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 Pb2+ 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 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 XPb (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 XPb (0.89–1.00) was different from that of the solids with low XPb (0.00–0.80). The average Ksp 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 (ΔGfo) 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 abstract 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. Electronic supplementary material The online version of this article (doi:10.1186/s12932-016-0034-8) contains supplementary material, which is available to authorized users.


Background
The apatite group minerals with the general formula M 5 (PO 4 ) 3 X have a wide compositional variation because of their huge isomorphic capacity and numerous substitutions of ions [1][2][3][4][5], which play an important role in many research areas, such as geology, environmental sciences, biomaterials, material science and technology [6][7][8][9].
Calcium hydroxyapatite [Ca-HAP] is the main component of vertebral animals' bones [10][11][12][13][14][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][11][12][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][17][18]. Lead apatite is the most stable lead form under various environmental conditions. It is now considered that the in situ immobilization of leadcontaminated 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 Pb 2+ and precipitation of pure hydroxypyromorphite [19,20]; (2) ion exchange between Ca 2+ ions in hydroxyapatite lattice and Pb 2+ ions in solution [19,21]. During the reaction of hydroxyapatite with Pb 2+ solution, a new hydroxyapatite-hydroxypyromorphite solid solution [(Pb x Ca 1−x ) 5 (PO 4 ) 3 (OH), Pb-Ca-HAP] with Pb 2+ ions occupying Ca 2+ 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 x Ca 1−x ) 5 (PO 4 ) 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][27][28][29]. Until now, no experiment on the dissolution mechanism, solubility product and other thermodynamic data of the (Pb x Ca 1−x ) 5 (PO 4 ) 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, Pb 5 (PO 4 ) 3 (OH)], lead-calcium hydroxyapatite solid solution [Pb-Ca-HAP (Pb x Ca 1−x ) 5 ( PO 4 ) 3 (OH)] with varying Pb/(Pb + Ca) molar ratios and calcium hydroxyapatite [Ca-HAP, Ca 5 (PO 4 ) 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 (Pb 2+ , Ca 2+ , PO 4 3− ) were investigated through batch experiments. The Lippmann diagram [30] for the (Pb x Ca 1−x ) 5 (PO 4 ) 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.

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: 5M 2+ +3PO 4 3− +OH − = M 5 (PO 4 ) 3 OH, 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(CH 3 COO) 2 ·H 2 O and Ca(CH 3 COO) 2 ·3H 2 O 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 CH 3 COONH 4 buffer solution was then mixed with each lead-calcium solution in 1L polypropylene bottle. After that, 500 mL of 0.12 mol/L NH 4 H 2 PO 4 solution was quickly added into the bottle with stirring ( Table 1). The resulting white suspension was adjusted to pH 7.50 with NH 4 OH, 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.

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 Pb 2+ , Ca 2+ and PO 4 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 HNO 3 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 % HNO 3 . 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.

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 x Ca 1−x ) 5 (PO 4 ) 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 x Ca 1−x ) 5 (PO 4 ) 3 (OH) solids belong to the apatite group of the hexagonal system P6 3 /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 Ca 2+ (0.100 nm) with larger Pb 2+ (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 x Ca 1−x ) 5 (PO 4 ) 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 x Ca 1−x ) 5 (PO 4 ) 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 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 PO 4 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 PO 4 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].  represents the surface P-OH groups [15,35]. The band at 1455 cm −1 for CO 3 2− vibration [36] and the band at 871 cm −1 for HPO 4 2− [10,11] are not visible in the FT-IR spectra of the present work.

Dissolution mechanism
The solution pH and aqueous element concentrations for the dissolution of (Pb x Ca 1−x ) 5  Dissolution of (Pb x Ca 1−x ) 5 (PO 4 ) 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 x Ca 1−x ) 5 (PO 4 ) 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 x Ca 1−x ) 5 (PO 4 ) 3 (OH) solids with high X Pb (0.89-1.00) is different from that of the (Pb x Ca 1−x ) 5 (PO 4 ) 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 0.89 Ca 0.11 ) 5 (PO 4 ) 3 OH], the aqueous Ca 2+ concentrations increased gradually with the dissolution time and achieved a stable state after 4320 h dissolution. The aqueous Pb 2+ 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 x Ca 1−x ) 5 (PO 4 ) 3 (OH) solids with low X Pb (0.00-0.80) or high X Ca , the aqueous Ca 2+ 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 Pb 2+ 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 Ca 2+ 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 x Ca 1−x ) 5 (PO 4 ) 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 0.89 Ca 0.11 ) 5 (PO 4 ) 3 OH], 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 x Ca 1−x ) 5 (PO 4 ) 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 Pb 2+ cations prefer to occupy the M(2) sites and smaller Ca 2+ cations prefer to occupy the M(1) sites in the apatite structure. When Pb 2+ cations substitute for Ca 2+ 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 Zhu  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 Pb 2+ formed a crystal that had the apatite structure, despite a total enlargement of the unit cell because of the larger Pb 2+ cations [11,16,17,[27][28][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 x Ca 1−x ) 5 [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 x Ca 1−x ) 5 (PO 4 ) 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 x Ca 1−x ) 5 (PO 4 ) 3 (OH) solid and the aqueous solution (Figs. 5, 6). The solution lead and phosphate concentrations are smaller than those for the (Pb x Ca 1−x ) 5 (PO 4 ) 3 (OH) dissolution in pure water at an initial pH of 2.00, the solubility of (Pb x Ca 1−x ) 5 (PO 4 ) 3 OH [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 x Ca 1−x ) 5 (PO 4 ) 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 x Ca 1−x ) 5 (PO 4 ) 3 OH may result in the transforming of PO 4 3− into HPO 4 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 Pb 2+ and Ca 2+ at the (Pb x Ca 1−x ) 5  In process (I)-(III), the diffusion and adsorption of protons onto the (Pb x Ca 1−x ) 5 (PO 4 ) 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), Pb 2+ , Ca 2+ and PO 4 3− can be released from the (Pb x Ca 1−x ) 5 (PO 4 ) 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 x Ca 1−x ) 5 (PO 4 ) 3 (OH) dissolution is strongly affected by the initial solution pH and the protonation and complexation reactions (2) (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 x Ca 1−x ) 5 (PO 4 ) 3 (OH) dissolution in the acidic solution (initial pH of 2.00) at 25 °C from 5040 to 7200 h.  Rearranging, Table 2 lists the calculated solubility products (K sp ) for (Pb x Ca 1−x ) 5 (PO 4 ) 3 OH, 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 x Ca 1−x ) 5 (PO 4 ) 3 OH] decreased almost linearly with the increasing X Pb from  3 OH], were also calculated ( Table 2). The solubility products (K sp ) for (Pb x Ca 1−x ) 5 (PO 4 ) 3 OH at 25 °C and an initial pH of 5.60 and 9.00 were also determined (Additional file 3: Appendix C).

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 ({Pb 2+ } 5 3 OH] tends to distribute preferentially towards the solid phase [25,46,47].

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][46][47][48][49][50][51][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 x Ca 1-x ) 5 (PO 4 ) 3 OH, its formula unit can be redefined as (Pb x Ca 1-x )(PO 4 ) 3/5 OH 1/5 , the formula units of the endmembers Pb 5 (PO 4 ) 3 OH and Ca 5 (PO 4 ) 3 OH can be redefined as Pb(PO 4 ) 3/5 OH 1/5 and Ca(PO 4 ) 3/5 OH 1/5 , respectively.
In Fig. 8a, the solutus curve of the Lippmann diagram is near the curve for the pure endmember Pb-HAP [Pb 5 (PO 4 ) 3 OH, x = 1.00]. For comparison with the Lippmann solutus curve, some hypothetical stoichiometric saturation curves for (Pb x Ca 1−x ) 5 (PO 4 ) 3 OH (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 [Pb 5 (PO 4 ) 3 OH] [46]. Because of the large difference between the solubility products of Pb 5 (PO 4 ) 3 OH and Ca 5 (PO 4 ) 3 OH, the stoichiometric saturation for the sparingly soluble Pb-HAP [Pb 5 (PO 4 ) 3 OH] is very close to the Lippmann solutus curve [46].  (Figs. 8a, 9a). In the beginning, the (Pb 0.51 Ca 0.49 ) 5 (PO 4 ) 3 OH 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 0.51 Ca 0.49 ) 5 (PO 4 ) 3 OH 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)SO 4 [46]. In the Lippmann diagram for the (Ba,Sr)SO 4 -H 2 O 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 SrSO 4 [46]. There are two possible limiting reaction paths [45], i.e., the stoichiometric dissolution of (Pb x Ca 1−x ) 5 (PO 4 ) 3 OH 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 x Ca 1-x ) 5

(PO 4 ) 3 OH, this exchange reaction could be
This reaction path follows the Lippmann solutus curve that can present some primary saturation states. Consequently, the sparingly soluble endmember Pb-HAP [Pb 5 (PO 4 ) 3 OH] will be gradually enriched in the solid phases, whereas the aqueous solution will become progressively rich in Ca 2+ when an equilibrium or a stable state is attained [46]. In the stoichiometric dissolution, the solid component does not change, but the activity ratios {Pb 2+ }/({Pb 2+ }+{Ca 2+ }) in the aqueous phase may vary as the reaction progresses.
The activity coefficients of Pb(PO 4 ) 3/5 OH 1/5 and Ca(PO 4 ) 3/5 OH 1/5 in the solid solution (Pb x Ca 1−x ) (PO 4 ) 3/5 OH 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 (K (Pb x Ca 1−x )(PO 4 ) 3/5 OH 1/5 ) as a function of the solid components to Eq. (18).  where K Pb(PO 4 ) 3/5 OH 1/5 and K Ca(PO 4 ) 3/5 OH 1/5 are the solubility products of Pb(PO 4 ) 3/5 OH 1/5 and Ca(PO 4 ) 3/5 OH 1/5 , respectively. The Lippmann diagram for the non-ideal solid solution (Pb x Ca 1−x ) 5 (PO 4 ) 3 OH 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 [Pb 5 (PO 4 ) 3 OH] 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 x Ca 1−x ) 5 (PO 4 ) 3 OH is very close to the curve for the sparingly soluble endmember and the Lippmann solutus curve for the ideal solid solution (Pb x Ca 1−x ) 5 (PO 4 ) 3 OH.
The solid solution (Pb x Ca 1−x ) 5 (PO 4 ) 3 OH 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 x Ca 1−x ) 5 (PO 4 ) 3 OH as a non-ideal solid solution is very similar to the diagram for (Pb x Ca 1−x ) 5 (PO 4 ) 3 OH 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 x Ca 1−x ) 5 (PO 4 ) 3 OH is not greatly affected by its non-ideality.

Solid-solution aqueous-solution reaction paths
The experimental data are plotted as ({Pb 2+ }+{Ca 2+ }) 5 (Fig. 9a, b, c). The saturation curves for Pb 5 (PO 4 ) 3 (OH) (x = 1.00) and Ca 5 (PO 4 ) 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 x Ca 1−x ) 5  Pb-Ca-HAP-01-9 Pb-Ca-HAP-02-9 Pb-Ca-HAP-03-9 Pb-Ca-HAP-04-9 Pb-Ca-HAP-05-9 Pb-Ca-HAP-06-9 Pb-Ca-HAP-07-9 Pb-Ca-HAP-08-9 Pb-Ca-HAP-09-9 Pb-Ca-HAP-10-9  For the (Pb x Ca 1−x ) 5 (PO 4 ) 3 OH 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 0.51 Ca 0.49 ) 5 (PO 4 ) 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 [Pb 5 (PO 4 ) 3 OH]. After 1 h dissolution, the aqueous solution was supersaturated with respect to (Pb 0.51 Ca 0.49 ) 5 (PO 4 ) 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 x Ca 1−x ) 5 (PO 4 ) 3 OH 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 [Pb 5 (PO 4 ) 3 OH] (Fig. 9b, c).

Solutus (a
The results show a continuous increase of the Ca 2+ ions in the aqueous phase and a continuous increase of the Pb-HAP [Pb 5 (PO 4 ) 3 OH] component in the solid phase (Table 1 The large difference between the solubility products of Pb 5 (PO 4 ) 3 OH and Ca 5 (PO 4 ) 3 OH can cause an preferential enrichment of the sparingly soluble Pb 5 (PO 4 ) 3 OH 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 Carich 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, Pb 5 (PO 4 ) 3 (OH)] is stable and significantly less soluble than calcium hydroxyapatite [Ca 5 (PO 4 ) 3 OH], 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 x Ca 1−x ) 5 (PO 4 ) 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 x Ca 1−x ) 5 (PO 4 ) 3 (OH). The aqueous element concentrations were greatly affected by X Pb during the dissolution. For the solids with high X Pb [(Pb 0.89 Ca 0.11 ) 5 (PO 4 ) 3 OH], the aqueous Ca 2+ concentrations increased gradually with the dissolution time and reached a stable state after 4320 h dissolution; the aqueous Pb 2+ 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 Ca 2+ 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 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; the aqueous phosphate concentrations showed the same evolution trend as the aqueous Ca 2+ concentrations. The dissolution process of (Pb x Ca 1−x ) 5 (PO 4 ) 3 (OH) with high X Pb (0.89-1.00) was different from that of (Pb x Ca 1−x ) 5 (PO 4 ) 3 (OH) with low X Pb (0.00-0.80), which was considered to be related to a small preference of larger Pb 2+ to occupy the M(II) sites and smaller Ca 2+ to occupy the M(I) sites in the apatite structure. For the dissolution of (Pb x Ca 1−x ) 5 (PO 4 ) 3 (OH) with high X Pb in the acidic solution, Pb 2+ , 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 x Ca 1−x ) 5 (PO 4 ) 3 (OH) with low X Pb in the acidic solution, Ca 2+ in the M(2) sites was preferentially released with respect to Pb 2+ in the M(2) sites.