Characterization, dissolution and solubility of the hydroxypyromorphite-hydroxyapatite solid solution [(PbxCa1-x)5(PO4)3OH] at 25 °C and pH 2-9.

BACKGROUND: The interaction between Ca-HAP and Pb(2+) solution can result in the formation of a hydroxyapatite-hydroxypyromorphite solid solution [(PbxCa1-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 (PbxCa1-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 [(PbxCa1-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 (XPb) of the solids. For the solids with high XPb [(Pb0.89Ca0.11)5(PO4)3OH], the aqueous Pb(2+) 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 XPb (0.00-0.80), the aqueous Pb(2+) 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 XPb (0.89-1.00) was different from that of the solids with low XPb (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 f (o) ) were determined to be -3796.71 and -6314.63 kJ/mol, respectively. The solubility decreased with the increasing Pb/(Pb + Ca) molar ratios (XPb) of (PbxCa1‒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 (PbxCa1-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 (PbxCa1-x)5(PO4)3(OH) was in equilibrium with the Ca-rich aqueous solution. Graphical abstractLippmann diagrams for dissolution of the hydroxypyromorphite-hydroxyapatite solid solution [(PbxCa1-x)5(PO4)3OH] at 25 ˚C and an initial pH of 2.00.

Background

The apatite group minerals with the general formula M5(<span class="Chemical">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].

<span class="Chemical">Calcium hydroxyapatite [<span class="Chemical">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 <span class="Chemical">calcium apatite can be used to immobilize or remove hazardous chemicals in <span class="Chemical">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 [(PbxCa1−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 <span class="Chemical">metal-bearing solid solution may form on the solid surface when the solid come into contact with a <span class="Chemical">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 (PbxCa1−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 (PbxCa1−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, <span class="Chemical">lead hydroxyapatite [<span class="Chemical">hydroxypyromorphite, Pb-HAP, Pb5(PO4)3(OH)], lead–calcium hydroxyapatite solid solution [Pb–Ca-HAP (PbxCa1−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+, PO43−) were investigated through batch experiments. The Lippmann diagram [30] for the (PbxCa1−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 <span class="Chemical">Pb-HAP, Pb–<span class="Chemical">Ca-HAP solid solution and Ca-HAP samples were synthesized according to the following precipitation reaction: 5M2++3PO43−+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 [(PbxCa1−x)5(PO4)3OH]

Sample No.	Volumes of the precursors (mL)				Solid composition	Residual solid composition after dissolution at 25 °C and an initial pH of 2.00 for 300 days
	0.4 M	0.4 M	4.4 M	0.12 M
	Pb(CH3COO)2·2H2O	Ca(CH3COO)2·H2O	CH3COONH4	NH4H2PO4
Pb–Ca-HAP-00	0	250	250	500	(Pb0.00Ca1.00)5(PO4)3OH	(Pb0.00Ca1.00)5(PO4)3OH
Pb–Ca-HAP-01	25	225	250	500	(Pb0.10Ca0.90)5(PO4)3OH	(Pb0.10Ca0.90)5(PO4)3OH
Pb–Ca-HAP-02	50	200	250	500	(Pb0.20Ca0.80)5(PO4)3OH	(Pb0.21Ca0.79)5(PO4)3OH
Pb–Ca-HAP-03	75	175	250	500	(Pb0.30Ca0.70)5(PO4)3OH	(Pb0.32Ca0.68)5(PO4)3OH
Pb–Ca-HAP-04	100	150	250	500	(Pb0.41Ca0.59)5(PO4)3OH	(Pb0.44Ca0.56)5(PO4)3OH
Pb–Ca-HAP-05	125	125	250	500	(Pb0.51Ca0.49)5(PO4)3OH	(Pb0.54Ca0.46)5(PO4)3OH
Pb–Ca-HAP-06	150	100	250	500	(Pb0.61Ca0.39)5(PO4)3OH	(Pb0.66Ca0.34)5(PO4)3OH
Pb–Ca-HAP-07	175	75	250	500	(Pb0.69Ca0.31)5(PO4)3OH	(Pb0.77Ca0.23)5(PO4)3OH
Pb–Ca-HAP-08	200	50	250	500	(Pb0.80Ca0.20)5(PO4)3OH	(Pb0.88Ca0.12)5(PO4)3OH
Pb–Ca-HAP-09	225	25	250	500	(Pb0.89Ca0.11)5(PO4)3OH	(Pb0.95Ca0.05)5(PO4)3OH
Pb–Ca-HAP-10	250	0	250	500	(Pb1.00Ca0.00)5(PO4)3OH	(Pb1.00Ca0.00)5(PO4)3OH

Summary of synthesis and composition of the <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1−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 <span class="Chemical">nitric acid solution and diluted to 100 mL with pure <span class="Chemical">water. The Pb2+, Ca2+and PO43− 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 <span class="Chemical">Ca-HAP, Pb–<span class="Chemical">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 <span class="Chemical">Pb2+(aq), Ca2+(aq), PO43−(aq), and OH−(aq) were first calculated using PHREEQC Version 3 [31], and then the ion activity products (IAPs) for (PbxCa1−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 PbHPO40, PbH2PO4+ and PbP2O72− 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)20, Pb(OH)3−, Pb(OH)42−, Pb3(OH)42+, Pb2OH3+, Pb4(OH)44+, PbHPO40, PbH2PO4+ and PbP2O72− for the total lead; Ca2+, CaOH+, CaHPO4, CaPO4− and CaH2PO4+ for the total calcium calculation. For the total phosphate, the aqueous species considered were PO43−, HPO42−, H2PO4−, H3PO40, PbHPO40, PbH2PO4+, PbP2O72−, 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 <span class="Chemical">Pb-HAP, Pb–<span class="Chemical">Ca-HAP and Ca-HAP precipitates obtained are the designed components of (PbxCa1−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 (PbxCa1−x)5(<span class="Chemical">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 XPb = 1.00 is identified as <span class="Chemical">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 XPb = 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 XPb 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 (PbxCa1−x)5(PO4)3(OH) solid shifts gradually to a higher-angle direction as the solid Pb/(Pb + Ca) molar ration (XPb) decreases, which indicated that (PbxCa1−x)5(PO4)3(OH) is a continuous solid solution within the whole range of XPb = 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 (PbxCa1−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 [(PbxCa1−x)5(PO4)3OH] before (a) and after dissolution at 25 °C and an initial pH of 2.00 for 300 days (b)

X-ray diffractograms (XRD) of the <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1−x)5(PO4)3OH] before (a) and after dissolution at 25 °C and an initial pH of 2.00 for 300 days (b)

Although <span class="Chemical">lead hydroxyapatite (<span class="Chemical">Pb-HAP) and calcium hydroxyapatite (Ca-HAP) are isomorphous, their FT-IR spectra have essential differences. Generally, the tetrahedral PO43− has four vibrational modes, i.e., the symmetric P–O stretching (v1), the O–P–O bending (v2), the P–O stretching (v3), and the O–P–O bending (v4). But in the undistorted state, only the absorptions for the vibrations v3 and v4 can be detected, the two other vibrations v1 and v2 become infrared inactive [12]. In the FT-IR spectra, the tetrahedral PO43− of Ca-HAP showed the vibrational bands at 962.83 cm−1 (ν2), 1045.76 and 1091.08 cm−1 (ν3), 567.96 and 602.67 cm−1 (ν4), which shifted to 938.24 cm−1 (ν2), 985.01 and 1031.77 cm−1 (ν3), 536.62–573.74 cm−1 (ν4) as the solid Pb/(Pb + Ca) molar ratio (XPb) increased from 0 to 1.00, respectively (Fig. 2). The bands at 471.53 cm−1 (ν1) and 633.05 cm−1 (ν4) diminish with increasing XPb and disappear as XPb > 0.80 because of the variation of the PO43− symmetry. All bands, especially the P–O stretching (v3) bands, weaken with the increasing XPb 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 CO32− vibration [36] and the band at 871 cm−1 for HPO42− [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 [(PbxCa1−x)5(PO4)3OH] before (a) and after dissolution at 25 °C and an initial pH of 2.00 for 300 days (b)

Fourier transform infrared (FT-IR) spectra of the <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1−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 (XPb) can greatly affect the morphology and crystal structure of the (PbxCa1−x)5(<span class="Chemical">PO4)3(OH) solid solution [2, 10, 13, 37]. With the increasing XPb, the lattice parameters increased gradually accompanying morphology variation (Fig. 3). The (PbxCa1−x)5(<span class="Chemical">PO4)3(OH) solids with XPb = 0–0.51 are usually prism crystals with a hexagonal pyramid as termination (particle size 50–100 nm); the solids with XPb = 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 XPb = 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 [(PbxCa1−x)5(PO4)3OH] before (a) and after dissolution at 25 °C and an initial pH of 2.00 for 300 days (b)

Field emission scanning electron micrographs (FE-SEM) and transmission electron microscope (TEM) images‎ of the <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1−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 <span class="Chemical">aqueous element concentrations for the dissolution of (PbxCa1−x)5(<span class="Chemical">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 [(PbxCa1−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 [(PbxCa1−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 [(PbxCa1−x)5(PO4)3OH] at 25 °C and an initial pH of 9.00 for 300 days

Change of the solution pH and elemental concentrations with time for dissolution of the <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1−x)5(PO4)3OH] at 25 °C and an initial pH of 2.00 for 300 days

Change of the solution pH and elemental concentrations with time for dissolution of the <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1−x)5(PO4)3OH] at 25 °C and an initial pH 5.60 for 300 days

Change of the solution pH and elemental concentrations with time for dissolution of the <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1−x)5(PO4)3OH] at 25 °C and an initial pH of 9.00 for 300 days

Dissolution of (PbxCa1−x)5(<span class="Chemical">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 (XPb) of the (PbxCa1−x)5(<span class="Chemical">PO4)3(OH) solids can greatly affect the element concentrations in the aqueous solutions. In general, the final solution pHs decrease with the increasing XPb of the solids.

The dissolution process of the (PbxCa1−x)5(<span class="Chemical">PO4)3(OH) solids with high XPb (0.89–1.00) is different from that of the (PbxCa1−x)5(<span class="Chemical">PO4)3(OH) solids with low XPb (0.00–0.80) (Fig. 4). For the solids with high XPb or low XCa [(Pb0.89Ca0.11)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 (PbxCa1−x)5(<span class="Chemical">PO4)3(OH) solids with low XPb (0.00–0.80) or high XCa, the <span class="Chemical">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 (XPb,<span class="Chemical">aq) are almost equal to the stoichiometric Pb/(Pb + Ca) atomic ratios (XPb,aq) of the corresponding (PbxCa1−x)5(PO4)3(OH) solids. Then, the aqueous Pb/(Pb + Ca) molar ratios (XPb,aq) decreased with time and were lower than the stoichiometric Pb/(Pb + Ca) ratios of the corresponding solids (XPb) (Additional file 2: Appendix B). For the solids with high XPb or low XCa [(Pb0.89Ca0.11)5(PO4)3OH], the aqueous Pb/(Pb + Ca) molar ratios (XPb,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 XPb (0.00–0.80), the aqueous Pb/(Pb + Ca) molar ratios (XPb,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 XPb of 0.00–0.80 and those with XPb of 0.89–1.00 is related to the differences in the crystal structure and morphology of the (PbxCa1−x)5(<span class="Chemical">PO4)3(OH) solids (Figs. 1, 2, 3). Crystallographically, two independent <span class="Chemical">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 XPb > 0.4, they also began to occupy the M(1) sites considerably, which could explain the discontinuity at around XPb = 0.4–0.6 in the curves of the a and c-axis parameters versus XPb [34]. The greatest deviations were noted at an intermediate XPb, 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 XPb of 0.8 [11]. For the dissolution of the (PbxCa1−x)5(PO4)3(OH) solids with high XPb 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 (PbxCa1−x)5(PO4)3(OH) solids with low XPb 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 XCa,aq than the solid XCa during the initial period of dissolution.

For the (PbxCa1−x)5(<span class="Chemical">PO4)3(OH) dissolution in pure <span class="Chemical">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 (PbxCa1−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 (PbxCa1−x)5(PO4)3(OH) dissolution in pure water at an initial pH of 2.00, the solubility of (PbxCa1−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 (PbxCa1−x)5(<span class="Chemical">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 <span class="Chemical">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 (PbxCa1−x)5(PO4)3OH may result in the transforming of PO43− into HPO42− 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 (PbxCa1−x)5(PO4)3(OH) surface. Therefore, a complete describing of the (PbxCa1−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 (PbxCa1−x)5(PO4)3(OH) surface; (III) Protonation and transformation of PO43− into HPO42− at the (PbxCa1−x)5(PO4)3(OH) surface in the acidic solution; (IV) Stoichiometric desorption of Pb2+, Ca2+ and PO43− from the (PbxCa1−x)5(PO4)3(OH) surface and complexation; (V) Re-adsorption of Pb2+ and/or PO43− from solution back onto the (PbxCa1−x)5(PO4)3(OH) surface; (VI) Attaining of a stable state.

In process (I)–(III), the diffusion and adsorption of protons onto the (PbxCa1−x)5(<span class="Chemical">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), <span class="Chemical">Pb2+, Ca2+ and PO43− can be released from the (PbxCa1−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 (PbxCa1−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 (PbxCa1−x)5(PO4)3(OH) dissolution in acidic solution or a decrease of the solution pH for the (PbxCa1−x)5(PO4)3(OH) dissolution in alkali solution.

In process (V), for (PbxCa1−x)5(<span class="Chemical">PO4)3(OH) with XPb ≤ 0.80, <span class="Chemical">Pb2+ ions are re-absorbed non-stoichiometrically from the solution onto the (PbxCa1−x)5(PO4)3(OH) surface, the aqueous lead concentrations and the solution Pb/(Pb + Ca) molar ratios decrease. For (PbxCa1−x)5(PO4)3(OH) with XPb ≥ 0.89, Pb2+ and PO43− ions are partially re-absorbed from the solution onto the (PbxCa1−x)5(PO4)3(OH) surface when an initial part of (PbxCa1−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 (PbxCa1−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 <span class="Chemical">aqueous lead, <span class="Chemical">calcium and phosphate species in the final equilibrated solutions (5040, 5760, 7200 h) are used to calculate the solubility products for the (PbxCa1−x)5(PO4)3OH solid solution.

The stoichiometric dissolution of the (PbxCa1−x)5<span class="Chemical">(PO4)3OH solid solution and the release of <span class="Chemical">Pb2+, Ca2+ and PO43− can be described according to Eq. (1). The solubility products (Ksp) for (PbxCa1−x)5(PO4)3OH are equal to the ion activity products (IAP) at equilibrium: where {} represents the thermodynamic activities of the aqueous Pb2+, Ca2+ and PO43−.

The standard free energy of reaction (ΔG) can be calculated from <span class="Chemical">Ksp at 298.15 K and 0.101 MPa (standard condition) by

For Eq. (1),

Rearranging,

Table 2 lists the calculated solubility products (<span class="Chemical">Ksp) for (PbxCa1−x)5<span class="Chemical">(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 (Ksp) for the solid solution [(PbxCa1−x)5(PO4)3OH] decreased almost linearly with the increasing XPb from 10−58.38±0.07 to 10−80.77±0.20. Based on the following literature data obtained [39], ΔG[Pb2+] = −24.39 kJ/mol, ΔG[Ca2+] = −553.54 kJ/mol, ΔG[PO43−] = −1018.8 kJ/mol, ΔG[OH−] = −157.3 kJ/mol, the free energies of formation, ΔG[(PbxCa1−x)5(PO4)3OH], were also calculated (Table 2). The solubility products (Ksp) for (PbxCa1−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 [(PbxCa1‒x)5(PO4)3OH] (25 °C and an initial pH of 2.00)

Sample	Dissolution time (h)	pH	Concentration (mmol/L)			logK sp	Average logK sp	ΔGfo (kJ/mol)	Average ΔGfo (kJ/mol)
			Pb	Ca	P
(Pb0.00Ca1.00)5(PO4)3OH	5040	4.75	0.00000	8.03	5.57	−58.46	−58.38	−6315.06	−6314.63
	5760	4.77	0.00000	8.03	5.59	−58.31		−6314.21
	7200	4.76	0.00000	8.04	5.58	−58.38		−6314.61
(Pb0.10Ca0.90)5(PO4)3OH	5040	4.55	0.00099	7.12	3.91	−62.39	−62.39	−6128.29	−6128.28
	5760	4.54	0.00111	7.14	3.95	−62.41		−6128.42
	7200	4.55	0.00106	7.13	3.93	−62.36		−6128.12
(Pb0.20Ca0.80)5(PO4)3OH	5040	4.46	0.00153	6.85	3.33	−64.99	−65.19	−5850.90	−5852.04
	5760	4.39	0.00172	6.85	3.36	−65.42		−5853.34
	7200	4.44	0.00153	6.67	3.32	−65.16		−5851.87
(Pb0.30Ca0.70)5(PO4)3OH	5040	4.36	0.00149	6.61	3.30	−67.59	−67.43	−5601.14	−5600.22
	5760	4.39	0.00171	6.62	3.32	−67.27		−5599.35
	7200	4.37	0.00170	6.60	3.31	−67.42		−5600.17
(Pb0.41Ca0.59)5(PO4)3OH	5040	4.45	0.00152	6.60	2.98	−69.07	−69.18	−5318.58	−5319.18
	5760	4.43	0.00151	6.60	3.02	−69.19		−5319.28
	7200	4.42	0.00152	6.61	3.00	−69.27		−5319.69
(Pb0.51Ca0.49)5(PO4)3OH	5040	4.43	0.00211	6.07	1.79	−71.35	−71.42	−5039.35	−5039.76
	5760	4.42	0.00215	6.07	1.79	−71.40		−5039.60
	7200	4.40	0.00215	6.07	1.81	−71.52		−5040.33
(Pb0.61Ca0.39)5(PO4)3OH	5040	4.32	0.00386	5.45	1.01	−73.84	−73.86	−4816.62	−4816.77
	5760	4.34	0.00401	5.39	1.01	−73.64		−4815.53
	7200	4.28	0.00391	5.38	1.00	−74.10		−4818.15
(Pb0.69Ca0.31)5(PO4)3OH	5040	4.30	0.00224	6.18	2.24	−75.01	−74.94	−4528.61	−4528.24
	5760	4.33	0.00230	6.17	2.28	−74.73		−4527.06
	7200	4.28	0.00231	6.16	2.26	−75.08		−4529.04
(Pb0.80Ca0.20)5(PO4)3OH	5040	4.12	0.00495	5.85	1.38	−77.40	−77.52	−4334.29	−4334.94
	5760	4.11	0.00468	5.89	1.40	−77.55		−4335.13
	7200	4.09	0.00487	5.85	1.42	−77.59		−4335.39
(Pb0.89Ca0.11)5(PO4)3OH	5040	3.41	0.11486	5.11	0.101	−81.11	−81.16	−4061.97	−4062.27
	5760	3.35	0.11197	5.00	0.107	−81.49		−4064.16
	7200	3.36	0.13127	5.06	0.128	−80.88		−4060.67
(Pb1.00Ca0.00)5(PO4)3OH	5040	2.63	3.75579	0.00	0.049	−80.96	−80.77	−3797.78	−3796.71
	5760	2.67	3.64382	0.00	0.046	−80.79		−3796.79
	7200	2.68	3.70270	0.00	0.050	−80.57		−3795.55

Analytical data and solubility determination of the <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1‒x)5(PO4)3OH] (25 °C and an initial pH of 2.00)

The average <span class="Chemical">Ksp values were estimated for <span class="Chemical">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) were determined to be −3796.71 and −6314.63 kJ/mol.

The average <span class="Chemical">Ksp for <span class="Chemical">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) for hydroxypyromorphite [Pb5(PO4)3OH] of −3796.71 kJ/mol is lower than −3773.968 kJ/mol that was calculated from the Ksp of 10−76.8 for hydroxypyromorphite [Pb5(PO4)3OH] [38]. The average Ksp 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 Ksp 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 Ksp values may be caused by the differences in experimental conditions [7].

In comparison, the average <span class="Chemical">Ksp 10−80.77±0.20 for <span class="Chemical">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 PO43− 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/<span class="Chemical">Ksp) could be used to assess the pure-phase equilibrium, where IAP is the ion activity product ({<span class="Chemical">Pb2+}5{PO43−}3{OH−} or {Ca2+}5{PO43−}3{OH−}) and Ksp 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 (XPb) of 0.69 [(Pb0.69Ca0.31)5(PO4)3OH]. The aqueous solutions are supersaturated with Ca5(PO4)3OH to the end of the dissolution experiment with (PbxCa1−x)5(PO4)3OH (XPb = 0.10–0.80). The aqueous solutions are considerably supersaturated with Pb5(PO4)3OH at the end of the experiment for all (PbxCa1−x)5(PO4)3OH solids. Generally, the SI values for Pb5(PO4)3OH decrease lineally with the increasing XPb of (PbxCa1−x)5(PO4)3OH. The dissolution–recrystallization can happen during the interaction between (PbxCa1−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

Calculated saturation indices for <span class="Chemical">Pb-HAP and <span class="Chemical">Ca-HAP

Lippmann diagram

Construction of the Lippmann diagram

The solid solution–<span class="Chemical">aqueous solution (SSAS) interaction plays an important role in the geochemical processes in <span class="Chemical">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” ΣΠSS of the solid solution [30]. The Lippmann’s “solidus” relation expresses the total activity product at thermodynamic equilibrium (ΣΠeq) as a function of the solid composition, and the Lippmann’s “solutus” relation is defined by expressing the total activity product at thermodynamic equilibrium (ΣΠeq) as a function of the <span class="Chemical">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 (PbxCa1‒x)5<span class="Chemical">(PO4)3OH, its formula unit can be redefined as (PbxCa1‒x)(<span class="Chemical">PO4)3/5OH1/5, the formula units of the endmembers Pb5(PO4)3OH and Ca5(PO4)3OH can be redefined as Pb(PO4)3/5OH1/5 and Ca(PO4)3/5OH1/5, respectively.

In constructing the Lippmann diagram, the total solubility product (ΣΠ) for (PbxCa1‒x)(<span class="Chemical">PO4)3/5OH1/5 can be expressed as [47]:where {} designates <span class="Chemical">aqueous activity. and , and , and are the mole fractions (x, 1−x), the activity coefficients and the thermodynamic solubility products of Pb(PO4)3/5OH1/5 and Ca(PO4)3/5OH1/5 in the solid solution (PbxCa1−x)(PO4)3/5OH1/5. This solidus equation expresses all possible thermodynamic saturation states for (PbxCa1−x)(PO4)3/5OH1/5 based on the solid component [53].

The solutus relation can be expressed as [47]:where and are the activity fractions for {<span class="Chemical">Pb2+} and {<span class="Chemical">Ca2+} in the aqueous phase, respectively. This equation expresses all possible thermodynamic saturation states for (PbxCa1−x)(PO4)3/5OH1/5 based on the aqueous composition [53].

The total solubility product () for (PbxCa1−x)(<span class="Chemical">PO4)3/5OH1/5 at stoichiometric saturation can be expressed as:where , {<span class="Chemical">Pb2+}x{Ca2+}(1−x){PO43−}3/5{OH−}1/5, is the stoichiometric saturation constant for (PbxCa1−x)(PO4)3/5OH1/5.

The total solubility products for the stoichiometric saturation with <span class="Chemical">Pb(PO4)3/5OH1/5 and <span class="Chemical">Ca(PO4)3/5OH1/5, and , can be expressed by their solubility products and , respectively:

The “total solubility product ” for the Pb–<span class="Chemical">Ca-HAP solid solution with the formula unit of (PbxCa1−x)5<span class="Chemical">(PO4)3OH can be calculated from the “total solubility product ” by

Finally, the Lippmann diagram for the Pb–<span class="Chemical">Ca-HAP solid solution as (PbxCa1−x)5<span class="Chemical">(PO4)3OH can be constructed by plotting the solidus and solutus as log (or log[]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 [(PbxCa1−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 (PbxCa1−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 (PbxCa1−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  = −1.16 and a  = 1.18

Lippmann diagrams for dissolution of the <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1−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 (PbxCa1−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 (PbxCa1−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  = −1.16 and a  = 1.18

In Fig. 8a, the solutus curve of the Lippmann diagram is near the curve for the pure endmember <span class="Chemical">Pb-HAP [Pb5(PO4)3OH, x = 1.00]. For comparison with the Lippmann solutus curve, some hypothetical stoichiometric saturation curves for (PbxCa1−x)5<span class="Chemical">(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 (<span class="Chemical">Pb0.51Ca0.49)5<span class="Chemical">(PO4)3OH is also calculated and plotted in comparison with the Lippmann solutus and solidus curves for the Pb–Ca-HAP solid solution [(PbxCa1−x)5(PO4)3OH] (Figs. 8a, 9a). In the beginning, the (Pb0.51Ca0.49)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 (Pb0.51Ca0.49)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 (PbxCa1−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 (PbxCa1‒x)5(PO4)3OH, this exchange reaction could be

Fig. 9

Plotting of the experimental data on the Lippmann diagrams for dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(PbxCa1−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

Plotting of the experimental data on the Lippmann diagrams for dissolution of the <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1−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 <span class="Chemical">Pb-HAP [Pb5(PO4)3OH] will be gradually enriched in the solid phases, whereas the <span class="Chemical">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 <span class="Chemical">Pb(PO4)3/5OH1/5 and <span class="Chemical">Ca(PO4)3/5OH1/5 in the solid solution (PbxCa1−x)(PO4)3/5OH1/5 can be approximated using the Redlich and Kister equation. The Guggenheim coefficients a and a were estimated by fitting the solubility products () as a function of the solid components to Eq. (18). where and are the solubility products of Pb(PO4)3/5OH1/5 and Ca(PO4)3/5OH1/5, respectively.

The Lippmann diagram for the non-ideal solid solution (PbxCa1−x)5<span class="Chemical">(PO4)3OH was calculated and constructed with the estimated Guggenheim parameters a = −1.16 and a = 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 <span class="Chemical">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 (PbxCa1−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 (PbxCa1−x)5(PO4)3OH.

The solid solution (PbxCa1−x)5<span class="Chemical">(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 (PbxCa1−x)5<span class="Chemical">(PO4)3OH as a non-ideal solid solution is very similar to the diagram for (PbxCa1−x)5(PO4)3OH as the ideal solid solution only with the difference of a slight upward convexity of the solidus curve at high XPb or a slight downward concavity of the solidus curve at low XPb [25], which indicates that the SSAS interaction for the solid solution (PbxCa1−x)5(PO4)3OH is not greatly affected by its non-ideality.

Solid-solution aqueous-solution reaction paths

The experimental data are plotted as ({<span class="Chemical">Pb2+}+{<span class="Chemical">Ca2+})5{PO43−}3{OH−} vs. XPb,aq in the Lippmann diagram for the ideal solid-solution (PbxCa1‒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 (PbxCa1−x)5(PO4)3OH dissolves in solution, the aqueous Pb2+ is converted into PbOH+, Pb(OH)20, Pb(OH)3−, Pb(OH)42−, Pb2OH3+, Pb3(OH)42+, Pb4(OH)44+, PbHPO40, PbH2PO4+ and PbP2O72−, and aqueous Ca2+ is converted into CaOH+, CaHPO4, CaPO4− and CaH2PO4+, aqueous PO43− is converted primarily into HPO42−, H2PO4−, H3PO40, 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 (PbxCa1−x)5<span class="Chemical">(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 (<span class="Chemical">Pb0.51Ca0.49)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 (Pb0.51Ca0.49)5(PO4)3(OH) and Pb-HAP. After that, the XPb,aq decreased with the decreasing logΣΠSS 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 (PbxCa1−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 XPb,aq values are significantly lower that XPb 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 <span class="Chemical">Ca2+ ions in the <span class="Chemical">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 <span class="Chemical">Pb5(PO4)3OH and <span class="Chemical">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 <span class="Chemical">hydroxypyromorphite–<span class="Chemical">hydroxyapatite solid solution [(PbxCa1−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 (XPb) of (PbxCa1−x)5(PO4)3(OH). The aqueous element concentrations were greatly affected by XPb during the dissolution. For the solids with high XPb [(Pb0.89Ca0.11)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 XPb (0.00–0.80), the aqueous <span class="Chemical">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 (PbxCa1−x)5(PO4)3(OH) with high XPb (0.89–1.00) was different from that of (PbxCa1−x)5(PO4)3(OH) with low XPb (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 (PbxCa1−x)5(PO4)3(OH) with high XPb 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 (PbxCa1−x)5(PO4)3(OH) with low XPb in the acidic solution, Ca2+ in the M(2) sites was preferentially released with respect to Pb2+ in the M(2) sites.

The average <span class="Chemical">Ksp values were estimated for <span class="Chemical">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) were determined to be −3796.71 and −6314.63 kJ/mol, respectively. The solubility of the solid solution (PbxCa1−x)5(PO4)3(OH) decreased with the increasing Pb/(Pb + Ca) molar ratios (XPb) of (PbxCa1−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 (PbxCa1−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 (PbxCa1−x)5(PO4)3(OH) was in equilibrium with the Ca-rich aqueous solution.