Characterization, dissolution and solubility of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH] at 25 °C and pH 2–9

Abstract

Background

The interaction between Ca-HAP and Pb²⁺ solution can result in the formation of a hydroxyapatite–hydroxypyromorphite solid solution [(Pb_xCa_1−x)₅(PO₄)₃(OH)], which can greatly affect the transport and distribution of toxic Pb in water, rock and soil. Therefore, it’s necessary to know the physicochemical properties of (Pb_xCa_1−x)₅(PO₄)₃(OH), predominantly its thermodynamic solubility and stability in aqueous solution. Nevertheless, no experiment on the dissolution and related thermodynamic data has been reported.

Results

Dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃(OH)] in aqueous solution at 25 °C was experimentally studied. The aqueous concentrations were greatly affected by the Pb/(Pb + Ca) molar ratios (X_Pb) of the solids. For the solids with high X_Pb [(Pb_0.89Ca_0.11)₅(PO₄)₃OH], the aqueous Pb²⁺ concentrations increased rapidly with time and reached a peak value after 240–720 h dissolution, and then decreased gradually and reached a stable state after 5040 h dissolution. For the solids with low X_Pb (0.00–0.80), the aqueous Pb²⁺ concentrations increased quickly with time and reached a peak value after 1–12 h dissolution, and then decreased gradually and attained a stable state after 720–2160 h dissolution.

Conclusions

The dissolution process of the solids with high X_Pb (0.89–1.00) was different from that of the solids with low X_Pb (0.00–0.80). The average K _sp values were estimated to be 10^{−80.77±0.20} (10^−80.57–10^−80.96) for hydroxypyromorphite [Pb₅(PO₄)₃OH] and 10^{−58.38±0.07} (10^−58.31–10^−58.46) for calcium hydroxyapatite [Ca₅(PO₄)₃OH]. The Gibbs free energies of formation (ΔG ^o _f ) were determined to be −3796.71 and −6314.63 kJ/mol, respectively. The solubility decreased with the increasing Pb/(Pb + Ca) molar ratios (X_Pb) of (Pb_xCa_1‒x)₅(PO₄)₃(OH). For the dissolution at 25 °C with an initial pH of 2.00, the experimental data plotted on the Lippmann diagram showed that the solid solution (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolved stoichiometrically at the early stage of dissolution and moved gradually up to the Lippmann solutus curve and the saturation curve for Pb₅(PO₄)₃OH, and then the data points moved along the Lippmann solutus curve from right to left. The Pb-rich (Pb_xCa_1−x)₅(PO₄)₃(OH) was in equilibrium with the Ca-rich aqueous solution.

Background

The apatite group minerals with the general formula M₅(PO₄)₃X have a wide compositional variation because of their huge isomorphic capacity and numerous substitutions of ions [1–5], which play an important role in many research areas, such as geology, environmental sciences, biomaterials, material science and technology [6–9].

Calcium hydroxyapatite [Ca-HAP] is the main component of vertebral animals’ bones [10–15]. Commonly, natural apatites as raw materials for the phosphate fertilizer industry contain some traces amount of various elements [10], among which lead and cadmium are predominantly risky and may be redistributed in natural waters, soil and agricultural products, especially in rice and vegetables. When these toxic heavy metals are taken into animals through food chains, they may concentrate in animals’ hard tissues through the possible substitution, which can cause osteoporotic processes and dental caries [10–13, 15].

Due to the large substitution capacity for various toxic trace elements, the natural or synthetic calcium apatite can be used to immobilize or remove hazardous chemicals in metal-contaminated soils and industrial wastewaters [4, 8, 11, 16–18]. Lead apatite is the most stable lead form under various environmental conditions. It is now considered that the in situ immobilization of lead-contaminated systems with phosphates is one of the appropriate and cost-effective technologies [19]. Two main mechanisms have been proposed for the immobilization of lead by hydroxyapatite, i.e., (1) hydroxyapatite dissolution, followed by phosphate reaction with dissolved Pb²⁺ and precipitation of pure hydroxypyromorphite [19, 20]; (2) ion exchange between Ca²⁺ ions in hydroxyapatite lattice and Pb²⁺ ions in solution [19, 21]. During the reaction of hydroxyapatite with Pb²⁺ solution, a new hydroxyapatite–hydroxypyromorphite solid solution [(Pb_xCa_1−x)₅(PO₄)₃(OH), Pb–Ca-HAP] with Pb²⁺ ions occupying Ca²⁺ sites formed and transformed in hydroxypyromorphite with times [22]. The existence of Pb–Ca-HAP as an intermediate phase was confirmed by X-ray diffractometer and electron microscopy analysis [23].

Solid solutions play a very important role in environmental and geochemical sciences because a metal-bearing solid solution may form on the solid surface when the solid come into contact with a metal-containing solution. The thermodynamic properties of the solid solution—aqueous solution equilibrium can greatly influence the transport and distribution of the toxic metals in water, rock and soil [24, 25]. Therefore, it’s necessary to know the physicochemical properties of the (Pb_xCa_1−x)₅(PO₄)₃(OH) solid solution, predominantly its thermodynamic solubility and stability in aqueous solution, whether for optimizing industrial processes relating to apatites, or for understanding mineral evolutions and natural phenomena [8]. Generally, the natural apatite is not a pure endmember but rather a solid solution [3]. Nevertheless, most of the researches about the apatite thermodynamic properties that have already been reported in literatures focus mainly on pure apatite [8, 16, 17, 26–29]. Until now, no experiment on the dissolution mechanism, solubility product and other thermodynamic data of the (Pb_xCa_1−x)₅(PO₄)₃(OH) solid solution [Pb–Ca-HAP] has been reported in literatures, even though the dissolution-related release of lead and phosphate from solid to solution has a potential effect on the cycling of the relevant elements.

In the present study, lead hydroxyapatite [hydroxypyromorphite, Pb-HAP, Pb₅(PO₄)₃(OH)], lead–calcium hydroxyapatite solid solution [Pb–Ca-HAP (Pb_xCa_1−x)₅(PO₄)₃(OH)] with varying Pb/(Pb + Ca) molar ratios and calcium hydroxyapatite [Ca-HAP, Ca₅(PO₄)₃(OH)] were firstly synthesized and characterized by chemical analysis, powder X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FT-IR), field emission scanning electron microscopy (FE-SEM) and field emission transmission electron microscopy (FE-TEM), and then the dissolution and release processes of elements (Pb²⁺, Ca²⁺, PO₄ ³⁻) were investigated through batch experiments. The Lippmann diagram [30] for the (Pb_xCa_1−x)₅(PO₄)₃(OH) solid solution was constructed to study the reaction path of the solid-water interaction and its possible effect on the solubility and distribution of lead and phosphate in the environment.

Experimental methods

Solid preparation and characterization

Solid preparation

The Pb-HAP, Pb–Ca-HAP solid solution and Ca-HAP samples were synthesized according to the following precipitation reaction: 5M²⁺+3PO₄ ³⁻+OH⁻ = M₅(PO₄)₃OH, where M = (Pb + Ca) for the solid solution and Pb or Ca for the end-member. Firstly, a series of 250 mL solutions of different Pb/(Pb + Ca) molar ratios were prepared by dissolving different amounts of Pb(CH₃COO)₂·H₂O and Ca(CH₃COO)₂·3H₂O into pure water, while the total amount of lead and calcium in each solution was maintained to be 0.4 mol/L. Two hundred and fifty millilitre of 4.4 mol/L CH₃COONH₄ buffer solution was then mixed with each lead–calcium solution in 1L polypropylene bottle. After that, 500 mL of 0.12 mol/L NH₄H₂PO₄ solution was quickly added into the bottle with stirring (Table 1). The resulting white suspension was adjusted to pH 7.50 with NH₄OH, stirred for 10 min at room temperature, and then aged at 100 °C for 48 h, as suggested by Yasukawa et al. [10]. Finally, the obtained precipitates were carefully washed with pure water and dried in an oven at 70 °C for 16 h.

Table 1 Summary of synthesis and composition of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH]

Characterization

To determine the chemical component of each obtained precipitate, 10 mg of the precipitate was firstly dissolved in 20 mL of 1 mol/L nitric acid solution and diluted to 100 mL with pure water. The Pb²⁺, Ca²⁺and PO₄ ³⁻ concentrations were then measured by the inductively coupled plasma—optical emission spectrometer (ICP-OES, Perkin-Elmer Optima 7000DV). All solid samples were also characterized using an X’Pert PRO powder X-ray diffractometer (XRD) with Cu Kα radiation (40 kV and 40 mA) at a scanning rate of 0.10°/min in a 2θ range of 10–80°. By comparing the recorded XRD pattern with the standard from the International Center for Diffraction Data (ICDD), the precipitates were crystallographically identified. Using the Fourier transform infrared spectrophotometer (FT-IR, Nicolet Nexus 470), all solids were also analyzed in KBr pellets within 4000–400 cm⁻¹. The field-emission scanning electron microscope (FE-SEM, Hitachi S-4800) and the field-emission transmission electron microscope (FE-TEM, Jeol JEM-2100F) were applied to observe the solid morphology.

Dissolution experiments

2.0 g of each Ca-HAP, Pb–Ca-HAP or Pb-HAP solid was first added into a series of 100 mL polypropylene bottles, which were then filled with 100 mL of HNO₃ solution (pH 2.00), ultrapure water (pH 5.60) or NaOH solution (pH 9.00). All bottles were capped and placed in water baths at 25 °C. From each bottle, the aqueous solutions (5 mL) were sampled at 22 time intervals (1, 3, 6, 12, 24, 48, 72, 120, 240, 360, 480, 720, 1080, 1440, 1800, 2160, 2880, 3600, 4320, 5040, 5760, 7200 h), filtered through 0.22 μm pore filters and stabilized in 25 mL volumetric flask using 0.2 % HNO₃. An equivalent volume of pure water (5 mL) was added into the bottle after each sampling. The dilution effects of the acidic and basic solutions throughout the experiments were considered in the calculation by using the program PHREEQC [31]. The aqueous concentrations of Pb, Ca and P were measured using ICP-OES. At the end of the dissolution experiment, the solids were collected from the bottles, rinsed, dried and characterized using XRD, FT-IR, FE-SEM and FE-TEM instruments in the same manner as previously described.

Thermodynamic calculations

The aqueous activities of Pb²⁺(aq), Ca²⁺(aq), PO₄ ³⁻(aq), and OH⁻(aq) were first calculated using PHREEQC Version 3 [31], and then the ion activity products (IAPs) for (Pb_xCa_1−x)₅(PO₄)₃(OH) were calculated according to the mass-action expressions. The minteq.v4.dat database with the addition of the thermodynamic data for PbHPO ⁰₄ , PbH₂PO₄ ⁺ and PbP₂O₇ ²⁻ from the llnl.dat database was used in the simulation. The minteq.v4.dat database contains thermodynamic data for the aqueous species and gas and mineral phases that are derived from the database files of MINTEQA2 [32, 33]. The aqueous species considered in the calculation included Pb²⁺, PbOH⁺, Pb(OH) ⁰₂ , Pb(OH) ⁻₃ , Pb(OH) ²⁻₄ , Pb₃(OH) ²⁺₄ , Pb₂OH³⁺, Pb₄(OH) ⁴⁺₄ , PbHPO ⁰₄ , PbH₂PO₄ ⁺ and PbP₂O₇ ²⁻ for the total lead; Ca²⁺, CaOH⁺, CaHPO₄, CaPO₄ ⁻ and CaH₂PO₄ ⁺ for the total calcium calculation. For the total phosphate, the aqueous species considered were PO₄ ³⁻, HPO₄ ²⁻, H₂PO₄ ⁻, H₃PO ⁰₄ , PbHPO₄ ⁰, PbH₂PO₄ ⁺, PbP₂O₇ ²⁻, CaHPO₄, CaPO₄ ⁻ and CaH₂PO₄ ⁺.

Results and discussion

Solid characterization

The chemical compositions of the prepared solids are related to the Pb/(Pb + Ca) molar ratios in the precursor solutions (Table 1). The compositions of the Pb-HAP, Pb–Ca-HAP and Ca-HAP precipitates obtained are the designed components of (Pb_xCa_1−x)₅(PO₄)₃(OH) with the (Pb + Ca)/P molar ratio of 1.67, and all of the Pb/(Pb + Ca) molar ratios are almost the same as the precursor solutions.

The XRD patterns showed that all (Pb_xCa_1−x)₅(PO₄)₃(OH) solids belong to the apatite group of the hexagonal system P6₃/m differing only in peak location, peak width and absolute intensity (Fig. 1). The solid with X_Pb = 1.00 is identified as lead phosphate hydroxide [hydroxypyromorphite, Pb-HAP] (Reference code 01-087-2477) with the calculated unit cell parameters of a = 0.989 nm and c = 0.748 nm, and the solid with X_Pb = 0.00 is recognized as calcium phosphate hydroxide [calcium hydroxyapatite, Ca-HAP] (Reference code 00-024-0033) with the calculated unit cell parameters of a = 0.944 nm and c = 0. 0.686 nm. Due to the substitution of Ca²⁺ (0.100 nm) with larger Pb²⁺ (0.119 nm) in the apatite structure [2, 10, 13], the lattice parameters a and c increased almost linearly with the increasing X_Pb from 0.944 to 0.989 nm and from 0.686 to 0.748 nm, respectively. However, an obvious deviation of both a and c lattice parameters from Vegard’s rule was also observed [34]. The reflection of the (Pb_xCa_1−x)₅(PO₄)₃(OH) solid shifts gradually to a higher-angle direction as the solid Pb/(Pb + Ca) molar ration (X_Pb) decreases, which indicated that (Pb_xCa_1−x)₅(PO₄)₃(OH) is a continuous solid solution within the whole range of X_Pb = 0–1.00 (Fig. 1). Some additional peaks other than hydroxypyromorphite have been also recognized in XRD patterns after the dissolution at initial pH 2.00 and 25 °C (Fig. 1), the peaks of PbHPO₄ [lead hydrogen phosphate, Reference code 00-029-0773] around 13.155° [2θ], the peaks of Pb₃(PO₄)₂ [lead phosphate, Reference code 00-025-1394] around 26.783, 28.559 and 29.250° [2θ] were also recognized, which means that PbHPO₄ and Pb₃(PO₄)₂ as secondary precipitate formed during the (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolution at the initial pH 2.00. But no secondary minerals were observed after the dissolution at the initial pHs 5.60 and 9.00 (Additional file 1: Appendix A). The result of the PHREEQC simulation also shows that the aqueous solutions were undersaturated with respect to any possible secondary minerals (e.g., massicot (PbO), litharge (PbO), PbO·0.3H₂O, plattnerite (PbO₂), Pb(OH)₂, Pb₂O(OH)₂, PbHPO₄, Pb₃(PO₄)₂; lime [CaO], portlandite [Ca(OH)₂], Ca₃(PO₄)₂(beta), CaHPO₄, CaHPO₄·2H₂O, Ca₄H(PO₄)₃·3H₂O), except in some cases of the dissolution at the initial pH 2.00, in which the aqueous solutions were saturated or nearly saturated with respect to PbHPO₄ and Pb₃(PO₄)₂.

Fig. 1

X-ray diffractograms (XRD) of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH] before (a) and after dissolution at 25 °C and an initial pH of 2.00 for 300 days (b)

Although lead hydroxyapatite (Pb-HAP) and calcium hydroxyapatite (Ca-HAP) are isomorphous, their FT-IR spectra have essential differences. Generally, the tetrahedral PO₄ ³⁻ has four vibrational modes, i.e., the symmetric P–O stretching (v ₁), the O–P–O bending (v ₂), the P–O stretching (v ₃), and the O–P–O bending (v ₄). But in the undistorted state, only the absorptions for the vibrations v ₃ and v ₄ can be detected, the two other vibrations v ₁ and v ₂ become infrared inactive [12]. In the FT-IR spectra, the tetrahedral PO₄ ³⁻ of Ca-HAP showed the vibrational bands at 962.83 cm⁻¹ (ν ₂), 1045.76 and 1091.08 cm⁻¹ (ν ₃), 567.96 and 602.67 cm⁻¹ (ν ₄), which shifted to 938.24 cm⁻¹ (ν ₂), 985.01 and 1031.77 cm⁻¹ (ν ₃), 536.62–573.74 cm⁻¹ (ν ₄) as the solid Pb/(Pb + Ca) molar ratio (X_Pb) increased from 0 to 1.00, respectively (Fig. 2). The bands at 471.53 cm⁻¹ (ν ₁) and 633.05 cm⁻¹ (ν ₄) diminish with increasing X_Pb and disappear as X_Pb > 0.80 because of the variation of the PO₄ ³⁻ symmetry. All bands, especially the P–O stretching (v ₃) bands, weaken with the increasing X_Pb due to the IR beam scattering of large particles [10]. The strong sharp bands at 3553.83–3571.67 cm⁻¹ represent the stretching vibrations of the bulk OH⁻ and the band at 3735.15–3736.56 cm⁻¹ represents the surface P-OH groups [15, 35]. The band at 1455 cm⁻¹ for CO₃ ²⁻ vibration [36] and the band at 871 cm⁻¹ for HPO₄ ²⁻ [10, 11] are not visible in the FT-IR spectra of the present work.

Fig. 2

Fourier transform infrared (FT-IR) spectra of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH] before (a) and after dissolution at 25 °C and an initial pH of 2.00 for 300 days (b)

The Pb/(Pb + Ca) atomic ratio (X_Pb) can greatly affect the morphology and crystal structure of the (Pb_xCa_1−x)₅(PO₄)₃(OH) solid solution [2, 10, 13, 37]. With the increasing X_Pb, the lattice parameters increased gradually accompanying morphology variation (Fig. 3). The (Pb_xCa_1−x)₅(PO₄)₃(OH) solids with X_Pb = 0–0.51 are usually prism crystals with a hexagonal pyramid as termination (particle size 50–100 nm); the solids with X_Pb = 0.61–0.69 are typically hexagonal columnar crystals with a hexagonal pyramid or a pinacoid as termination, which elongate along the c axis (200–600 nm); the solids with X_Pb = 0.80–1.00 are characteristically prism crystals with a hexagonal pyramid as termination (2–20 µm) [34]. The hydroxypyromorphite (Pb-HAP) particles have an average length and width of 7.00 µm (3.43–10.43 µm) and 3.76 µm (1.83–4.88) before dissolution, and 6.85 µm (3.81–11.87 µm) and 4.04 µm (2.96–5.14 µm) after dissolution at 25 °C and an initial pH of 2.00.

Fig. 3

Field emission scanning electron micrographs (FE-SEM) and transmission electron microscope (TEM) images‎ of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH] before (a) and after dissolution at 25 °C and an initial pH of 2.00 for 300 days (b)

Dissolution mechanism

The solution pH and aqueous element concentrations for the dissolution of (Pb_xCa_1−x)₅(PO₄)₃(OH) [Pb–Ca-HAP] at 25 °C and different initial pHs (2.00, 5.60 and 9.00) versus time are illustrated in Figs. 4, 5 and 6.

Fig. 4

Change of the solution pH and elemental concentrations with time for dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH] at 25 °C and an initial pH of 2.00 for 300 days

Fig. 5

Change of the solution pH and elemental concentrations with time for dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH] at 25 °C and an initial pH 5.60 for 300 days

Fig. 6

Change of the solution pH and elemental concentrations with time for dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH] at 25 °C and an initial pH of 9.00 for 300 days

Dissolution of (Pb_xCa_1−x)₅(PO₄)₃(OH) in the acidic solution is stoichiometric in the early stage of dissolution and then always non-stoichiometric to the end of the dissolution experiments. For the dissolution at 25 °C and an initial pH of 2.00 (Fig. 4), the solution pH increased from 2.00 to 2.96–4.96 after 360 h dissolution and reached a stable state with pH 2.63–4.77 after 5040 h dissolution. The Pb/(Pb + Ca) atomic ratios (X_Pb) of the (Pb_xCa_1−x)₅(PO₄)₃(OH) solids can greatly affect the element concentrations in the aqueous solutions. In general, the final solution pHs decrease with the increasing X_Pb of the solids.

The dissolution process of the (Pb_xCa_1−x)₅(PO₄)₃(OH) solids with high X_Pb (0.89–1.00) is different from that of the (Pb_xCa_1−x)₅(PO₄)₃(OH) solids with low X_Pb (0.00–0.80) (Fig. 4). For the solids with high X_Pb or low X_Ca [(Pb_0.89Ca_0.11)₅(PO₄)₃OH], the aqueous Ca²⁺ concentrations increased gradually with the dissolution time and achieved a stable state after 4320 h dissolution. The aqueous Pb²⁺ concentrations increased rapidly with the dissolution time and achieved a peak value within 240–720 h, and then decreased gradually and attained a stable state after 5040 h dissolution. The aqueous phosphate concentration increased rapidly with time and achieved a peak value within 1–12 h, and then decreased gradually and attained a stable state after 2160 h dissolution. For the hydroxypyromorphite dissolution at 25 °C and an initial pH of 2.00 (Fig. 4), the aqueous lead concentrations increased constantly and reached a stable state after 720 h dissolution; the phosphate could be quickly released and reached the peak solution concentrations within 1 h dissolution, and then the aqueous phosphate concentration decreased and reached a stable state after 720 h; the solution pHs increased from 2.00 to 2.96 within 360 h and then varied between 2.58 and 3.16 (Fig. 4).

For the (Pb_xCa_1−x)₅(PO₄)₃(OH) solids with low X_Pb (0.00–0.80) or high X_Ca, the aqueous Ca²⁺ concentrations increased slowly with time and reached a peak value after 1200–1800 h dissolution, and then decreased slightly and were relatively stable after 4320 h. The aqueous Pb²⁺ concentrations increased quickly with time and reached a peak value within 1–12 h, and then decreased gradually and attained a stable state after 720–2160 h dissolution. The aqueous phosphate concentrations showed a similar evolution trend to that of the aqueous Ca²⁺ concentrations.

At the early stage of the dissolution (within 1 h), the aqueous Pb/(Pb + Ca) molar ratios (X_Pb,aq) are almost equal to the stoichiometric Pb/(Pb + Ca) atomic ratios (X_Pb,aq) of the corresponding (Pb_xCa_1−x)₅(PO₄)₃(OH) solids. Then, the aqueous Pb/(Pb + Ca) molar ratios (X_Pb,aq) decreased with time and were lower than the stoichiometric Pb/(Pb + Ca) ratios of the corresponding solids (X_Pb) (Additional file 2: Appendix B). For the solids with high X_Pb or low X_Ca [(Pb_0.89Ca_0.11)₅(PO₄)₃OH], the aqueous Pb/(Pb + Ca) molar ratios (X_Pb,aq) decreased gradually from 0.90 to 0.02 with the increasing time and achieved a stable state after 5040 h dissolution. For the solids with low X_Pb (0.00–0.80), the aqueous Pb/(Pb + Ca) molar ratios (X_Pb,aq) decreased rapidly from 0.00–0.79 to 0.00–0.004 after 72 h dissolution and then achieved a stable state.

The difference in the dissolution processes between the solids with X_Pb of 0.00–0.80 and those with X_Pb of 0.89–1.00 is related to the differences in the crystal structure and morphology of the (Pb_xCa_1−x)₅(PO₄)₃(OH) solids (Figs. 1, 2, 3). Crystallographically, two independent metal atoms, i.e., the M(1) atom and the M(2) atom, exist in the HAP lattice. Six O atoms and an OH surrounded the M(2) atom, while only six O atoms surrounded the M(1) atom almost octahedrally. Larger Pb²⁺ cations prefer to occupy the M(2) sites and smaller Ca²⁺ cations prefer to occupy the M(1) sites in the apatite structure. When Pb²⁺ cations substitute for Ca²⁺ cations in the apatite lattice, they occupied almost solely the M(2) sites, until, at X_Pb > 0.4, they also began to occupy the M(1) sites considerably, which could explain the discontinuity at around X_Pb = 0.4–0.6 in the curves of the a and c-axis parameters versus X_Pb [34]. The greatest deviations were noted at an intermediate X_Pb, whereas the entire replacement by Pb²⁺ formed a crystal that had the apatite structure, despite a total enlargement of the unit cell because of the larger Pb²⁺ cations [11, 16, 17, 27–29, 38], or the change of the a-axis parameter had a break at X_Pb of 0.8 [11]. For the dissolution of the (Pb_xCa_1−x)₅(PO₄)₃(OH) solids with high X_Pb in the acidic solution, Pb²⁺ cations, which occupy nearly all the M(2) sites [2, 39], can be preferentially released because of the interaction of the solution H⁺ with the OH surrounding the M(2) atom. For the dissolution of the (Pb_xCa_1−x)₅(PO₄)₃(OH) solids with low X_Pb in the acidic solution, Ca²⁺ cations in the M(2) sites can be preferentially released with respect to Pb²⁺ cations in the M(2) sites [2, 39], which will cause a higher aqueous X_Ca,aq than the solid X_Ca during the initial period of dissolution.

For the (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolution in pure water (pH 5.60) and the solution of initial pH 9.00, the solution pH values, lead and phosphate concentrations reached a stable state after 5040 h dissolution, which indicated a possible attainment of a steady-state between the (Pb_xCa_1−x)₅(PO₄)₃(OH) solid and the aqueous solution (Figs. 5, 6). The solution lead and phosphate concentrations are smaller than those for the (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolution in pure water at an initial pH of 2.00, the solubility of (Pb_xCa_1−x)₅(PO₄)₃OH [Pb–Ca-HAP] at an initial pH of 5.60 or 9.00 is significantly lower that that at an initial pH of 2.00 (Figs. 5, 6).

For the (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolution at an initial pH of 2.00 or 5.60, all solution pHs are higher than the initial pH values. pH of final solutions is buffered by various species of phosphates. The significant H⁺ consuming at the beginning of the dissolution indicates that the H⁺ sorption onto negatively charged oxygen ions of phosphate groups of the solid solution (Pb_xCa_1−x)₅(PO₄)₃OH may result in the transforming of PO₄ ³⁻ into HPO₄ ²⁻ at the solid surface in the acidic solution and promote the dissolution process. Additionally, the depleting of H⁺ ions during the solid dissolution may also result from the coexisting exchange of 2H⁺ for Pb²⁺ and Ca²⁺ at the (Pb_xCa_1−x)₅(PO₄)₃(OH) surface. Therefore, a complete describing of the (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolution should include following processes: (I) Diffusion of H⁺ from solution to the solid-solution interface; (II) H⁺ adsorption/desorption at the (Pb_xCa_1−x)₅(PO₄)₃(OH) surface; (III) Protonation and transformation of PO₄ ³⁻ into HPO₄ ²⁻ at the (Pb_xCa_1−x)₅(PO₄)₃(OH) surface in the acidic solution; (IV) Stoichiometric desorption of Pb²⁺, Ca²⁺ and PO₄ ³⁻ from the (Pb_xCa_1−x)₅(PO₄)₃(OH) surface and complexation; (V) Re-adsorption of Pb²⁺ and/or PO₄ ³⁻ from solution back onto the (Pb_xCa_1−x)₅(PO₄)₃(OH) surface; (VI) Attaining of a stable state.

In process (I)–(III), the diffusion and adsorption of protons onto the (Pb_xCa_1−x)₅(PO₄)₃(OH) surface can increase the solution pH from 2.00 to 2.96–4.96 within 360 h for the dissolution at an initial pH of 2.00. In process (IV) and (V), Pb²⁺, Ca²⁺ and PO₄ ³⁻ can be released from the (Pb_xCa_1−x)₅(PO₄)₃(OH) surface to the aqueous solution. Many possible reactions should be considered in describing the apatite dissolution due to its structural complexity [7]. The reaction (1) for the (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolution is strongly affected by the initial solution pH and the protonation and complexation reactions (2)–(6), which can result in an increase of the aqueous pH for the (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolution in acidic solution or a decrease of the solution pH for the (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolution in alkali solution.

$$\begin{aligned} &\left( {{\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1- {\text{x}}}} } \right)_{5} \left( {{\text{PO}}_{4} } \right)_{3} {\text{OH }} \\ & \quad = \, 5{\text{xPb}}^{2 + } + \, \left( {5 - 5{\text{x}}} \right){\text{Ca}}^{2 + } + \, 3{\text{PO}}_{4}^{3 - } + {\text{ OH}}^{ - }\end{aligned}$$

(1)

$${\text{PO}}_{4}^{3 - } + {\text{ nH}}^{ + } \leftrightarrow {\text{ H}}_{\text{n}} {\text{PO}}_{ 4}^{{\left( {3 - {\text{n}}} \right) - }} \quad \left( {{\text{n}} = 1, \, 2, \, 3} \right)$$

(2)

$${\text{Pb}}^{2 + } + {\text{nOH}}^{ - } \leftrightarrow {\text{ Pb}}\left( {\text{OH}} \right)_{\text{n}}^{{({\text{n}} - 2) - }} \quad \left( {{\text{n}}\;{ = }\;1,\;2,\;3,\;4} \right)$$

(3)

$${\text{Pb}}^{2 + } + {\text{ H}}_{\text{n}} {\text{PO}}_{ 4}^{{\left( {3 - n} \right) - }} \leftrightarrow {\text{ PbH}}_{\text{n}} {\text{PO}}_{ 4}^{{({\text{n}} - 1) + }} \quad \left( {{\text{n}}\;{ = }\;1,\;2} \right)$$

(4)

$${\text{Ca}}^{2 + } + \;{\text{OH}}^{ - } \leftrightarrow {\text{ Ca}}\left( {\text{OH}} \right)^{ + }$$

(5)

$${\text{Ca}}^{2 + } + {\text{ H}}_{\text{n}} {\text{PO}}_{4}^{{\left( {3 - {\text{n}}} \right) - }} \leftrightarrow {\text{ CaH}}_{\text{n}} {\text{PO}}_{4}^{{\left( {1 - {\text{n}}} \right) - }} \quad \left( {{\text{n}} = 0, \, 1, \, 2} \right)$$

(6)

In process (V), for (Pb_xCa_1−x)₅(PO₄)₃(OH) with X_Pb ≤ 0.80, Pb²⁺ ions are re-absorbed non-stoichiometrically from the solution onto the (Pb_xCa_1−x)₅(PO₄)₃(OH) surface, the aqueous lead concentrations and the solution Pb/(Pb + Ca) molar ratios decrease. For (Pb_xCa_1−x)₅(PO₄)₃(OH) with X_Pb ≥ 0.89, Pb²⁺ and PO₄ ³⁻ ions are partially re-absorbed from the solution onto the (Pb_xCa_1−x)₅(PO₄)₃(OH) surface when an initial part of (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolves, the aqueous lead and phosphate concentrations decrease. Consequently, a new surface layer can form, which may have a different chemical composition from the bulk solid (Table 1). Due to the very low solubility of apatite, its dissolution is ever non-stoichiometric at the atomic level and includes a series of chemical reactions [7]. Finally, sorption and desorption of lead and phosphate reach a stable state. The aqueous lead and phosphate concentrations are almost invariable for the (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolution in the acidic solution (initial pH of 2.00) at 25 °C from 5040 to 7200 h.

Determination of solubility

The activities of the aqueous lead, calcium and phosphate species in the final equilibrated solutions (5040, 5760, 7200 h) are used to calculate the solubility products for the (Pb_xCa_1−x)₅(PO₄)₃OH solid solution.

The stoichiometric dissolution of the (Pb_xCa_1−x)₅(PO₄)₃OH solid solution and the release of Pb²⁺, Ca²⁺ and PO₄ ³⁻ can be described according to Eq. (1). The solubility products (K _sp) for (Pb_xCa_1−x)₅(PO₄)₃OH are equal to the ion activity products (IAP) at equilibrium:

$$K_{sp} = {\text{ IAP }} = \, \left\{ {{\text{Pb}}^{2 + } } \right\}^{{5{\text{x}}}} \left\{ {{\text{Ca}}^{2 + } } \right\}^{{5 - 5{\text{x}}}} \left\{ {{\text{PO}}_{4}^{3 - } } \right\}^{3} \left\{ {{\text{OH}}^{ - } } \right\}$$

(7)

where {} represents the thermodynamic activities of the aqueous Pb²⁺, Ca²⁺ and PO₄ ³⁻.

The standard free energy of reaction (ΔG ^o _r ) can be calculated from K _sp at 298.15 K and 0.101 MPa (standard condition) by

$$\Delta G_{r}^{o} = \, - 5.708{ \log }K_{sp}$$

(8)

For Eq. (1),

$$\begin{aligned} \Delta G_{r}^{o} & = 5{\rm x} \Delta G_{f}^{o}[ {\rm Pb}^{2 + }] + ( 5 - 5{\rm x})\Delta G_{f}^{o} [{\rm Ca}^{2 + }] + 3\Delta G_{f}^{o} [{\rm PO}_{4}^{3 -}] \\ &\quad + \Delta G_{f}^{o}[{{\rm OH}}^{ - } ] - \Delta G_{f}^{o}[{{\rm OH}}^{-}] \\ & \quad -\Delta{G}_f^o[({{\rm Pb}}_{{\rm x}}{{\rm Ca}}_{1-{\rm x}})_5({\rm PO}_{4})_3{\rm OH}] \end{aligned}$$

(9)

Rearranging,

$$\begin{aligned}&\Delta G_{f}^{o} \left[ {\left( {{\text{Pb}}_{\text{x}} {\text{Ca}}_{{1 - {\text{x}}}} } \right)_{5} \left( {{\text{PO}}_{4} } \right)_{3} {\text{OH}}} \right] \, \\ & = 5{\text{x}}\Delta G_{f}^{o} \left[ {{\text{Pb}}^{2 + } } \right] + \left( {5 - 5{\text{x}}} \right)\Delta G_{f}^{o} \left[ {{\text{Ca}}^{2 + } } \right] \\ &\quad + 3\Delta G_{f}^{o} \left[ {{\text{PO}}_{4}^{3 - } } \right] + \Delta G_{f}^{o} [{\text{OH}}^{ - } ] \, - \Delta G_{r}^{o} \\ \end{aligned}$$

(10)

Table 2 lists the calculated solubility products (K _sp) for (Pb_xCa_1−x)₅(PO₄)₃OH, as well as the pH, Pb, Ca and P analyses at 25 °C and an initial pH of 2.00. The solubility products (K _sp) for the solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH] decreased almost linearly with the increasing X_Pb from 10^{−58.38±0.07} to 10^{−80.77±0.20}. Based on the following literature data obtained [39], ΔG ^o _f [Pb²⁺] = −24.39 kJ/mol, ΔG ^o _f [Ca²⁺] = −553.54 kJ/mol, ΔG ^o _f [PO₄ ³⁻] = −1018.8 kJ/mol, ΔG ^o _f [OH⁻] = −157.3 kJ/mol, the free energies of formation, ΔG ^o _f [(Pb_xCa_1−x)₅(PO₄)₃OH], were also calculated (Table 2). The solubility products (K _sp) for (Pb_xCa_1−x)₅(PO₄)₃OH at 25 °C and an initial pH of 5.60 and 9.00 were also determined (Additional file 3: Appendix C).

Tables 2 Analytical data and solubility determination of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1‒x)₅(PO₄)₃OH] (25 °C and an initial pH of 2.00)

The average K _sp values were estimated for hydroxypyromorphite [Pb₅(PO₄)₃OH] of 10^{−80.77±0.20} (10^−80.57–10^−80.96) at 25 °C, for Ca₅(PO₄)₃OH of 10^−58.38 (10^−58.31–10^−58.46) at 25 °C. The corresponding Gibbs free energies of formation (ΔG ^o _f ) were determined to be −3796.71 and −6314.63 kJ/mol.

The average K _sp for hydroxypyromorphite [Pb₅(PO₄)₃OH] of 10^{−80.77±0.20} is comparable with the value reported for lead chloropyromorphite [Pb₅(PO₄)₃Cl] of 10^−83.61 [6]. Whereas, the Gibbs free energy of formation (ΔG ^o _f ) for hydroxypyromorphite [Pb₅(PO₄)₃OH] of −3796.71 kJ/mol is lower than −3773.968 kJ/mol that was calculated from the K _sp of 10^−76.8 for hydroxypyromorphite [Pb₅(PO₄)₃OH] [38]. The average K _sp for calcium hydroxyapatite [Ca₅(PO₄)₃OH] was calculated to be 10^{−58.38±0.07} (10^−58.31–10^−58.46) at 25 °C in in the present work. Various K _sp values for Ca₅(PO₄)₃OH are reported in literatures, e.g., 10⁻⁵⁹ [40], 10^−58.3 [41], 10⁻⁵⁷ [42], 10^−58±1 [26], and 10^−57.72 [43]. The large discrepancies in K _sp values may be caused by the differences in experimental conditions [7].

In comparison, the average K _sp 10^{−80.77±0.20} for Pb₅(PO₄)₃OH is approximately 23.77–21.77 log units lower than 10⁻⁵⁷–10⁻⁵⁹ for Ca₅(PO₄)₃OH, i.e., Pb₅(PO₄)₃OH is extremely less soluble than Ca₅(PO₄)₃OH, which shows that it is favorable for the transformation of Ca₅(PO₄)₃OH to Pb₅(PO₄)₃OH in presence of aqueous Pb²⁺ [44]. In the amendments of lead-contaminated soils with natural and synthetic phosphates, it is found that earlier dissolution of calcium hydroxyapatite [Ca₅(PO₄)₃OH] can cause the following precipitation of the lead-bearing hydroxypyromorphite [Pb₅(PO₄)₃OH] [19, 21–23]. Ca₅(PO₄)₃OH dissolves continuously as the result of forming less soluble Pb₅(PO₄)₃OH [41]. The transport-controlled Ca₅(PO₄)₃OH dissolution can provide PO₄ ³⁻ for the Pb₅(PO₄)₃OH precipitation, which in turn consumes aqueous Pb²⁺ [44].

Saturation index for calcium and lead hydroxyapatite

Thermodynamic analyses can be carried out first by supposing the potential pure-phase equilibrium relationships [45]. The saturation index (SI = log IAP/K _sp) could be used to assess the pure-phase equilibrium, where IAP is the ion activity product ({Pb²⁺}⁵{PO₄ ³⁻}³{OH⁻} or {Ca²⁺}⁵{PO₄ ³⁻}³{OH⁻}) and K _sp is the solubility product of the pure-phase. If SI is close to zero, the solution is saturated with the solid; if SI is positive, the solution is supersaturated with the solid; and if SI is negative, the solution is undersaturated with the solid. The SI calculated for Ca-HAP [Ca₅(PO₄)₃OH] has an obvious difference in the variational trend from that for Pb-HAP [Pb₅(PO₄)₃OH] (Fig. 7). The maximum saturated index (SI) values for Ca₅(PO₄)₃OH appeared at the Pb/(Pb + Ca) molar ratio (X_Pb) of 0.69 [(Pb_0.69Ca_0.31)₅(PO₄)₃OH]. The aqueous solutions are supersaturated with Ca₅(PO₄)₃OH to the end of the dissolution experiment with (Pb_xCa_1−x)₅(PO₄)₃OH (X_Pb = 0.10–0.80). The aqueous solutions are considerably supersaturated with Pb₅(PO₄)₃OH at the end of the experiment for all (Pb_xCa_1−x)₅(PO₄)₃OH solids. Generally, the SI values for Pb₅(PO₄)₃OH decrease lineally with the increasing X_Pb of (Pb_xCa_1−x)₅(PO₄)₃OH. The dissolution–recrystallization can happen during the interaction between (Pb_xCa_1−x)₅(PO₄)₃OH and aqueous solution, and the less soluble component Pb-HAP [Pb₅(PO₄)₃OH] tends to distribute preferentially towards the solid phase [25, 46, 47].

Fig. 7

Calculated saturation indices for Pb-HAP and Ca-HAP

Lippmann diagram

Construction of the Lippmann diagram

The solid solution–aqueous solution (SSAS) interaction plays an important role in the geochemical processes in water, rock and soil. However, the thermodynamic data about SSAS systems are still scarcely available, although the method to describe reaction paths and end points of equilibrium in SSAS systems has been discussed broadly [25, 45–52].

The sum of the partial activity products of the two endmembers can be defined as the “total activity product” ΣΠ_SS of the solid solution [30]. The Lippmann’s “solidus” relation expresses the total activity product at thermodynamic equilibrium (ΣΠ_eq) as a function of the solid composition, and the Lippmann’s “solutus” relation is defined by expressing the total activity product at thermodynamic equilibrium (ΣΠ_eq) as a function of the aqueous solution composition. The Lippmann diagram is a phase diagram that presents graphically the “solidus” and “solutus” relation.

When several sites for one formula unit of the substituting ions exist, the relationship between the component activities and the molar ratios of the substituting ions can simply be described by transforming it to a “one-substituting-ion” formula. For the solid solution (Pb_xCa_1‒x)₅(PO₄)₃OH, its formula unit can be redefined as (Pb_xCa_1‒x)(PO₄)_3/5OH_1/5, the formula units of the endmembers Pb₅(PO₄)₃OH and Ca₅(PO₄)₃OH can be redefined as Pb(PO₄)_3/5OH_1/5 and Ca(PO₄)_3/5OH_1/5, respectively.

In constructing the Lippmann diagram, the total solubility product (ΣΠ) for (Pb_xCa_1‒x)(PO₄)_3/5OH_1/5 can be expressed as [47]:

$$\begin{aligned} &\Sigma \Pi_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1 { - }{\text{x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \\ &= \left( {\left\{ {{\text{Pb}}^{2 + } } \right\} + \{ {\text{Ca}}^{2 + } \} } \right)\left\{ {{\text{PO}}_{4}^{3 - } } \right\}^{3/5} \left\{ {{\text{OH}}^{ - } } \right\}^{1/5} \\ \; & = {\text{K}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} {\text{X}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \gamma_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \\ &\quad + {\text{K}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} {\text{X}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \gamma_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \\ \end{aligned}$$

(11)

where {} designates aqueous activity. ${\text{X}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$ and ${\text{X}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$, $\gamma_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$ and $\gamma_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$, ${\text{K}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$ and ${\text{K}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$ are the mole fractions (x, 1−x), the activity coefficients and the thermodynamic solubility products of Pb(PO₄)_3/5OH_1/5 and Ca(PO₄)_3/5OH_1/5 in the solid solution (Pb_xCa_1−x)(PO₄)_3/5OH_1/5. This solidus equation expresses all possible thermodynamic saturation states for (Pb_xCa_1−x)(PO₄)_3/5OH_1/5 based on the solid component [53].

The solutus relation can be expressed as [47]:

$$\begin{aligned} &{{\Sigma }}\Pi_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1- {\text{x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \\ & = \frac{1}{{\frac{{{\text{X}}_{{{\text{Pb}}^{ 2+ } , {\text{aq}}}} }}{{{\text{K}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \gamma_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} }} + \frac{{{\text{X}}_{{{\text{Ca}}^{ 2+ } , {\text{aq}}}} }}{{{\text{K}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \gamma_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} }}}} \end{aligned}$$

(12)

where ${\text{X}}_{{{\text{Pb}}_{{}}^{2 + } ,{\text{aq}}}}$ and ${\text{X}}_{{{\text{Ca}}_{{}}^{2 + } ,{\text{aq}}}}$ are the activity fractions for {Pb²⁺} and {Ca²⁺} in the aqueous phase, respectively. This equation expresses all possible thermodynamic saturation states for (Pb_xCa_1−x)(PO₄)_3/5OH_1/5 based on the aqueous composition [53].

The total solubility product ($\Sigma \Pi_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1- {\text{x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$) for (Pb_xCa_1−x)(PO₄)_3/5OH_1/5 at stoichiometric saturation can be expressed as:

$$\begin{aligned} &{{\Sigma }}\Pi_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1 -{\text{ x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \\ & = \frac{{{\text{K}}_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1 - {\text{ x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} }}{{({\text{X}}_{{{\text{Pb}}^{ 2+ } , {\text{aq}}}} )^{{{\text{X}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} }} ({\text{X}}_{{{\text{Ca}}^{ 2+ } , {\text{aq}}}} )^{{{\text{X}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} }} }}\end{aligned}$$

(13)

where ${\text{K}}_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1- {\text{x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}^{{}}$, {Pb²⁺}^x{Ca²⁺}^(1−x){PO₄ ³⁻}^3/5{OH⁻}^1/5, is the stoichiometric saturation constant for (Pb_xCa_1−x)(PO₄)_3/5OH_1/5.

The total solubility products for the stoichiometric saturation with Pb(PO₄)_3/5OH_1/5 and Ca(PO₄)_3/5OH_1/5, ${{\Sigma }}\Pi_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$ and ${{\Sigma }}\Pi_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$, can be expressed by their solubility products ${\text{K}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$ and ${\text{K}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$, respectively:

$${{\Sigma }}\Pi_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} = \frac{{{\text{K}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} }}{{({\text{X}}_{{{\text{Pb}}^{ 2+ } , {\text{aq}}}} )^{{{\text{X}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} }} }}$$

(14)

$${{\Sigma }}\Pi_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} = \frac{{{\text{K}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} }}{{({\text{X}}_{{{\text{Ca}}^{ 2+ } , {\text{aq}}}} )^{{{\text{X}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} }} }}$$

(15)

The “total solubility product ${{\Sigma }}\Pi_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1- {\text{x}}}} )_{ 5} ( {\text{PO}}_{ 4} )_{ 3} {\text{OH}}}}$” for the Pb–Ca-HAP solid solution with the formula unit of (Pb_xCa_1−x)₅(PO₄)₃OH can be calculated from the “total solubility product ${\Sigma}\Pi_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1- {\text{x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$” by

$$\begin{aligned} &{\Sigma \Pi }_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1- {\text{x}}}} )_{ 5} ( {\text{PO}}_{ 4} )_{ 3} {\text{OH}}}} \\ & = \left( {\left\{ {{\text{Pb}}^{2 + } } \right\} + \{ {\text{Ca}}^{2 + } \} } \right)^{5} \left\{ {{\text{PO}}_{4}^{3 - } } \right\}^{3} \left\{ {{\text{OH}}^{ - } } \right\} \\ & = \, \left[ {\left( {\left\{ {{\text{Pb}}^{2 + } } \right\} + \{ {\text{Ca}}^{2 + } \} } \right)\left\{ {{\text{PO}}_{4}^{3 - } } \right\}^{3/5} \left\{ {{\text{OH}}^{ - } } \right\}^{1/5} } \right]^{5} \\ & = \, \left[ {{\Sigma}\Pi_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1- {\text{x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} } \right]^{5}\end{aligned}$$

(16)

Finally, the Lippmann diagram for the Pb–Ca-HAP solid solution as (Pb_xCa_1−x)₅(PO₄)₃OH can be constructed by plotting the solidus and solutus as log ${{\Sigma }}\Pi_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1 -\text{ }{\text{x}}}} )_{ 5} ( {\text{PO}}_{ 4} )_{ 3} {\text{OH}}}}$ (or log[${{\Sigma }}\Pi_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1 -{\text{ x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$]⁵) on the ordinate vs two superimposed aqueous and solid phase mole fraction scales on the abscissa (Fig. 8a). The curves are calculated from the solubility products for Pb₅(PO₄)₃OH of 10^−80.77 and Ca₅(PO₄)₃OH of 10^−58.38 of the present work.

Fig. 8

Lippmann diagrams for dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH] at 25 °C and an initial pH of 2.00. a Assuming an ideal solid-solution. Hypothetical partial-equilibrium reaction path for the dissolution of the solid phase (Pb_xCa_1−x)₅(PO₄)₃OH (x = 0.51) is drawn in the arrowed solid lines. Solid arrows show primary saturation states; b Long-dotted or dashed curves depict the series of possible stoichiometric saturation states for the (Pb_xCa_1−x)₅(PO₄)₃OH solid solution (x = 0.00, 0.20, 0.41, 0.61, 0.80 and 1.00); c Assuming a non-ideal solid-solution based on the estimated Guggenheim parameters a ₀  = −1.16 and a ₁  = 1.18

In Fig. 8a, the solutus curve of the Lippmann diagram is near the curve for the pure endmember Pb-HAP [Pb₅(PO₄)₃OH, x = 1.00]. For comparison with the Lippmann solutus curve, some hypothetical stoichiometric saturation curves for (Pb_xCa_1−x)₅(PO₄)₃OH (x = 0.00, 0.20, 0.41, 0.61, 0.80 and 1.00) are also calculated and plotted in Fig. 8b. The Lippmann solutus curve and the stoichiometric saturation curves are similar in shape, and the stoichiometric saturation curves are close to the solutus curve as the solid-components are near the less soluble endmember Pb-HAP [Pb₅(PO₄)₃OH] [46]. Because of the large difference between the solubility products of Pb₅(PO₄)₃OH and Ca₅(PO₄)₃OH, the stoichiometric saturation for the sparingly soluble Pb-HAP [Pb₅(PO₄)₃OH] is very close to the Lippmann solutus curve [46].

The hypothetical reaction path for (Pb_0.51Ca_0.49)₅(PO₄)₃OH is also calculated and plotted in comparison with the Lippmann solutus and solidus curves for the Pb–Ca-HAP solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH] (Figs. 8a, 9a). In the beginning, the (Pb_0.51Ca_0.49)₅(PO₄)₃OH solid dissolves stoichiometrically in aqueous solution and its reaction path moves up vertically to the Lippmann solutus curve, which shows that the mole fraction for the aqueous solution is the same as the initial solid solution component [53]. And then, the (Pb_0.51Ca_0.49)₅(PO₄)₃OH solid dissolves non-stoichiometrically and the reaction path moves along the solutus curve towards the more soluble endmember Ca-HAP. This is in accordance with the result of the dissolution experiment for (Ba,Sr)SO₄ [46]. In the Lippmann diagram for the (Ba,Sr)SO₄–H₂O system, the reaction pathways show initial congruent dissolution up to the solutus curve, followed by incongruent dissolution along the solutus curve towards the more soluble endmember SrSO₄ [46]. There are two possible limiting reaction paths [45], i.e., the stoichiometric dissolution of (Pb_xCa_1−x)₅(PO₄)₃OH up to the first point of saturation (primary saturation) with a secondary solid phase, either a solid-solution phase or a pure solid phase, and the following non-stoichiometric dissolution with an increasing substitution reaction [45, 46]. For the solid solution (Pb_xCa_1‒x)₅(PO₄)₃OH, this exchange reaction could be

$$\left( {{\text{Pb}}_{\text{x}} {\text{Ca}}_{{1 - {\text{x}}}} } \right)_{5} \left( {{\text{PO}}_{4} } \right)_{3} {\text{OH }} + \, 5\Delta i{\text{Pb}}^{2 + } = \, \left( {{\text{Pb}}_{{{\text{x}} + \Delta i}} {\text{Ca}}_{{1 - {\text{x}} - \Delta i}} } \right)_{5} \left( {{\text{PO}}_{4} } \right)_{3} {\text{OH }} + \, 5\Delta i{\text{Ca}}^{2 + }$$

(17)

Fig. 9

Plotting of the experimental data on the Lippmann diagrams for dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃OH]. a 25 °C and an initial pH of 2.00, the arrows indicated the evolution directions of the aqueous solution during the solid solution–aqueous solution interaction; b 25 °C and an initial pH of 5.60; c 25 °C and an initial pH of 9.00

This reaction path follows the Lippmann solutus curve that can present some primary saturation states. Consequently, the sparingly soluble endmember Pb-HAP [Pb₅(PO₄)₃OH] will be gradually enriched in the solid phases, whereas the aqueous solution will become progressively rich in Ca²⁺ when an equilibrium or a stable state is attained [46]. In the stoichiometric dissolution, the solid component does not change, but the activity ratios {Pb²⁺}/({Pb²⁺}+{Ca²⁺}) in the aqueous phase may vary as the reaction progresses.

The activity coefficients of Pb(PO₄)_3/5OH_1/5 and Ca(PO₄)_3/5OH_1/5 in the solid solution (Pb_xCa_1−x)(PO₄)_3/5OH_1/5 can be approximated using the Redlich and Kister equation. The Guggenheim coefficients a ₀ and a ₁ were estimated by fitting the solubility products (${\text{K}}_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1- {\text{x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$) as a function of the solid components to Eq. (18).

$$\begin{aligned} &{ \ln }\;{\text{K}}_{{ ( {\text{Pb}}_{\text{x}} {\text{Ca}}_{{ 1- {\text{x}}}} ) ( {\text{PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \\ &= {\text{x}}\left( {1 - {\text{x}}} \right)a_{0} + {\text{ x}}\left( {1 - {\text{x}}} \right)\left( {{\text{x}} - \left( {1 - {\text{x}}} \right)} \right)a_{1} \\ & \quad + \, \left( {1 - {\text{x}}} \right){ \ln }\left[{\text{K}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} \left( {1 - x} \right)\right] \\ & \quad + {\text{ xln}} \left[{\text{K}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }} {\text{x}})\right] \end{aligned}$$

(18)

where ${\text{K}}_{{{\text{Pb(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$ and ${\text{K}}_{{{\text{Ca(PO}}_{ 4} )_{ 3 / 5} {\text{OH}}_{ 1 / 5} }}$ are the solubility products of Pb(PO₄)_3/5OH_1/5 and Ca(PO₄)_3/5OH_1/5, respectively.

The Lippmann diagram for the non-ideal solid solution (Pb_xCa_1−x)₅(PO₄)₃OH was calculated and constructed with the estimated Guggenheim parameters a ₀  = −1.16 and a ₁  = 1.18 (Fig. 8c). The diagram in the Fig. 8c is a typical Lippmann diagram for the solid solution with a negative enthalpy of mixing. The stoichiometric saturation curve for pure Pb-HAP [Pb₅(PO₄)₃OH] is similar to the Lippmann solutus curve and close to the solutus curve as the solid components are near the sparingly soluble Pb-HAP [46]. Due to the large difference between the solubility products of the two pure endmembers Pb-HAP (10^−80.77) and Ca-HAP (10^−58.38), the Lippmann solutus curve for the non-ideal solid solution (Pb_xCa_1−x)₅(PO₄)₃OH is very close to the curve for the sparingly soluble endmember and the Lippmann solutus curve for the ideal solid solution (Pb_xCa_1−x)₅(PO₄)₃OH.

The solid solution (Pb_xCa_1−x)₅(PO₄)₃OH can be treated as an ideal one in constructing the Lippmann diagram because the Lippmann solutus position is insensitive to the excess Gibbs free energy of mixing, although the position of the Lippmann solidus can be obviously affected [46] (Fig. 8c). This phenomenon is observed in all SSAS systems with a large difference between the solubility products of two endmembers, for which the excess Gibbs free energy of mixing has a small effect on the Lippmann solutus position [46]. The Lippmann diagram constructed for (Pb_xCa_1−x)₅(PO₄)₃OH as a non-ideal solid solution is very similar to the diagram for (Pb_xCa_1−x)₅(PO₄)₃OH as the ideal solid solution only with the difference of a slight upward convexity of the solidus curve at high X_Pb or a slight downward concavity of the solidus curve at low X_Pb [25], which indicates that the SSAS interaction for the solid solution (Pb_xCa_1−x)₅(PO₄)₃OH is not greatly affected by its non-ideality.

Solid-solution aqueous-solution reaction paths

The experimental data are plotted as ({Pb²⁺}+{Ca²⁺})⁵{PO₄ ³⁻}³{OH⁻} vs. X_Pb,aq in the Lippmann diagram for the ideal solid-solution (Pb_xCa_1‒x)₅(PO₄)₃OH (Fig. 9a, b, c). The saturation curves for Pb₅(PO₄)₃(OH) (x = 1.00) and Ca₅(PO₄)₃(OH) (x = 0.00) are also plotted in the diagram. In general, the positions of the data points on the Lippmann diagram are related to the rates of dissolution and precipitation, the aqueous speciation, and the degree of the formation of secondary phases. When (Pb_xCa_1−x)₅(PO₄)₃OH dissolves in solution, the aqueous Pb²⁺ is converted into PbOH⁺, Pb(OH) ⁰₂ , Pb(OH) ⁻₃ , Pb(OH) ²⁻₄ , Pb₂OH³⁺, Pb₃(OH) ²⁺₄ , Pb₄(OH) ⁴⁺₄ , PbHPO ⁰₄ , PbH₂PO₄ ⁺ and PbP₂O₇ ²⁻, and aqueous Ca²⁺ is converted into CaOH⁺, CaHPO₄, CaPO₄ ⁻ and CaH₂PO₄ ⁺, aqueous PO₄ ³⁻ is converted primarily into HPO₄ ²⁻, H₂PO₄ ⁻, H₃PO ⁰₄ , CaHPO₄, CaPO₄ ⁻ and CaH₂PO₄ ⁺. The speciations can result in a smaller activity ratio of the aqueous Pb²⁺ to Ca²⁺. The speciations of the aqueous Pb²⁺ and Ca²⁺ are considered in plotting the experimental data on the Lippmann diagram by calculating the activities of Pb²⁺ and Ca²⁺ with PHREEQC.

For the (Pb_xCa_1−x)₅(PO₄)₃OH dissolution at 25 °C and an initial pH of 2.00, the plotting of the experimental data on the Lippmann diagram shows that the (Pb_0.51Ca_0.49)₅(PO₄)₃(OH) solid dissolved in the aqueous solution stoichiometrically at the early stage and approached to the Lippmann solutus and the saturation curves for pure Pb-HAP [Pb₅(PO₄)₃OH]. After 1 h dissolution, the aqueous solution was supersaturated with respect to (Pb_0.51Ca_0.49)₅(PO₄)₃(OH) and Pb-HAP. After that, the X_Pb,aq decreased with the decreasing logΣΠ_SS value, and the data points moved along the Lippmann solutus curve from right to left (Fig. 9a), indicating that the reaction path for the solid dissolution includes an early stoichiometric dissolution up to the Lippmann solutus curve which is then followed by some possible substitution reactions [45, 46]. For the (Pb_xCa_1−x)₅(PO₄)₃OH dissolution at an initial pH of 5.60 or 9.00, the plotting of the experimental data on the Lippmann diagram illustrates that the X_Pb,aq values are significantly lower that X_Pb of the solids, which means that all solids dissolved in the aqueous solution non-stoichiometrically and approached to the Lippmann solutus and the saturation curves for pure Pb-HAP [Pb₅(PO₄)₃OH] (Fig. 9b, c).

The results show a continuous increase of the Ca²⁺ ions in the aqueous phase and a continuous increase of the Pb-HAP [Pb₅(PO₄)₃OH] component in the solid phase (Table 1; Fig. 9). A solid phase with a component near the pure Pb-HAP [Pb₅(PO₄)₃OH] can form because of the very low solubility of Pb-HAP [Pb₅(PO₄)₃OH] and the great supersaturation of the aqueous solution with Pb-HAP, and the relatively high solubility of Ca-HAP [Ca₅(PO₄)₃OH] and the undersaturation of the aqueous solution with Ca-HAP.

The large difference between the solubility products of Pb₅(PO₄)₃OH and Ca₅(PO₄)₃OH can cause an preferential enrichment of the sparingly soluble Pb₅(PO₄)₃OH in the solid phase [25, 51], i.e., a Pb-HAP-rich solid phase is to be in equilibrium with a Pb-poor aqueous phase or a Ca-HAP-poor solid phase in equilibrium with a Ca-rich aqueous phase. Therefore, it is practical to solidify/stabilize Pb-contaminated soils and Pb-containing hazardous wastes by using phosphates (apatites). Since lead hydroxyapatite [hydroxypyromorphite, Pb₅(PO₄)₃(OH)] is stable and significantly less soluble than calcium hydroxyapatite [Ca₅(PO₄)₃OH], it can be considered for safe disposal of industrial and mineral processing Pb-containing wastes and lead ions can be effectively removed from Pb-contaminated wastewaters by using hydroxyapatite.

Conclusions

The characterization with XRD, FT-IR, SEM and TEM showed that the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1−x)₅(PO₄)₃(OH)] with apatite structure was not found to change obviously after dissolution except in some cases of the dissolution at the initial pH 2.00. In general, the final solution pHs decreased with the increasing Pb/(Pb + Ca) molar ratios (X_Pb) of (Pb_xCa_1−x)₅(PO₄)₃(OH). The aqueous element concentrations were greatly affected by X_Pb during the dissolution. For the solids with high X_Pb [(Pb_0.89Ca_0.11)₅(PO₄)₃OH], the aqueous Ca²⁺ concentrations increased gradually with the dissolution time and reached a stable state after 4320 h dissolution; the aqueous Pb²⁺ concentrations increased rapidly with time and reached a peak value after 240–720 h dissolution, and then decreased gradually and attained a stable state after 5040 h dissolution; the aqueous phosphate concentrations increased rapidly with time and achieved a peak value after 1–12 h dissolution, and then decreased gradually and attained a stable state after 2160 h dissolution.

For the solids with low X_Pb (0.00–0.80), the aqueous Ca²⁺ concentrations increased slowly with time and reached a peak value after 1200–1800 h dissolution, and then decreased slightly and were relatively stable after 4320 h dissolution; the aqueous Pb²⁺ concentrations increased quickly with time and reached a peak value after 1–12 h dissolution, and then decreased gradually and attained a stable state after 720–2160 h dissolution; the aqueous phosphate concentrations showed the same evolution trend as the aqueous Ca²⁺ concentrations. The dissolution process of (Pb_xCa_1−x)₅(PO₄)₃(OH) with high X_Pb (0.89–1.00) was different from that of (Pb_xCa_1−x)₅(PO₄)₃(OH) with low X_Pb (0.00–0.80), which was considered to be related to a small preference of larger Pb²⁺ to occupy the M(II) sites and smaller Ca²⁺ to occupy the M(I) sites in the apatite structure. For the dissolution of (Pb_xCa_1−x)₅(PO₄)₃(OH) with high X_Pb in the acidic solution, Pb²⁺, which occupied nearly all the M(2) sites, could be preferentially released because of the interaction of the solution H⁺ with the OH surrounding the M(2) atom. For the dissolution of (Pb_xCa_1−x)₅(PO₄)₃(OH) with low X_Pb in the acidic solution, Ca²⁺ in the M(2) sites was preferentially released with respect to Pb²⁺ in the M(2) sites.

The average K _sp values were estimated for hydroxypyromorphite [Pb₅(PO₄)₃OH] of 10^−80.77 (10^−80.57–10^−80.96) at 25 °C, for hydroxyapatite [Ca₅(PO₄)₃OH] of 10^−58.38 (10^−58.31–10^−58.46) at 25 °C, the Gibbs free energies of formation (ΔG ^o _f ) were determined to be −3796.71 and −6314.63 kJ/mol, respectively. The solubility of the solid solution (Pb_xCa_1−x)₅(PO₄)₃(OH) decreased with the increasing Pb/(Pb + Ca) molar ratios (X_Pb) of (Pb_xCa_1−x)₅(PO₄)₃(OH). For the dissolution at 25 °C and an initial pH of 2.00, the experimental data plotted on the Lippmann diagram showed that the solid solution (Pb_xCa_1−x)₅(PO₄)₃(OH) dissolved congruently during the early stage of dissolution and moved gradually up to the Lippmann solutus curve, and then followed by incongruent dissolution and the data points moved along the Lippmann solutus curve from right to left, i.e., towards the more soluble endmember [Ca₅(PO₄)₃OH]. The Pb-rich or Ca-poor (Pb_xCa_1−x)₅(PO₄)₃(OH) was in equilibrium with the Ca-rich aqueous solution.