Å) and thorium (1.00 Å). In order to ensure the quantitative incorporation of thorium, it appeared necessary to consider the coupled substitution [50].

Nd3++PO43Th4++SiO44E18

instead of the substitution scheme:

Nd3++FTh4++O2E19

Indeed, in the first way, homogeneous and single-phase solid solutions were prepared from Ca9Nd(PO4)5(SiO4)F2 to Ca9Th(PO4)4(SiO4)2F2 leading to full neodymium substitution. Associated small increase of the unit cell parameters results from the simultaneous replacement of phosphate groups by bigger silicate. It was accompanied by a significant change in the grain morphology. These results contrast with those obtained when the coupled substitution according to Eq. 19 was performed, which confirmed the limitation of about 10 wt.% in the Th substitution [50]. Good resistance of the materials to influence of aqueous solutions enables their utilization for the immobilization of tetravalent actinides in phosphate ceramics [49].

6.1.11. Silver-substituted apatite

The favorable biocompatibility of hydroxyapatite (HA) makes it a popular bone graft material as well as a coating layer on metallic implant. One common and accepted strategy to prevent the implant-related infections is to create antibacterial properties for the implant. Silver ions can be either incorporated into the apatite during the co-precipitation process (AgHAP-CP) or subjected to the ion exchange with calcium ions in apatite (AgHAP-IE). The incorporation of silver ions into apatite is based on the equation [51]:

10yCa2++yAg++6PO43++2yOHCa10yAgyPO46OH2yE20

where y is the molar amount of silver to be incorporated. However, the distribution of silver ions in AgHAP-CP and AgHAP-IE was different, thus affecting the antibacterial action.

6.1.12. Cadmium-substituted apatites

The absorption of cadmium cations in apatites is relevant both from the medical standpoint of cadmium uptake by human bones, as well as since cadmium migration in nature involves the absorption and desorption equilibria with natural minerals, including apatites. Cadmium has a slight preference for Ca(I) site in fluorapatite and for Ca(II) site in hydroxyapatite [7],[52]. The interactions between these two ions (Cd and Ca) during absorption and ionic change processes in apatites present therefore considerable practical and theoretical interest. Cadmium is also a frequent heavy toxic pollutant element in water [7].

Calculated energy differences (E) between these sites are of 12 and 8 kJ·mol−1 for fluorapatite and hydroxylapatite, respectively. The preference is not strong, and however, a part of the sites of the other type is also occupied by cadmium ions. The relative site occupation can be expressed by the equation [7]:

P=probabilityofsubstitutionatCa1siteprobabilityofsubstitutionatCa2site=46expEkTE21

where E = E(Cd2+ or Zn2+ on Ca(1)) – E(Cd2+ or Zn2+ on Ca(2)). At T = 298 K, P = 85 and 17 Cd2+ in fluorapatite and hydroxylapatite, respectively. From the value of P and from the fact that the sum of the two probabilities is 1, one can calculate that the probability of the lower-energy site occupancy is of 99% and 94%, respectively.

Badraouiet al [53] reported that the maximum amount of cadmium substitution for strontium in the system Sr10−xCdx(PO4)6Z2 (Z = OH and F) accounts for about 40 at% in HAP and for 60 at% in FAP. The increase of cadmium content induces stronger decrease of the c-axis with respect to the a-axis. The structure refinements evidence found a statistical distribution of Cd atoms in Sr10−xCdx(PO4)6(OH)2 and a light preference for M(1) site in Sr10−xCdx(PO4)6(F)2. The stability of the system M10−xM’x(PO4)6Z2 (M and M’ = Ca, Pb, Cd, Sr and Z = OH and F) is strongly affected by the polarizability. As a matter of fact, complete miscibility is possible even when the cations exhibit great size differences, provided they are not both soft acids. Otherwise, the presence of two cations with quite different radii and relevant polarizabilities induces important distortions of the apatite unit cell and PO4 tetrahedra and consequently limits the possibility of mutual substitution.

6.2. Anionic substitution at X-site

Pentavalent arsenic, vanadium and chromium substitution can completely replace phosphorus in calcium, strontium and barium fluor- and chlorapatites. Calcium fluor-vanadate, -arsenate and -chromate structures were distorted compared to normal hexagonal apatite. Manganese completely replaced phosphorus only in barium apatites, while chromium and manganese could not be incorporated into lead apatites. Excluding these exceptions, continuous solid solutions were formed between the phosphate and/or vanadate and the chromate or manganese analogues for given divalent and halide ions [54]. The substitution of CO32− ions at X- (carbonate-apatite of A-type) and Z-site (carbonate-apatite of B-type) was already described in Section 4.6.

6.2.1. Arsenate substitution in hydroxylapatite

The arsenate (As5+) substitution in the hydroxylapatite structure was examined byLeeet al [55]. The investigation with samples of hydroxylapatite, the As5+-substituted analogue (synthetic analogue of mineral johnbaumite, Section 1.6.3) and of intermediate compositions does not provide any evidence of lowering the symmetry below P63/m. A series of arsenate-substituted hydroxyapatite was also prepared through aqueous precipitation method byZhuet al [56]. Prepared solid solutions (Ca5(PxAs1−xO4)3(OH)) showed apatite structure for the whole arsenate/phosphate series. With decreasing arsenate content, the particles changed from smaller needle-like to large tabular crystals and the unit cell dimensions a and c increased but not in fair agreement with Vegard’s law[1] - [57]. In FT-IR spectra, the area of phosphate peak was gradually suppressed and the area of arsenate peak increased as the proportion of arsenate increased.

Complete PO43− ↔ AsO43− substitution was also recognized in experimental studies of apatite analogues, such as in the system Sr5(PO4)3OH-Sr5(AsO4)3OH [58]. The Rietveld refinement of Sr5(AsO4)3Cl (penta­strontium tris­[arsenate(V)] chloride, 890.31 g·mol−1) from high-resolution synchrotron data was performed byBellet al [59]. The hexagonal compound crystallizes in the same structure (Fig. 8) as other halogenoapatites in the space group P63/mwith the cell parameters: a = 10.1969 Å, c = 7.28108 Å, V = 655.63 Å3, c:a = 0.7140 and Z = 2. The structure consists of isolated tetrahedral AsO43− anions (As atom and two O atoms have m-symmetry), separated by two crystallographically independent Sr2+ cations, which are located on mirror planes and threefold rotation axes, respectively. One Sr atom is coordinated by nine O atoms and the other one by six. Chloride anions (site symmetry 3¯) are at 2a sites and are located in the channels of the structure.

Fig. 8.

The structure of Sr5(AsO4)3Cl apatite (perspective view along the c-axis).

6.2.2. Vanadate substitution in hydroxylapatite

The synthesis of synthetic alkaline-earth vanadate hydroxylapatites from hydroxide fluxes was performed byMugaveroet al [60]. The hexagonal Sr5(VO4)3OH apatite (penta­strontium tris­[vanadate(V)] hydroxide, Fig. 9(a)) possesses the P63/mspace group with the cell parameters: a = 10.0570 Å, c = 7.4349 Å, c:a = 0.7393 and V = 651.24 Å3. The structure of Ba5(VO4)3OH (penta­barium tris­[vanadate(V)] hydroxide) apatite is shown in Fig. 9(b). It crystallizes in hexagonal system with the space group P63/mand the cell parameters: a = 10.4589 Å, c = 7.8476 Å, c:a = 0.7503 and V = 743.43 Å3.

Fig. 9.

The structure of Sr5(VO4)3OH (a) and Ba5(VO4)3OH (b) apatite viewed along the c-axis.

The compounds (solid solution) of the composition of Pb5(PxV1−xO4)3Cl (0 ≤ x ≤ 1), which are synthetic analogues of minerals pyromorphite, vanadinite and endlichite, were synthesized for the first time byChernorukovet al [61] via high-temperature solid-phase reactions:

4.5PbNO32+0.5PbCl2+3xNH42HPO4+1.51xV2O5Pb5PxV1xO43Cl+9NO2+2.25O2+6xNH3+4.5xH2OE22

Fig. 10.

Fragment of Pb5(VO4)3Cl crystal structure [61].

The variations of unit cell parameters as a function of composition respect Vegard’s law. These compounds are structurally built of discrete phosphate or vanadate tetrahedra linked to one another by lead polyhedra, which form joint layers (Fig. 10). Apatite-type structures offer typically two crystallographic positions for cations differing in the coordination number and local symmetry. Lead atoms occupying the first positions form polyhedra shaped as three-capped trigonal prisms of PbO9 having the symmetry C3, the columns of which run along the threefold axis. Distorted two-capped trigonal prisms of PbO6Cl2 residing in the second positions have local symmetry С1.

6.2.3. Chromium analogues of apatite

The syntheses of chromium (Cr(V) [62]) analogues of apatite were described in literature including the following compounds [63],[64],[65],[66],[67],[67],[69],[70],[71],[72]:

  • Ca5(CrO4)3OH, which is isomorphous to hydroxyapatite (Section 1.5.2): space group P63/m, a = 9.683 Å and c = 7.010 Å, a:c = 1:0.7239, V = 569.20 Å3, Z = 2.

  • Sr5(CrO4)3OH with predicted lattice constants a = 9.9561 Å and c = 7.488 Å.

  • Ba5(CrO4)3OH.

  • Ca5(CrO4)3F with predicted lattice constants a = 9.733 Å and c = 7.0065 Å

  • Ca5(CrO4)3Cl with predicted lattice constants a = 10.1288 Å and c = 6.7797 Å.

  • Sr5(CrO4)3F with predicted lattice constants a = 9.9349 Å and c = 7.5037Å.

  • Sr5(CrO4)3Cl with lattice constant a = 10.125 Å and c = 7.328Å.

  • Sr5(CrO4)3Br with predicted lattice constants a = 10.2895 Å and c = 7.2712 Å.

These compounds are in general prepared by the ignition of mixture of alkaline-earth carbonates, hydroxides or oxides with Cr2O3 in the presence of water vapor. Ca3(CrO4)2 compound (orthochromate), which is isomorphous with Ca3(PO4)2, is formed as an intermediate by carrying out the synthesis in dry atmosphere; this compound is often identified as 9CaO·4CrO3·Cr2O3 [63],[73],[74],[75].

Theoretical compositions and formula weights of chromium apatite analogues are given in Table 5.

CompoundComposition [wt.%]M
MCrOZH[g.mol−1]
Ca5(CrO4)3OH35.4427.5936.790.18565.39
Sr5(CrO4)3OH54.5519.4225.900.13803.09
Ba5(CrO4)3OH65.2914.8319.780.101051.64
Ca5(CrO4)3F35.3227.4933.843.35567.38
Ca5(CrO4)3Cl34.3326.7232.886.07583.33
Sr5(CrO4)3F54.4219.3723.852.36805.08
Sr5(CrO4)3Cl53.3318.9923.374.31821.53
Sr5(CrO4)3Br50.5918.0122.179.23865.98

Table 5.

Theoretical compositions of chromium apatite analogues (M(CrO3)4Z).

Sr10(CrO4)6F2 possesses typical hexagonal structure of apatite with the space group P63/m, which was refined using the powder neutron diffraction (Fig. 11) for the first time byBaikieet al [71]. As other chromium analogues of apatite, the material contains chromium in +5 (pentavalent) oxidation state. The material shows the paramagnetic behavior.

Fig. 11.

Structural representation of Sr10(CrO4)6F2 apatite with SrO6 octahedra and CrO4 tetrahedra: larger and smaller spheres mark F and O atoms, respectively. The unit cell is indicated by black lines [71].

The crystal structure (Fig. 12) and the magnetic properties of strontium chromate phase (Sr5(CrO4)3(Cu0.586O)) with apatite-like structure were determined byTyutyunnikandBazuev[76]. The sample was prepared by solid-state synthesis via the thermal treatment of the mixture of stoichiometric amount of SrCO3, Cr2O3 and CuO at the temperature of 1200°C in air for 36 h.

Fig. 12.

Crystal structure of Sr5(CrO4)3(Cu0.586O): (a) projection along the c-axis and (b) side view showing the infinite [CuO]− chains and the coordination polyhedra of Cr and Sr atoms [76].

This phase crystallizes in the space group P63/mwith hexagonal unit cell parameters: a = 10.0292 Å and c = 7.4623 Å, V = 650.033 Å and Z = 2. The compound is stable up to 1200°C in air. It was found that copper in the form of Cu+ cations is located in infinite linear (CuO) chains inserted into the tunnels parallel to hexagonal c-axis. The chains contain about 40% vacancies in copper positions. The valence states of Cr and Cu may be mainly +5 and +1, respectively [76].

6.2.4. Selenium analogues of apatite

Selenium oxyanion-substituted hydroxyapatite (SeHAP) was synthesized as a promising material for the treatment of bone cancer to reduce the probability of recurrence, because selenium plays an important role in protein functions and it has significant effect on the induction of cancer cell apoptosis [77]. Another study indicated that selenite (SeO42−) or selenite (SeO32−) oxyanions exert their cancer chemopreventive effects by direct oxidation of critical thiol-containing cellular substrates and that they are more efficacious anticarcinogenic agents than selenomethionine or selenomethylselenocysteine with a lack of oxidation capability [3],[78].

Selenium was incorporated into the hydroxyapatite lattice by replacing some of the phosphate groups with selenite groups. SeO42− (selenate) ion has tetrahedral structure like PO43− ion (Fig. 5 and Table 4 in Section 1.2), but it is slightly larger (2.49 Å) in diameter than phosphate ion, which is 2.38 Å in diameter. By contrast, SeO32− (selenite) ion has very similar diameter (2.39 Å), but it has a quite different flat trigonal pyramid geometry. The substitution of bivalent selenium oxyanions forms positively charged vacancy compensated by simultaneous decalcification and dehydroxylation according to the reaction [3],[79]:

Ca10PO46OH2+xSeOn2Ca10xPO46xSeOnxOH2x+xPO43+Ca2++xOHE23

The SeHAP crystal lattice parameters increased slightly as the Se concentration increased when the Se/P ratios were less than 0.5 [80]. All samples prepared via the precipitation method from aqueous solution byKolmaset al [79] contained significant amount of carbonates, especially of B-type. Thus, for these samples, the formula Ca10−x(PO4)6−x(SeOn)x(OH)2−x (Eq. 23) should be written as Ca10−x−y(PO4)6−x−y(SeOn)x(CO3)y(OH)2−x−y. Hydroxyapatites containing selenate ions are non-toxic, whereas hydroxyapatite with the highest concentration of selenites is toxic.

6.3. Substitution at Z-site

6.3.1. Nitrogen-containing apatites

Nitrogen was incorporated into hydroxyapatite by dry ammonia treatments at temperatures between 900 and 1200°C in the presence of graphite. The process of synthesis of cyanamidapatite (Ca10(PO4)6CN2, Ca10(PO4)6NCN) can be described by the following chemical equations [13]:

2NH3+CH2CN2+2H2E24
Ca10PO46OH2+H2CN2Ca10PO46CN2+2H2OE25

Ammonia reacts with graphite during the thermal treatment forming [CN2]2− ions (Eq. 24). These cyanamide ions interchange with moveable OH ions situated on the sixfold screw axis of apatite to form cyanamidapatite (Eq. 25). A similar reaction is known for the synthesis of calcium cyamide from calcium oxide:

CaO+2NH3+2CCaCN2+CO+3H2E26

The treatments at temperatures above 1200°C or long-term treatments destroy the apatite lattice completely through the phosphate reduction. Cyanimide ions lose their sites in the apatite lattice and the nitrogen content decreases [13]. The synthesis of Ca10(PO4)6CN2 apatite provides the evidence that the hydroxylapatite structure is able to incorporate larger organic molecules [81].

Direct transformation of TCP (Ca3(PO4)2) into cyanamidapatite according to the reaction:

3Ca3PO42+H2CN2Ca9PO45HPO4HCN2E27

was also proposed byHabelitzet al [82].

6.3.2. Peroxide-doped apatites

Although “oxygenated” apatites were not much investigated compared to other substituted apatites, some past studies have, however, reported the possibility of apatitic channels to incorporate oxygenated species such as H2O2 or O2 or molecular ions including O22− (the peroxide ion) and superoxide O2−. They are single-phase nanocrystalline apatites, where part of apatitic OH ions are replaced by oxygenated species. Typically by peroxide ions (quantified) and at least the traces of superoxide ions can be prepared by the precipitation from aqueous calcium and phosphate solutions in the presence of H2O2 under medium room temperature [83],[84].

The local structure of hydroxyl-peroxy apatite was described byYuet al [85]. Hydroxyl-peroxy apatite contains a small amount of partially dehydroxylated hydroxyapatite phase and calcium hydroxide. The incorporation of peroxide ions into the lattice of HAP causes the perturbations of hydrogen environments and slight changes in its crystal morphology. The distance between H in some structural OH- and adjacent O along the c-axis becomes longer instead of forming the hydrogen bond after the incorporation of peroxide ions.

According to the concentration of peroxide ions in hydroxyl-peroxy apatite and the theoretical value, the corresponding formula for the hydroxyl-peroxy apatite is proposed as follows [85]:

Ca10(PO4)6(OH)1.34−2x(O2)0.33(O)x0.33+x.

Fig. 13.

Possible configuration of hydroxyl ions, peroxide or oxide ions and vacancies in the channel along the crystallographic c-axis in hydroxyl-peroxy apatite. O, H atoms and vacancies are presented by large gray circles, small open circles and gray squares, respectively. Filled small circles represent H atoms perturbed by the incorporation of peroxide ions [85].

A scheme of possible configurations of hydroxyl ions, peroxide or oxide ions and vacancies in the channel along the crystallographic c-axis in hydroxyl-peroxy apatite is illustrated in Fig. 13. Peroxide ions incorporated into HAP are located in the channel of apatite structure through the substitution of a portion of OH radicals, and the material is a solid solution of hydroxyl- and peroxide apatite.

Zhaoet al [86] reported that a new hydrogen bond was formed between peroxide ions and adjacent OH radicals in hydroxyl-peroxy apatite. According to the literature [430,446], the formation of hydrogen bond would induce a downfield shift of corresponding proton resonance. Some authors reported a linear correlation of the isotopic proton chemical shift with the O-H…O distance, which was a measure of the hydrogen bond strength.Zhaoet al [86] suggested the following mechanism for the incorporation of O22−:

2OHO+2+H2OE28

where [] was the vacancy. O2− ion was active and could react with O2 to produce O22−.

O+212O2O22E29

Peroxide ions associated with the vacancies were situated placed in the channel of HA lattice along the c-axis through the substitution of a portion of OH radicals. The molecular ions constituted a symmetric vibrator with a stretching vibration active in Raman spectrometry. This vibration was recorded at 750 cm−1 in the Raman spectra of O22−-containing HA samples. The final product was a solid solution of hydroxyl- and peroxide-apatite. However, the existence of peroxide ions in the HA lattice caused the contraction of the unit-cell dimensions of HA materials. In addition, a new hydrogen bond was formed between peroxide ions and adjacent OH radicals, which was determined by using molecular spectroscopy analysis. During annealing treatment in air, peroxide ions decomposed and the substituted OH radicals re-entered the HA lattice, resulting in the elimination of the structural aberrations caused by the incorporation of peroxide ions. The concentration of peroxide ions present in HA samples was measured by chemical analysis [86].

6.3.3. Chalcogenide phosphate apatites

The synthesis and the structure of four new chalcogenide[1] - [87] phosphate apatitic phases of the composition given by the formula:

  1. Ca10(PO4)6S: a = 9.4619 Å, c = 9.8342 Å, c:a = 0.7223 and V = 529.88 Å3 (Fig. 14(a));

  2. Sr10(PO4)6S: a = 9.8077 Å, c = 9.2089 Å, c:a = 0.7350 and V = 600.53 Å3 (Fig. 14 (b));

  3. Ba10(PO4)6S: a = 10.2520 Å, c = 7.6590 Å, c:a = 0.7471 and V = 697.14 Å3 (Fig. 14(c));

  4. Ca10(PO4)6Se: a = 9.5007 Å, c = 9.8406 Å, c:a = 0.7200 and V = 534.73 Å3 (Fig. 14 (d)).

were reported byHenninget al [88].

Fig. 14.

The structure of Ca(PO4)6S (a), Sr(PO4)6S (b), Ba(PO4)6S (c) and Ca(PO4)6Se (d) viewed along the c-axis.

These four apatites are isostructural and crystallize in the trigonal space group P3 over bar with the chalcogenide ion positioned at (001/2). Sulfoapatites show no ability to absorb H2S in the way that oxyapatite absorbs H2O at elevated temperatures. This can be attributed to the position of sulfide ion and the way it influences the crystal structure around vacant chalcogenide position at (000) [88].

6.3.4. Metaborate ion-containing apatite phase

Strontium borate-phosphate Sr10(PO4)5.5(BO4)0.5(BO2)[1] - was prepared from SrCO3, NH4H2PO4 and H3BO3 at high temperature (from 1150 to 1550°C) and was found to be free of alkali metal compounds. Sr10(PO4)5.5(BO4)0.5(BO2) phase is a derivative of the apatite crystal structure with metaborate ion at Z-site: space group P3, a = 9.7973 Å, c = 7.3056 Å, V = 607.29 Å3, Z = 1 [89],[90],[91].

The strontium sites are found to be fully occupied, while [PO4] tetrahedra are partially replaced by [BO4] groups. The crystal structure contains Sr cations occupying the 6g (Sr(1)) and 2d (Sr(2), Sr(3)) sites, isolated tetrahedral [PO4]/[BO4] groups and linear [BO2]ˉ groups located in hexagonally shaped (trigonal antiprismatic) channels formed by Sr(1) atoms and running along [001] (Fig. 15). The space group of the present compound is reduced to P3, because the orientation of the [PO4]/[BO4] tetrahedra destroys the mirror plane characteristic for the apatite crystal structure (P63/m) [89],[91].

Fig. 15.

Crystal structure of Sr10(PO4)5.5(BO4)0.5(BO2): projection along [001] showing the hexagonally shaped channels formed by Sr(1) around the threefold inversion axis (Z = (P0.95B0.05) (a) and side view emphasizing the linear [BO2]− groups and the corresponding trigonal antiprisma formed by Sr(1) (b) [89].

6.4. Solid solutions of apatites

Crystalline solid solutions[1] - [92] of apatites are frequently encountered where the possibility and type depend on the condition of formation or preparation, thermal history after formation and the end-members of the series [2]. The structure of ternary solid solution of hexagonal (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 byHugheset al [93]. Phosphate tetrahedra and Ca(l) polyhedra of both structures are generally very similar to analogous polyhedra in the end-member fluor-, chlor- and 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 sequence[1] - [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]:

Ca5PO43xAsO4x32ySO4ySiO4y]2yOH,F,C1E30

where x = 0 – 3 and y = 0 – 1.5 were found in altered calcareous xenoliths within the ignimbrite 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 ignimbrite as follows: brucite-marble, spurrite (Ca5(SiO4)2CO3 [96]), humite (Mg7(SiO4)3(F,OH)2 [97]) and larnite[1] - (Ca2SiO4 [98],[99],[100],[101]) zones. They are associated with both high-temperature 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,[1] - and secondary low-temperature minerals: calcium hydrosilicates (hillebrandite [113], awfillite [114], bultfonteinite [115]), hydrogarnets [116] and minerals of the ettringite group [117].

The minerals of the apatite supergroup often form elongated cracked hexagonal or pseudo-hexagonal 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]:

2RO43SO42+SiO44E30

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 pfu[1] - to 0), for example [95]:

  1. Svabite:

    Ca5[(AsO4)2.01(PO4)0.33(SiO4)0.33(SO4)0.33]3[F0.58(OH)0.30Cl0.12]Ʃ1;

  2. As-bearing fluorapatite:

    Ca5[(PO4)1.56(AsO4)1.06(SiO4)0.19(SO4)0.19]3[F0.59(OH)0.35Cl0.06]Ʃ1;

  3. As-bearing hydroxylellestadite:

    Ca5[(SiO4)1.25(SO4)1.25(AsO4)0.43(PO4)0.07]3[(OH)0.70Cl0.20F0.10]Ʃ1;

  4. Si, S-bearing hydroxylapatite:

    Ca5[(PO4)0.95(SO4)0.93(SiO4)0.93(AsO4)0.19]3[(OH)0.67Cl0.18F0.15]Ʃ1;

  5. Hydroxylellestadite:

    Ca5[(SO4)1.49(SiO4)1.49(PO4)0.02]3[(OH)0.74F0.13Cl0.13]Ʃ1.

The crystals of As-bearing phases belonging to the investigated solid solution are heterogeneous and small in size. Therefore, X-ray single-crystal data were obtained for only Si, S, As-bearing 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 byOndaet al [118]. The lattice parameters increased linearly with increasing content of vanadium 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 bySugiyamaet al [119] and used as catalysts in oxidative dehydrogenation of propane. The catalytic activity[1] - 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 composition of Na6.45Ca3.55(SO4)6(FxCl1−x)1.55, where x = 0 – 1, was refined byPiotrowskiet al [120] in the P63/mspace group (Z = 1). The sulfate tetrahedra and the two symmetrically independent 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 and F content compared to phosphate apatites. The mean value of (Cl + F) for the solid solution equals 1.55(6) atoms per unit cell compared to the ideal value of 2 atoms per unit cell observed in phosphate 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 < nCl/nCl + nF < 0.33, where nCl and nF 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, Section 1.6.4). Isostructural with vanadinite Pb5(VO4)3Cl, these three constituents form a ternary system within the apatite group of P63/msymmetry (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].

A number of compounds of the mimetite Pb5(AsO4)3Cl-pyromorphite Pb5(PO4)3Cl solid-solution series were synthesized at room temperature byBajdaet al [121] and investigated with Raman and infrared spectroscopy. The peak positions of the dominant antisymmetric stretching (ν3) and bending (ν4) 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 solutions [121].

Solid solutions of Pb8M2(XO4)6 lead alkali apatites were studied byMayeret 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/mhexagonal apatite structure and form true solid solutions.

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

  • Ca2Y8(SiO4)6O2 – Ca8Y2(PO4)6O2;

  • Ca2La8(SiO4)6O2 – Ca8La2(PO4)6O2;

  • Ca2Y8(SiO4)6O2 –Y10(SiO4)4(BO4)2O2;

  • Mg2Y8(SiO4)6O2 – Y10(SiO4)4(BO4)2O2;

  • Pb4+ 3Pb2+ 5Y2(SiO4)6O2 – Pb2+ 2Y8(SiO4)6O2;

  • Ca10(PO4)6(OH)2 – Ca4Y6(SiO4)6(OH)2;

  • M10(PO4)6F2 – M10(PO4)6F2 (M = Sr, Ba, Pb);

  • M10(PO4)6F2 – M10(MnO4)6F2 (M = Sr, Ba, Pb).

6.5. Trace elements and their isotopes

Since apatite is an important accessory mineral in most common rock types, it is often used in trace element and isotope investigations of igneous and metamorphic rocks [123]. Stable isotope compositions of biologically precipitated apatite in bone, teeth and scales are widely used to obtain the information on the diet, behavior and physiology of extinct organisms and to reconstruct past climate in terrestrial and marine conditions [124].

Broad spectrum of substitutions in the apatite lattice allows the incorporation of various isotopes, which offer a number of instruments for the interpretation of paleoenvironment and diagenesis. The relative stability of francolite compared to other sedimentary minerals led to an enormous number of studies and applications. Various isotopes occupy the Ca2+ and PO43− sites in the lattice of apatite (Fig. 16).

Fig. 16.

Possible isotopic substitutions in the structure of francolite [125].

Since the earliest application in deep-time study of Late Cretaceous paleotemperatures in 1950, the oxygen isotope paleothermometry is based on the temperature dependence of oxygen isotope fractionation between authigenic minerals[1] - [126] and ambient waters. Under the equilibrium conditions, the 18O/16O ratio of sedimentary carbonate and phosphate minerals depends only on the temperature of precipitation and on the 18O/16O ratio of ambient water. Thermodynamic relationships and bond vibrational frequencies can be used to determine the mineral-water isotopic fractionation relations but not with the precision and accuracy necessary for the paleothermometry. Such an application requires the calibrations based on mineral-water oxygen exchange experiments at high temperatures, mineral precipitation experiments at low temperatures and/or natural experiments using minerals grown under known conditions [127],[128].

Carbon, oxygen and sulfur isotopes are used to reconstruct the oxygenation stages of the sediments during organic matter degradation and precipitation of apatite. The application of this method gives good results for modern and Neogene deposits. In older occurrences, the signature of carbon and oxygen composition is commonly overprinted by diagenetic and burial diagenesis [125],[129]. The carbon isotope ratios of apatite can be used to interpret the source of carbon in magmas and metamorphic fluids using the assumption that the carbon isotope fractionations between phases are small in igneous and metamorphic systems [123].

The carbon isotope analysis of bioapatites was first applied to terrestrial mammals in early 1980s [130],[131],[132]. While it is now known that some bones do undergo the C-isotope exchange extremely readily, collagen, bone and enamel record different periods of time during the life of a single individual, and the diet may change. That means, there is a fundamental ambiguity (preservation vs. normal intraindividual differences) in interpreting the isotopic differences among different tissues. Unfortunately, early results were taken to imply that all bioapatites are unreliable, and it was not until the 1990s that it became accepted that the tooth enamel, at least, is a robust recorder of diet. Thus, the early work ofLee-Thorpandvan der Merwe[133],[134] was a struggle against the tide of misplaced opinions [129].

Fossil biogenic apatites display the trace element compositions that can record environmental and biological signals, give insights into past water compositions or be used for dating paleontological and archeological bones and teeth. The mechanisms of the process of trace element and their isotopes incorporation into apatites of skeletal phosphatic tissues are described byReynardandBalter[135]:

  1. Partitioning between aqueous fluids and crystals;

  2. Surface adsorption, complexation and chelation;

  3. Diffusion processes.

6.5.1. Partitioning of divalent cations

Partitioning of divalent cations is defined by the chemical equilibrium expressing the divalent cation (Me2+) exchange between apatite and aqueous solutions [135]:

Me2+aq+CaapatitessCaaq2++MeapatitessE31

where (aq) and (ss) refer to the aqueous solution and to the solid solution, respectively. The equilibrium constant of Eq. 31 can be written as

KDMe2+Ca=xMeapatitexCaapatitemMe2+mCa2+=KTCaapatiteKTMeapatiteλCaapatiteλMeapatiteγMe2+γCa2+E32

where x is the molar fraction in apatite solid solution, m is the molality in water, λ is the activity coefficient of the component in the solid solution, K(T) is the solubility product of the end-member at temperature T and γ is the ion activity in the aqueous solution, the ratio of which in water is assumed to be equal to one. The activity coefficients in regular solid-solution model are described by Margules parameters[1] - [136] and can be approximated by the elastic energy due to the deformation of the host crystal lattice around the substituted cation [135],[137]:

WGij=4πNAEri2rjri2+13rjri3E33

where NA is the Avogadro number, E is the Young’s modulus of the crystal, ri is the ionic radius of cation normally occupying the site in the i-compound (Ca in apatite) and rj is the ionic radius of the substituted cation in compound j. The elasticity of hydroxyapatite gives E = 114 ± 2 GPa.

At low concentrations (XMe−apatite << 1) like those of trace elements in biogenic apatites, Eq. 32 is reduced to the relationships [135]:

KDMe2+Ca=KTCaapatiteKTMeapatiteexpWGMeCaRT=expGideal+WMeCaRTE34

where the term exp (-ΔGideal/RT) is the free enthalpy change of the reaction 31, equivalent to the ratio of end-member solubility products. Unlike carbonates, the data of solubility products and thermodynamics for end-member apatites are scarce. When no data are available for the solubility and enthalpy of formation of the end-members, it is assumed that the elastic energy term dominates over the partitioning, i.e. ΔGideal ≪ WGMeCa. Promising ways for obtaining the enthalpies of formation and the substitution energies are the first-principle calculations [138] and the atomistic modeling [135],[139].

For heterovalent substitutions, the equilibrium reaction becomes complex since complementary substitutions are necessary to maintain the charge balance in the crystal. Typically, the substitution of trivalent elements of important rare-earth series requires the compensation by Na+ for Ca2+ at an adjacent site or even more complex substitution scheme involving carbonate groups or fluorine. In that case, most thermodynamic data required for the calculation of the equilibrium constant are not available. Among the series of elements with the same charge and substitution scheme, the pattern of equilibrium constants, or of distribution coefficients, can be approximated by combining Eqs. 33 and 34 [135]:

KD=KD0exp4πNAEeffr02rjr02+13rjr03/RTE35

where Eeff is the effective Young’s modulus and r0 is the optimum radius for maximum equilibrium constant KD0, all of which will depend on the charge of the considered series of elements. These parameters can be adjusted to experimental data such as partition coefficients between minerals and liquids and lead to parabola-like curves, the position and curvature of which depend on the charge of the element. This approach was applied so far only to rare-earth elements in apatite, where the relative partition coefficients were extrapolated from magmatic temperatures around 800°C to low temperatures appropriate for fossil diagenesis [135].

6.5.2. Complexation of metal cations

The complexation of metal cations in aqueous fluids involves binding with a broad range of molecules from simple inorganic ones (e.g. carbonates, phosphates and sulfates) to complex organic ones (humic acids, amino acids, proteins, enzymes, etc.). For molecules with several bonding sites and structural flexibility (e.g. multidentate or chelator), the complexation is thermodynamically favored with respect to the complexation with several monodentates having one bonding site; the process is named chelation. Chelators can be adsorbed on mineral surfaces while remaining complexed to metallic cations. The pattern of the partition coefficients associated with this process was measured for rare-earth elements complexed with humic acids and manganese oxides. It shows null fractionation along the whole series; the effect of chelation is therefore to screen the trace element in the crystal or ligand field and to suppress the fractionation associated with ionic radius variations and tetrad effects, and most of the anomalies associated with redox of Ce [140]. Similar effects might occur for the adsorption of chelated metals on other mineral surfaces and in particular phosphates. In addition to chelators, the transition metals also form complexes with proteins and enzymes that interact with bones and teeth in living organisms and may influence their incorporation in bioapatite [135].

6.5.3. Diffusion processes

Solid-state diffusion in crystals is a thermally activated process governed by the enthalpy of formation and of migration of defects and usually well described by the Arrhenius relation [135]:

D=D0expΔHaRTE36

where D0 is the pre-exponential factor corresponding to the diffusion coefficient at infinite temperature and ΔHa is the activation enthalpy (or energy) of the diffusion process. The extrapolation of high-temperature diffusion data of trace elements in apatite shows that these processes are inefficient at temperatures below 300°C, which cover the conditions of diagenetic alteration up to low-grade metamorphism [135],[141].

The differing initial and boundary conditions imposed in three sets of diffusion experiments:

  1. Ion implantation;

  2. In-diffusion with powder sources experiment;

  3. Out-diffusion.

consequently resulting in different solutions to the diffusion equation. However, in all cases, the process can be described as one-dimensional, concentration-independent diffusion [141].

Fig. 17.

The summary of data diffusion for cations and anions in apatite (a) [142] and the diffusion of Sm and Nd for various minerals and oxides (a) [141].

A plot of diffusivities of various cations and anions in apatite is shown in Fig. 17(a). The diffusivities of Mn are similar to those of Sr and about an order of magnitude slower than those of Pb. On the other hand, the diffusion of Mn2+ in apatite is about two orders of magnitude faster than the diffusion of (trivalent) REE when coupled substitutions according to Eqs. 4 and 5 are involved [141],[142]. The diffusion coefficients of Nd and Sm in various minerals and related oxides are plotted in Fig. 17(b). The diffusion of REE in apatite is relatively fast; when only simple REE exchange is involved, it is among the fastest in rock-forming minerals for which the data exist. Even when the chemical diffusion involving coupled exchange is considered, REE transport in apatite is considerably faster than the REE diffusion in other accessory minerals [141].

Notes

  • 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.
  • Rare-earth elements or metals (REE or REM) are Sc, Y and lanthanoids [40]. Light rare-earth elements (LREE) are Sc, La, Ce, Pr, Nd, Pm, Sm, Eu and Gd (7 elements from La to Eu are known as the cerium group or cerium-group lanthanides). Heavy rare-earth elements (HREE) are Y, Tb, Dy, Ho, Er, Tm, Yb and Lu. The definition of LREE and HREE is based on the electron configuration. LREEs possess unpaired 4f electron from 0 to 7 (half-filled 4f electron shell). HREEs have paired electron (the clockwise and counterclockwise spinning election) [39],[41]. The element with half-filled f-electron shell (Eu) shows enhanced stability of its particular electron configuration [43]. In some cases, REEs are divided into three groups including (1) LREE (La – Pm), (2) MREE (middle rare-earth element, Sm – Dy) and (3) HREE (Ho – Lu) [42].
  • The actinides occupy the second row of the f-block in the periodic table. The actinide group or actinoids (An) include 14 elements with atomic numbers from 90 (Th) to 103 (Lr) [43]. The elements with atomic numbers greater than 92 (U) are termed as transuranes. The elements with atomic numbers greater than 100 are named as the super-heavy elements (SHE). There is also the concept of the periodic table developed by G.T. Seaborg predicting a new inner transition series of 32 elements (from 122 to 153 element), called the superactinite series [45],[46]. Only actinium, thorium, uranium and (in trace quantities) protactinium and plutonium are primordial, while the elements from neptunium onwards are present on Earth solely through artificial generation [46].
  • Vegard’s law, first pronounced in 1921, states that the lattice parameter of a solid solution of two phases with similar structures is a linear function of lattice parameters of the two end-members [57].
  • The elements from the chalcogenide group (or oxygen group family) belonging to Group 16 (VI A) of the periodic table: O, S, Se, Te and Po. Elements sulfur, selenium and tellurium are also termed as the elements from the sulfur subgroup [87].
  • See also Section 5.3.
  • For the purposes of nomenclature, a complete solid-solution series without structural order of ions defining the end-members 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 end-members. 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].
  • Statistical model where a random sequence k, the probability distribution p(k) of which satisfies the equation [94]:
  • 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].
  • 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.
  • The abbreviation for per formula unit (pfu), see also Footnote 36 in Chapter 1.
  • The utilization of apatites as catalysts is described in Section 10.7.
  • The minerals of sedimentary rocks are subdivided into two main groups [126]: authigenic (formed on their present position) and allogenic (transported to its current position from elsewhere). Both groups will be further described in Chapter 7.
  • The Margules equation expresses the Gibbs free energy (GE) of binary liquid mixture (x1 + x2 = 1) in the symmetric form [136]:

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Petr Ptáček (April 13th 2016). Substituents and Dopants in the Structure of Apatite, Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications, Petr Ptacek, IntechOpen, DOI: 10.5772/62213. Available from:

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