Introduction

Apatite is a group of minerals with geological, biological, and environmental importance (e.g., Ma et al. 1993; Lang et al. 1995; Elliott 2002). Its general formula is M14M26(BO4)6X2, and its crystal structure is hexagonal in most cases (space group P63/m; Hughes and Rakovan 2002). In the hexagonal crystal structure, the isolated BO4 tetrahedra (z = 1/4, 3/4) are linked by the M1 cations in ninefold (6 + 3) coordination and M2 cations in an irregular sevenfold (6 + 1) coordination. The triclusters of M2 cations define a large c-axis channel that accommodates the X anions. Extensive chemical substitutions can take place at all these different crystallographic sites (Pan and Fleet 2002, and references therein), with the M1 and M2 sites primarily occupied by large cations such as Na+, Ca2+, Mn2+, Cd2+, Ba2+, Sr2+, Pb2+, Al3+, and rare-earth elements (REE3+), the B site commonly by P5+, V5+, As5+, S6+, Si4+, and the X site by halides, oxy-anions, vacancies, and small neutral molecules such as H2O. They subsequently lead to numerous solid solutions, as demonstrated by the experimental investigations of Miyake et al. (1986; (Ca,Pb)10(PO4)6F2, (Ca,Pb)10(PO4)6Cl2, and (Ca,Pb)10(PO4)6(OH)2), Kreidler and Hummel (1970; Ca10(PO4,VO4)6F2), and Ruszala and Kostiner (1975; Ca10(PO4)6(Cl,OH)2), to name but a few. To our knowledge, however, few investigations in the literature paid much attention to the behavior of the solid solutions of apatites (e.g., Adler 1964, 1968; Baker 1966; Cockbain 1968; Kreidler and Hummel 1970; Grisafe and Hummel 1970; Boechat et al. 2000; Chernorukov et al. 2010; Knyazev et al. 2011).

Due to some environmental issues such as lead contamination of soil and high-level radioactive waste, Pb- and V-bearing apatites recently gained significant attention in the scientific world (e.g., Gupta et al. 1986; Ma et al. 1993; Frost et al. 2003; Kim et al. 2005; Dong et al. 2005; Eon et al. 2006; Frost and Palmer 2007; Zhang et al. 2007; Liu et al. 2008, 2011a; Fleet et al. 2010; Chernorukov et al. 2010; Knyazev et al. 2011). As mentioned above, Pb and V can readily enter the structure of apatites and form compounds such as lead fluorapatite (Pb10(PO4)6F2) and lead fluorvanadate apatite (Pb10(VO4)6F2) (Merker and Wondratschek 1959). The structure of lead fluorapatite has been well determined by powder and single-crystal X-ray diffraction studies (Belokoneva et al. 1982; Suzuki et al. 1984; Miyake et al. 1986; Kim et al. 2000; Badraoui et al. 2006; Fleet et al. 2010), whereas that of lead fluorvanadate apatite is still waiting for future detailed single-crystal X-ray diffraction investigation (Merker and Wondratschek 1959). It also has been well established that there is a complete solid solution between lead fluorapatite and lead fluorvanadate apatite (Grisafe and Hummel 1970; Kreidler and Hummel 1970). Little is known about its solid solution behavior.

In the present study, we have synthesized this series of apatites and measured its Raman feature and thermal expansivity, so that its solid solution behavior can be better understood. Another study about its compressibility using diamond-anvil cell coupled with synchrotron X-ray radiation is in progress.

Experiment

A solid solution series between lead fluorapatite [Pb10(PO4)6F2] and lead fluorvanadate apatite [Pb10(VO4)6F2], with its composition of Pb10[(PO4)6-x (VO4) x ]F2 (x designed as 0, 1, 2, 3, 4, 5 and 6; Table 1), was synthesized in a conventional muffle furnace via solid-state reaction. The starting materials used in the synthesizing experiments were mechanical powder mixtures made of lead fluoride (PbF2), lead oxide (PbO), phosphorus pentoxide (P2O5), and vanadium oxide (V2O5). Since P2O5 powder readily absorbs moisture from air, we added to the starting materials 5% more P2O5 than required by the chemical formulas (by weight). These mixtures were pretreated at 110°C in a drying oven for 48 h and then encapsulated in Pt tubes with a diameter of 5 mm and a length of 50 mm by using arc-welding technique. The synthesizing conditions were 1 atm, 700°C, and 72 h. According to the literature data (e.g., Grisafe and Hummel 1970; Kreidler and Hummel 1970; Podsiadlo 1990; Zhang et al. 2007; Liu et al. 2008, 2011a; Chernorukov et al. 2010; Knyazev et al. 2011), synthesizing apatites with the solid-state reaction method is generally easy, and apparent apatite formation has been demonstrated down to at least 300°C in a few hours. For the lead apatites, the melting point of Pb10(PO4)6F2 at 1 atm is about 1,098°C (Podsiadlo 1990), whereas that of Pb10(VO4)6F2 has not been experimentally determined yet. Since the complete replacement of PO4 by VO4 lowers the melting temperature by about 150°C in the solid solution of Pb10(PO4)6Cl2–Pb10(VO4)6Cl2 (Chernorukov et al. 2010), the melting temperature of Pb10(VO4)6F2 is most likely close to about 900°C. Our synthesizing temperature of 700°C, therefore, should not be far away from the melting curve of the solid solution of Pb10[(PO4)6-x (VO4) x ]F2, which in turn should promote the equilibrium state in the synthesizing experiments.

Table 1 Composition of apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2
Full size table

We examined the synthetic products by using optical microscopy, scanning electron microscopy (SEM; Quanta 200 FEG), powder X-ray diffraction (XRD; X’Pert Pro MPD system), and electron microprobe analysis (EMPA; JEOL JXA-8100). The EMPA analytical conditions were as follows: accelerating voltage 15 keV, beam current 10 nA, 30 s counting at peak, and 10 s on background. The instrument was calibrated for Pb, V, and P using standards of PbCrO4-crocoite (Tasmania, Australia; SPI standard #20), synthetic V–P–K–O glass (SAC/TC38), and Ca10(PO4)6F2-apatite (Ontario, Canada; SPI standard #4), respectively. We applied the ZAF correction procedure to all EMPA analyses. The F content was not analyzed by the electron microprobe in the wavelength dispersive mode, but examined by it in the energy dispersive mode.

Raman spectra were collected on polished single crystals of the apatites with a confocal micro-Raman system (Renishaw system RM-1000) in a back-scattering geometry at ambient temperature (25°C). All samples were excited by the 514.5 nm line of an Ar+ ion laser operating at 20 mW. The Raman spectra were recorded with a counting time of 10 s, a data range from 200 to 2,000 cm−1, 1 accumulation, a slit of 50 μm, and a 20× objective. The corresponding spectral resolution was 1 cm−1.

High-T X-ray diffraction data were collected by using an X’Pert Pro MPD system, which had an attached Anton Paar HTK-1200 N oven running with a Eurotherm temperature controller (Eurotherm 2604; type S thermocouple checked against the melting point of NaCl). This heating system can reach 1,200°C with an accuracy of ±2°C. Other details of the X’Pert Pro MPD diffractometer system include a Cu target, operation voltage of 40 kV, and current of 40 mA, as used in our previous studies (Liu et al. 2010, 2011b; Hu et al. 2011). High-T experiments were conducted up to 800°C, and the heating and data-collection procedures were as follows: after collection of the X-ray diffraction data at a given temperature, the sample was heated up to the next setpoint by 10°C/min and then allowed to relax for 5 min before collection of the powder diffraction spectrum. X-ray data were collected between 10 and 70°2θ, with a scanning step length of 0.017°2θ and a scanning time of 10 s for each scanning step. The alignment of the X-ray diffractometer system was done with a standard of silicon crystalline powder at ambient temperature only. Due to the thermal expansion of the furnace and sample holder components and the powder sample itself, the sample position was slightly changed at high temperatures. Following the data-processing procedure verified in Hu et al. (2011), the influence of this small sample displacement was appropriately corrected by a full powder X-ray pattern refinement using the MDI’s program Jade 5.0 (Material Data, Inc.), which led to unit-cell parameters with high accuracy.

Results and discussion

The electron back-scatter images (Fig. 1) showed that the synthesizing experiments with the intermediate starting compositions produced two phases, with the dominant phase identified as apatite by the powder X-ray diffraction data (Fig. 2). The trace phase, varying from experiment to experiment (Table 1), attained a volume proportion up to at most 5%, so that it could not be readily detected by the X-ray. Here, we want to point out that the presence of some trace phase in the apatite-synthesizing experiments using solid-state reaction method seems very common (Zhang et al. 2007; Liu et al. 2011a), although in most investigations, no critical SEM examination was conducted to check for it (Grisafe and Hummel 1970; Kreidler and Hummel 1970; Chernorukov et al. 2010; Knyazev et al. 2011). Since the main subject of this study is about the solid solution behavior of lead fluorapatite and lead fluorvanadate apatite, it is appropriate to ignore the trace phases.

Fig. 1
figure 1

Electron back-scatter images showing the textures of the synthesized materials: a HL019, b HL021, and c HL016. Ap apatite, X unidentified trace phase. The unidentified trace phase appears as a V2O5-rich crystalline phase in HL021, whereas it appears as a PbO-rich melt-like phase in HL016. To better illustrate the textures, we deliberately selected to show here the trace phase-enriched parts of the experimental products

Full size image
Fig. 2
figure 2

XRD patterns of the apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2 at room temperature. All major peaks but one (indicated by the asterisk) can be assigned to apatite. For the two samples with x = 5 and x = 6, slight peak-splitting was observed but not obvious in this diagram (see Supplementary Information for more detailed illustration)

Full size image

The EMPA data (Table 1) suggested that the compositions of the lead apatites Pb10[(PO4)6-x (VO4) x ]F2 were generally homogeneous, indicating good equilibrium state in our synthesizing experiments. Considering the high synthesizing temperature and the long experimental duration, this is not surprising. On the other hand, the EMPA data potentially suggested that these synthetic lead apatites might be non-stoichiometric: the Pb/(P + V) molar ratio of the lead apatites (1.56 ± 0.04) ranges from 1.51 to 1.60. Previously, Liu et al. (2008) and Fleet et al. (2010) observed a non-stoichiometry for their synthetic lead apatites prepared by using the solid-state reaction method (Pb/(P + V) = 1.56). In comparison, Boechat et al. (2000) observed a non-stoichiometry for their synthetic calcium phosphate and vanadate apatite solid solution prepared by precipitation from solutions (the Ca/(P + V) ratio, from 1.72 to 1.83, is much larger than the ideal value of 1.67). It thus appears that synthetic apatites are usually non-stoichiometric, which is apparently incompatible with the well-known fact of ready and extensive substitution of different ions in the apatite structure. Further examination of the EMPA data from this study suggests (Table 1 and SIFig. 1 of the Supplementary Information), however, that the measured Pb contents of the apatites are not accurate enough, but the measured P and V contents are generally overestimated (the overestimation is about 15% in the case of P while it is about 20% in the case of V). It follows that the non-stoichiometry of synthetic apatites might be just an artifact caused by the EMPA analytical method; apatites are infamous for quantitative analyses because of the combination of F (Cl or OH) and O, and good standards for Pb and V are usually unavailable. We therefore tend to believe that our synthetic lead apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2 compositionally met our original designs.

Mixing behavior

Powder X-ray diffraction patterns at ambient P–T conditions, shown in Fig. 2, clearly indicate that the major products from the synthesizing experiments are indeed apatites. For the two samples with high vanadium content (x = 5 and 6), some splitting of the diffraction peaks was observed (see more details in SIFig. 2 of the Supplementary Information), potentially suggesting slight crystal structure distortion. Similar phenomenon was observed for the calcium fluorarsenate and fluorvanadate apatites with more than 80% P replaced by V (Grisafe and Hummel 1970; Mercier et al. 2007).

The unit-cell parameters of Pb10(PO4)6F2 (Table 2) are much comparable to the values given out by Merker and Wondratschek (1959), Kreidler and Hummel (1970), Grisafe and Hummel (1970), Kim et al. (2000), Liu et al. (2008) and Fleet et al. (2010), but in disagreement with Knyazev et al. (2011). Presumably, the apatites synthesized by Knyazev et al. (2011) were of the composition Pb9(PO4)6, considering the close agreement of the unit-cell parameters from the studies of Knyazev et al. (2011) and Hata et al. (1980; more discussion later). In addition, the unit-cell parameters of Pb10(VO4)6F2 (Table 2) are also much comparable to the values given out by Merker and Wondratschek (1959), Kreidler and Hummel (1970), and Grisafe and Hummel (1970).

Table 2 Unit-cell parameters of apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2
Full size table

The unit-cell parameters of the solid solution of the lead apatites Pb10[(PO4)6-x (VO4) x ]F2 at ambient P–T conditions are shown in Fig. 3. For this solid solution, the replacement of P by V causes the a-axis of the apatites to expand (up to about 3.4%), but leaves the c-axis more or less unchanged (less than 1%), leading to a decreased c/a ratio of the unit cell (up to about 2.7%). Obvious in Fig. 3 is the insignificant deviation from ideal mixing for all unit-cell parameters, suggesting that the Vegard’s law generally holds for this solid solution. Specifically, the deviation from the Vegard’s law in the cases of the a-axis, c-axis, and volume is negative for the apatites with x < 4 and positive for the apatites with x > 4; this pattern, however, is reversed in the case of the c/a ratio. For the calcium phosphate and vanadate apatite solid solution in comparison (Ca10[(PO4)6-x (VO4) x ](OH)2; Kim et al. 2000; Boechat et al. 2000), insignificant deviation from the Vegard’s law is also observed for all the unit-cell parameters (Fig. 3).

Fig. 3
figure 3

Effect of composition on the unit-cell parameters of the apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2 (filled circles; this study) and Ca10[(PO4)6-x (VO4) x ](OH)2 (filled squares): a the a-axis; b the c-axis; c the volume; and d the c/a ratio. Data for the Ca10[(PO4)6-x (VO4) x ](OH)2 solid solution are from Kim et al. (2000; x = 0.0) and Boechat et al. (2000; x = 0.3, 1.5, 3.0, 4.5 and 6.0). The composition of the apatites from Kim et al. (2000) was not quantified, whereas those from Boechat et al. (2000) were constrained by inductively coupled plasma

Full size image

Volume-composition relationship of a binary solid solution such as the one investigated here is usually regarded as a good indicator of the general thermodynamic properties of the solid solution. As pointed out by Kerrick and Darken (1975), the larger the difference is in the molar volumes between two end-members of a binary system, the greater the possibility is for them to deviate away from an ideal solid solution. For binary oxide systems and silicate systems which behave ideally, the maximum difference in the molar volumes is about 5% (Kerrick and Darken 1975). The maximum volume difference in the Pb10[(PO4)6-x (VO4) x ]F2 binary solid solution is about 8% (Table 2), that of the Ca10[(PO4)6-x (VO4) x ](OH)2 solid solution about 8% (Kim et al. 2000; Boechat et al. 2000), that of Pb10[(PO4)6-x (VO4) x ]Cl2 about 6.5% (Chernorukov et al. 2010), and that of Pb10(PO4)6(F2-x Cl x ) about 2.4% (Knyazev et al. 2011). All these solid solutions are non-ideal. The non-ideal solid solution behavior of the first three apatite solid solutions is understood by referring to the large difference of the volumes between the end-members, while that of the Pb10(PO4)6(F2-x Cl x ) solid solution is probably related to the different positions of the F and Cl atoms in the c-axis channel of the apatites (Kim et al. 2000).

As previously mentioned, the synthetic apatites from Chernorukov et al. (Pb10[(PO4)6-x (VO4) x ]Cl2; 2010) and Knyazev et al. (Pb10(PO4)6(F2-x Cl x ); 2011) might be problematic, so that the solid solution behavior of the apatites established by these two studies should be treated with great caution. Due to the much lower experimental temperatures and much shorter synthesizing durations (at 350–700°C for about 10 h; Chernorukov et al. 2010; Knyazev et al. 2011), these apatites were too fine to be compositionally analyzed. Additionally, SEM was not employed to check for any potential trace phases. The open porcelain crucible used in the synthesizing experiments, however, might lead to the loss of Pb to porcelain and the loss of F and Cl to open air during sample-synthesizing at high temperatures (Hata et al. 1980), which eventually should result in some trace phases and variable apatite compositions. This possibility has been well hinted by the room-T volume of the assumed Pb10(PO4)6F2 apatite (621.3 Å3; Knyazev et al. 2011), which is close to the volume of the Pb9(PO4)6 apatite (~615 Å3; Hata et al. 1980) rather than the well-established value of about 600 Å3 for the Pb10(PO4)6F2 apatite (Merker and Wondratschek 1959; Kreidler and Hummel 1970; Grisafe and Hummel 1970; Kim et al. 2000; Liu et al. 2008; Fleet et al. 2010). On the other hand, the Pb10(PO4)6Cl2 apatite synthesized by Chernorukov et al. (2010) and Knyazev et al. (2011) appeared problem-free since its volume was very compatible with the literature data (~631 Å3; Merker and Wondratschek 1959; Kreidler and Hummel 1970; Grisafe and Hummel 1970; Kim et al. 2000). Nevertheless, the uncertainty in the apatite compositions certainly impaired the proposed regular solution models for these two binary systems.

Raman feature

Both lead fluorapatite and lead fluorvanadate apatite have the crystal structure of P63/m, with six tetrahedral BO4 units in the primitive unit cell Pb10[(PO4)6-x (VO4) x ]F2. The vibrational spectrum of apatites is mainly about the BO4 ions. For the free form of BO4 ion (B = P or V, with symmetry of T d), the symmetric stretching mode ν 1 is nondegenerate, asymmetric stretching mode ν 3 is triply degenerate, and the corresponding bending vibrations ν 2 and ν 4 are doubly degenerate and triply degenerate, respectively (Beran et al. 2004). In the crystal structure of the apatites, the distorted BO4 ions with the site symmetry of C s (Bhatnager 1971) should have 4 stretching bands and 5 bending bands (1ν 1 + 3ν 3 + 2ν 2 + 3ν 4 = 9), which are all Raman-active. If strong interaction among the BO4 ions and coupling of their vibrational modes present, these bands should further split into 15 internal vibrational modes (6Ag, 3E1g, and 6E2g), as predicted by the factor-group analysis (Klee 1970; Levitt and Condrate 1970), which include 2ν 1 (Ag + E2g), 5ν 3 (2Ag + E1g + 2E2g), 3ν 2 (A1g + E1g + E2g), and 5ν 4 (2Ag + 2E2g + E1g).

The Raman spectra of the solid solution of lead fluorapatite and lead fluorvanadate apatite are shown in Fig. 4. The bands from 900 to 1,050 cm−1 are assigned to the ν 1 symmetric stretching vibration and ν 3 asymmetric stretching vibration of the phosphate ion, while those from 700 to 900 cm−1 are assigned to the vanadate ion (Adler 1964, 1968; Levitt and Condrate 1970; Bhatnager 1971). As the composition changes, both the spectrum shape and band position vary systematically.

Fig. 4
figure 4

Raman spectra of the apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2. In order to remove the difference in the analytical condition among different analyses, the sum of the intensities of the symmetric stretching vibration of the PO4 3− and VO4 3− ions was defined as 1, and subsequently the spectrum was normalized to it

Full size image

The band-component analyses of the Raman spectra of the phosphate and vanadate ions are shown in Fig. 5, with the former best illustrated using the V-free sample (HL019) and the latter using the P-free sample (HL010). In the 900–1,050 cm−1 region (Fig. 5a), four bands are generally detected for the phosphate ion at 933.4, 967.9, 1,002.6, and 1,017.4 cm−1. In accordance with the literature data (Table 3), the first band is attributed to the symmetric stretching vibration of the PO4 3− ion, while the left three bands are attributed to the asymmetric stretching vibration. In the 700–900 cm−1 region (Fig. 5b), two bands are clearly observed for the vanadate ion at 830.3 and 792.3 cm−1. Since the Raman band at 830.3 cm−1 is asymmetric, another band at 818.3 cm−1 may be resolved. In addition, there is a very weak band at 745.6 cm−1 which highly possibly belongs to the vanadate ion. According to the literature data (Adler 1968; Levitt and Condrate 1970; Bhatnager 1971; Frost et al. 2003; Eon et al. 2006; Zhang et al. 2007), we assign the band at 830.3 cm−1 to the symmetric stretching vibration and other bands to the asymmetric stretching vibration of the vanadate ion (Table 3). Since both ions have 1ν 1 band and 3ν 3 bands, their symmetric states are thus similar and both P and V are on a C s site, indicating negligible factor-group effect (Levitt and Condrate 1970; Bhatnager 1971). In contrast, Frost and Palmer (2007) deconvoluted their spectra into more components and claimed a reduced symmetry for the PO4 3− ions in the pyromorphite Pb10(PO4)6Cl2.

Fig. 5
figure 5

Raman spectroscopic analysis for PO4 3− (a) and VO4 3− (b) in the stretching region. Spectrum shown in (a) was taken on HL019 whereas that in (b) was taken on HL010 (Table 1)

Full size image
Table 3 Band-component analysis of the Raman spectrum of the PO4 3− and VO4 3− cations in apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2 (stretching vibration)
Full size table

The Raman frequencies of the PO4 3− and VO4 3− symmetric stretching mode ν1 of the solid solution between lead fluorapatite and lead fluorvanadate apatite (Table 4) are shown in Fig. 6. Apparently, the frequencies are almost linearly correlated with the composition and gradually shift to lower wavenumbers as the content of V increases. It follows that the P and V cations in the BO4 tetrahedra must gradually change their sizes as their proportions vary (Hardcastle and Wachs 1991; Popović et al. 2005). This phenomenon is fully compatible with early observations made with the PO4 − substituted vanadinite (Adler 1964) and the calcium phosphate and vanadate hydroxyapatite solid solution (Boechat et al. 2000). Since the BO4 tetrahedron is the most incompressible structural unit in the apatite structure (Comodi et al. 2001), its large influence on the sizes of P and V seems reasonable.

Table 4 Symmetric stretching vibration of the PO4 3− and VO4 3− cations in apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2
Full size table
Fig. 6
figure 6

Effect of composition on the symmetric stretching vibration of the PO4 3− and VO4 3− ions

Full size image

Additionally, the Raman data from this investigation have demonstrated that the frequencies of the PO4 3− and VO4 3− symmetric stretching mode ν1 of the solid solution between lead fluorapatite and lead fluorvanadate apatite well correlate with the PO4 3− and VO4 3− contents. The established equations, shown in Fig. 6, apparently provide an inexpensive and convenient analytical method for the contents of these components in lead apatites.

Thermal expansivity

The high-T X-ray data suggest that the lead fluorapatite and lead fluorvanadate apatite solid solution is stable (or metastable due to potential kinetic reasons) up to at least 600°C. At 700°C, these apatites start to be unstable, which seems surprising since they were synthesized at 700°C and 1 atm. The major difference between the synthesizing experiments and high-T X-ray diffraction experiments is that the former was conducted in closed system, whereas the latter was carried out in open air. As suggested by Hata et al. (1980), synthesizing apatites in open air at high temperatures might lead to different and volatile-free product (for example, Pb9(PO4)6).

The room-P unit-cell parameters at temperatures up to 600°C (Table 2) are shown in Fig. 7. Apparently, these unit-cell parameters are generally in a good linear relation with T, indicating that the thermal expansion coefficients are T-independent in the investigated temperature range. Consequently, we fitted the room-P unit-cell parameters at different temperatures with the equation \( j = j_{0} {\text{e}}^{{\alpha_{j} (T - T_{0} )}} \) to derive the thermal expansion coefficients \( \alpha_{j} = j^{ - 1} (\partial j/\partial T) \), where j stands for a, c, or V. The derived thermal expansion coefficients are listed in Table 5 and shown in Fig. 8. Evidently, the thermal expansion coefficients generally vary linearly with the composition, and the maximum amount of variation in the volumetric thermal expansion coefficients is about 13% (from 7.30(15) × 10−5/oC for Pb10(PO4)6F2 to 8.28(22) × 10−5/oC for Pb10(VO4)6F2). The increase in the thermal expansivity caused by the substitution of the VO4 tetrahedra for the PO4 tetrahedra should be expected since the V–O bonds are longer and weaker than the P–O bonds.

Fig. 7
figure 7

Evolution of unit-cell parameters a, c, V, and c/a of the apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2 with temperature

Full size image
Table 5 Thermal expansion coefficients of apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2
Full size table
Fig. 8
figure 8

Effect of composition on the thermal expansion coefficient of the apatite solid solution Pb10[(PO4)6-x (VO4) x ]F2

Full size image

The thermal expansivity of various calcium apatites has been experimentally investigated at room pressure, and the unit-cell parameters are generally in good linear relationship with temperature at least up to 600°C (Fischer et al. 1983; Bauer and Klee 1993; Brunet et al. 1999; Tonegawa et al. 2010). For the purpose of comparison, we have reprocessed the V-T data (T ≤ 600°C) in the literature and obtained α V  = 4.5(5) × 10−5/oC for Ca10(PO4)6(OH)2 (Fischer et al. 1983), α V  = 3.9(2) × 10−5/oC for Ca10(PO4)6(OH)2 (Brunet et al. 1999), α V  = 4.3(1) × 10−5/oC for Ca10(PO4)6F2 (Brunet et al. 1999), α V  = 3.56(1) × 10−5/oC for Ca10(PO4)6Cl2 (Brunet et al. 1999), and α V  = 4.0(2) × 10−5/oC for type A carbonate apatite (Ca10(PO4)6(CO3); Tonegawa et al. 2010).

Recently, the thermal expansivity of some lead apatites was experimentally investigated by Chernorukov et al. (2010) and Knyazev et al. (2011), which did not disclose any details about their high-T X-ray diffraction experiments. We also reprocessed their V-T data (T ≤ 600°C) and obtained α V  = 5.2(1) × 10−5/oC for Pb10(VO4)6Cl2 (Chernorukov et al. 2010), α V  = 4.9(1) × 10−5/oC for Pb10(PO4)6Cl2 (Knyazev et al. 2011), and α V  = 4.7(2) × 10−5/oC for Pb10(PO4)6F2 (Knyazev et al. 2011). Apparently, the thermal expansivity of Pb10(PO4)6F2 obtained by Knyazev et al. (2011) is much different to our result (α V  = 7.30(15) × 10−5/oC; Table 5). For the Pb10[(PO4)6-x (VO4) x ]Cl2 solid solution, the variation in the thermal expansivity is about 6%, which is only about half of that of the Pb10[(PO4)6-x (VO4) x ]F2 solid solution. It has to point out here that the results from Chernorukov et al. (2010) and Knyazev et al. (2011), however, must be viewed with great caution, considering the potential problems in their synthetic samples as mentioned earlier.

For the calcium apatites, the maximum amount of variation in the thermal expansivity caused by the compositional difference on the X site is about 26% (from 3.56(1) × 10−5/oC for Ca10(PO4)6Cl2 to 4.5(5) × 10−5/oC for Ca10(PO4)6(OH)2). For the lead apatites, the maximum amount of variation in the thermal expansivity caused by the compositional difference on the X site is much less, about 4% (from 4.9(1) × 10−5/oC for Pb10(PO4)6Cl2 to 4.7(2) × 10−5/oC for Pb10(PO4)6F2), according to the V-T data from Knyazev et al. (2011). It appears that the effect of the X-site compositional difference on the thermal expansivity of apatites is very variable, and much affected by the ion species on the M site.

As to the effect of the B-site compositional difference on the thermal expansivity, this study suggested a value of about 13% for the Pb10[(PO4)6-x (VO4) x ]F2 solid solution, and the data from Chernorukov et al. (2010) and Knyazev et al. (2011) suggested a value of about 6% for the Pb10[(PO4)6-x (VO4) x ]Cl2 solid solution. Thus, the effect of the B-site compositional difference on the thermal expansivity is also variable and affected by the X species.

As to the effect of the M-site compositional difference on the thermal expansivity, the existing investigations suggested values of about 38% for the (Ca10-x Pb x )(PO4)6Cl2 solid solution (Brunet et al. 1999; Chernorukov et al. 2010) and 70% for the (Ca10-x Pb x )(PO4)6F2 solid solution (Brunet et al. 1999; This study). If the data of the problematic Pb10(PO4)6F2 apatite from Knyazev et al. (2011; 4.7(2) × 10−5/oC) is used, the effect of the M-site compositional difference on the thermal expansivity of the (Ca10-x Pb x )(PO4)6F2 solid solution decreases to just about 9%, which is unusually low. Anyhow, it is reasonable to conclude that the effect of the M-site compositional difference on the thermal expansivity is not only variable, but also affected by the X species.

Summarily, the influence of the X-site and B-site compositional difference on the thermal expansivity of apatites is generally small, while that of the M-site compositional difference is large. This argument is in good agreement with the crystallographic features of apatites (Sha et al. 1994; Comodi et al. 2001) and available compression data at ambient temperature (Brunet et al. 1999; Matsukage et al. 2004; Liu et al. 2008, 2011a, c; Fleet et al. 2010).