Dissolution and solubility of the arsenate–phosphate hydroxylapatite solid solution [Ca₅(P_xAs_1–xO₄)₃(OH)] at 25°C

Additional keywords: aqueous solution, evolution, Lippmann diagram, reaction path.

Calcium phosphate hydroxylapatite [Ca₅(PO₄)₃(OH)] is a naturally occurring material as a major component of animal bones and teeth.^[1] On the industrial front it is being used as luminophosphors and as raw materials for the manufacture of several phosphatic fertilisers.^[2,3] Hydroxylapatite shows a high capacity for substitutions of Ca and PO₄^3– by other cations and anions due to its crystal structure and chemical composition,^[4] significant among which from the point of view of arsenic poisoning being the substitution of PO₄^3– by AsO₄^3– resulting in the formation of its isomorph, arsenate hydroxylapatite (AsHAP).^[5–7]

Arsenic toxicity is a global health problem affecting many millions of people.^[8] Occurrences of dissolved arsenic in surface and ground waters and observed adverse health effects have emphasised the need for better understanding of reactions that govern arsenic mobility in the environment.^[9] The presence of dissolved phosphate in many natural settings raises the possibility that intermediate compositions between Ca₅(PO₄)₃(OH) and Ca₅(AsO₄)₃(OH) may form in preference to endmember compositions.^[9] Arsenic concentrations in phosphate minerals are variable but can reach high concentrations, for example up to 1000 mg kg^–1 in apatite.^[10] Mining, milling, transporting of phosphate ores, manufacturing of phosphate fertilisers and using phosphate fertilisers containing arsenic are ways in which the workers, public and the environment are exposed to the enhanced natural toxicity hazard of arsenic and other trace metals.^[11,12]

Arsenate is isostructural and isoelectronic with phosphate, which may facilitate arsenic(V) removal from water and wastewater using hydroxylapatite.^[13] The existing literature confirms the occurrence of this substitution reaction spread over the entire compositional range and can be utilised to throw light on its mechanism to arrive at the possibility of removal of incorporated arsenic.^[2] Arsenic sequestration by compound formation produces a low-solubility apatite-like structure of the general form Ca₁₀(As_xP_yO₄)₆(OH)₂.^[14]

Solid solutions are geochemically and environmentally important because the interaction of dissolved toxic metals with minerals frequently results in the precipitation of metal-bearing solid solutions on the mineral surfaces or in rock or sediment pores. As a result, metals can be removed from natural waters and the thermodynamic properties of these solid solutions have a vital influence on the transport and fate of toxic metals in the environment.^[15] Some synthesis experiments at ambient temperatures were conducted to evaluate the conditions of formation and solubilities of different calcium arsenates.^[11,16,17] Hydroxylapatite (HAP) is one of the most stable forms of calcium phosphate and exhibits a low solubility (K_sp =10^–53.02–10^–53.51); however, the solubility of AsHAP [Ca₅(AsO₄)₃(OH)] is significantly greater than that of HAP,^[11,18–22] which suggested that phosphate substitution in the arsenate compound could significantly reduce their solubilities.^[21–24]

The thermodynamic properties of solid solutions have a vital influence on the transport and fate of toxic metals in the environment. Therefore, a thorough knowledge of the thermodynamics of materials containing mixed crystals allows us to optimise passive and permeable remediation barriers and other environmental technologies.^[15] The study of solid solution–aqueous solution (SSAS) systems has garnered much attention from environmental geochemists because they have been demonstrated to play major roles in the mobility of dissolved metals in contaminated environments.^[25] Only a few studies have been carried out on the dissolution and stability of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions, for which little information exists in the literature. Consequently, there are insufficient data upon which to assess the true environmental risk of arsenic posed by these minerals.^[5]

In the present study, a series of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions (AsPHA) with different P/(P+As) atomic ratios were prepared by a precipitation method. The resulting solid solution particles were characterised by various techniques. This paper reports the results of a study that monitors the dissolution and release of constituent elements from synthetic arsenate-phosphate hydroxylapatite solid solutions using batch dissolution experiments. The SSAS reaction paths are also discussed using the Lippmann diagram to evaluate the potential effect of such solid-solutions on the mobility of arsenic in the environment.

The experimental details for the preparation of the samples by precipitation were based on the following equation: 5Ca²⁺+3XO₄^3– + OH^– = Ca₅(XO₄)₃(OH). Where X = phosphorus or arsenic for the endmembers and (P+As) for the solid solutions.

The Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions (AsPHA) were synthesised by controlled mixing of a slurry of 100-mL 0.5-M Ca(OH)₂ and a solution of 60-mL 0.5-M H₃PO₄ and H₃AsO₄, so that a Ca/(P+As) molar ratio in the mixed solution was 1.67. Reagent grade chemicals and ultrapure water were used for the synthesis and all experiments. The amounts of H₃PO₄ and H₃AsO₄ were varied in individual syntheses to obtain synthetic solids with different mole fractions of Ca₅(PO₄)₃(OH) (Table 1). The initial solutions were slowly mixed in a covered beaker over a course of 10 min at room temperature (23 ± 1°C). The resulting solution was kept at 70°C and stirred at a moderate rate (100 rpm) using a stirrer bar. After a week, the precipitates were allowed to settle. The resultant precipitates were then washed thoroughly with ultrapure water and dried at 110°C for 24 h.

Table 1.  Summary of synthesis and composition of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solution

The compositions of the samples were determined. The residual calcium, phosphate and arsenate concentrations in the decanted solutions were analysed to calculate the compositions of the precipitates. In addition, ~10 mg of sample was digested in 20 mL of 1-M HNO₃ solution, and then diluted to 100 mL with ultrapure water. It was analysed for Ca and As using a PE Model AAnalyst 700 atomic absorption spectrometer (PerkinElmer, Waltham, MA, USA), phosphate using an ion chromatography (Metrohm 790, Metrohm AG, Herisau, Switzerland) or a PE Lambda 20 UV-visible spectrometer (PerkinElmer). All synthetic solids were characterised by powder X-ray diffraction (XRD) with an X’Pert PRO diffractometer (PANalytical B.V., Almelo, the Netherlands) using Cu Kα radiation (40 kV and 40 mA). The XRD measurements for unit cell parameter calculation were performed within a 2θ range 10–80° with a scanning rate of 0.10° min^–1. Crystallographic identification of the synthesised apatites was accomplished by comparing the experimental XRD patterns to standards compiled by the International Center for Diffraction Data (ICDD), which were card #00-009-0432 for hydroxylapatite and #00-033-0265 calcium arsenate hydroxide. The morphology was analysed by scanning electron microscopy (Jeol JSM-6380LV, Japan Electron Optics Ltd., Tokyo). The samples were measured in a form of KBr pellets over the range of 4000–400 cm^–1 using a FT-IR spectrophotometer (Nicolet Nexus 470, Thermo Fisher Scientific Inc., Waltham, MA, USA).

Half a gram of the synthetic solid was placed in a 250-mL polypropylene bottle. HNO₃ solution (150 mL, 0.01 M) was added into each bottle. The bottles were capped and placed in a temperature-controlled water bath (25°C). Water samples (3 mL) were taken from each bottle on 16 occasions (1 h, 3 h, 6 h, 12 h, 1 day, 2 days, 3 days, 5 days, 10 days, 15 days, 20 days, 30 days, 45 days, 60 days, 90 days, 120 days). After each sampling, the sample volume was replaced with an equivalent amount of ultrapure water. The samples were filtered using 0.20-µm pore diameter membrane filters, transferred into 25-mL volumetric flasks and then diluted with 0.2% HNO₃ to the mark. Calcium was analysed by using an atomic absorption spectrometer and phosphate using ion chromatography. After 2880-h dissolution, the solid samples were taken from each bottle, washed, dried and characterised using XRD, SEM and FT-IR in the same manner as described above.

Associated with each dissolution is an assemblage of solid phases, a solution phase containing dissolved calcium, phosphate, arsenate and a pH value. Assuming equilibrium has been reached, the values of these parameters can be calculated using established theoretical principles.^[26,27] In this study, the simulations were performed using PHREEQC (Version 2.15) together with its most complete literature database minteq.v4.dat, which bases on the ion dissociation theory. The input is free-format and uses order-independent keyword data blocks that facilitate the building of models that can simulate a wide variety of aqueous-based scenarios.^[26]

The activities of Ca²⁺(aq), PO₄^3–(aq), AsO₄^3–(aq), and OH^–(aq) were calculated by using PHREEQC. The saturation indexes were also calculated with respect to calcium phosphates and arsenates, such as HAP, AsHAP, Ca₈(HPO₄)₂(PO₄)₄·5H₂O, Ca₃(AsO₄)₂, Ca₃(AsO₄)₂·4H₂O, Ca₄(OH)₂(AsO₄)₂·4H₂O, Ca(H₂AsO₄)₂, CaHAsO₄, CaHPO₄·2H₂O, Ca₃(PO₄)₂ and portlandite.

The composition of the synthetic solid depends on the initial Ca : P : As mole ratio in the starting solution. Results suggest that the crystals were almost the intended composition of Ca₅(P_xAs_1–xO₄)₃(OH). The relative molar ratios of arsenic to phosphorus for all samples were almost the same as those of raw solutions (Table 1). The atomic Ca/(As+P) ratio was 1.67, which corresponds to a stoichiometric ratio of apatite.^[20]

XRD, FT-IR and SEM analyses were performed on the solids before and after the dissolution experiments (Figs 1–3). As illustrated in the figures, the results of the analyses on materials before the dissolution were almost indistinguishable from the following reaction. No evidence of other mineral precipitation was observed in the dissolution experiment.

Fig. 1.  X-ray diffraction patterns of the Ca₅(P_xAs_1–xO₄)₃OH solid solutions before (a) and after (b) dissolution at 25°C for 2880 h.

Fig. 2.  Infrared spectra of the Ca₅(P_xAs_1–xO₄)₃OH solid solutions before (a) and after (b) dissolution at 25°C for 2880 h.

Fig. 3.  Scanning electron micrographs of the Ca₅(P_xAs_1–xO₄)₃OH solid solutions before (a) and after (b) dissolution at 25°C for 2880 h.

The XRD pattern of the obtained solids indicated the formation of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions, which have the apatite type structure (Fig. 1). They are hexagonal and belong to the space group P6₃/m.^[28] HAP and AsHAP are the two endmembers of a structural family series. When subjected to XRD, they produce the same reflections; but the reflections exist at different two-theta values, i.e. the reflective planes are the same but ‘d’ spacings are different. The incorporation of arsenic in the apatite lattice causes a shift in the ‘d’ spacing.^[20] All the compounds have indicated the formation of an apatite phase differing only in reflection location, reflection width and absolute intensity of the diffraction patterns. They show that the obtained crystals consist only of the solid solution phase, which belongs to the apatite type structure. The tetrahedral covalent radius of AsO₄^3– (1.18 Å) being higher than that of PO₄^3– (1.10 Å), the lattice of AsHAP can be supposed to be less firmly bound than that of HAP.^[5] The reflection peaks of HAP and AsHAP were slightly different from each other. The reflections of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions shifted gradually to a higher-angle direction when the mole fraction of Ca₅(AsO₄)₃(OH) of the solids decreased.^[20]

The normal modes of the tetrahedral phosphate ion are: v₁, symmetric P–O stretching; v₂, OPO bending; v₃, P–O stretching; and v₄, OPO bending.^[29] The infrared spectra of prepared white powders are shown in Fig. 2. The fundamental vibrational modes of PO₄^3– tetrahedra of apatite phase are witnessed in the region at 960–962 cm^–1 (ν₂), 1036–1041 cm^–1 (ν₃), 564–571, 602–605 cm^–1 (ν₄) and 468–471 cm^–1 (ν₁). The peaks of AsO₄^3– appeared at 842–876 cm^–1 (ν₃) and 422–432 cm^–1 (ν₄). The location of the phosphate peaks and the arsenate peaks was noted for the whole series of substituted apatites. The peaks of AsO₄^3– increased and the peaks of PO₄^3– decreased with increasing the As content of samples, i.e. the area of the phosphate peak being gradually suppressed and that of the arsenate peak increased as the proportion of the arsenate increased.^[20]

As shown in Fig. 3, SEM observation indicated the solids with high mole fraction of Ca₅(AsO₄)₃(OH) between 0.46 and 1.0 were typically fine crystals (particle size <2 µm). The crystal size obtained in these experiments increases with decreasing mole fraction of Ca₅(AsO₄)₃(OH) in the solid solution. With the mole fraction of Ca₅(AsO₄)₃(OH) between 0 and 0.46, the apatites were large tabular crystals (particle size >10 µm), which do not show the hexagonal or rod shape of the crystals characteristic of apatites.^[20]

In general, the aqueous concentrations of elements were strongly dependent on the mole fraction of the endmember Ca₅(AsO₄)₃(OH) in the Ca₅(P_xAs_1–xO₄)₃(OH) solid solution. Because Ca₅(AsO₄)₃(OH) has a higher solubility than Ca₅(PO₄)₃(OH), the higher the mole fraction of Ca₅(AsO₄)₃(OH) in the Ca₅(P_xAs_1–xO₄)₃(OH) solid solution, the higher the solubility of the solid solution. In the present experiment, the dissolution occurred primarily within the first 480 h. After 480 h, the dissolution rate declined rapidly and a steady-state condition was achieved (Fig. 4). The aqueous pH values increased with the increasing dissolution time rapidly in the first hour and reached stable values (Fig. 4). The aqueous Ca concentrations increased rapidly at the beginning of the dissolution and reached a peak value in 3–6 h, and then declined. After 48–72-h dissolution, the aqueous Ca concentrations increased slowly once again and achieved an equilibrium state after 240 h (Fig. 4). The concentrations of aqueous phosphate species increased very fast at the beginning of dissolution and reached a peak value within the first hour of dissolution. After that, the concentrations of aqueous phosphate species declined rapidly with time and reached stable values after 240–360-h dissolution (Fig. 4). The concentrations of aqueous arsenate species increased with the increasing dissolution time at the beginning of the dissolution experiment. After reaction for ~480 h, the concentrations remained unaltered (Fig. 4).

Fig. 4.  Aqueous element concentrations versus time for dissolution of the Ca₅(P_xAs_1–xO₄)₃OH solid solutions at 25°C.

The final aqueous pH values and the concentrations of aqueous Ca, phosphate and arsenate species were strongly related to the mole fraction of Ca₅(PO₄)₃(OH) in the solid samples (Fig. 5). Generally, the aqueous OH^– concentrations increased with the increase in the concentrations of aqueous arsenate species and the decrease in the concentrations of aqueous phosphate species (Fig. 5). This solubility behaviour is consistent with that of phase-pure Ca₅(AsO₄)₃(OH). Ca₅(AsO₄)₃(OH) becomes more soluble at lower pH and less soluble at high pH. Thus, the presence of Ca₅(AsO₄)₃(OH) controls the composition of the solution phase.^[11] This is possibly the result of the stronger hydrolisation ability of AsO₄^3– than that of PO₄^3–, i.e. this could be explained on the basis of the higher dissociation constants of H₃AsO₄ (K₁ = 4.0 × 10^–3, K₂ =1.0 × 10^–7 and K₃ = 3.2 × 10^–12) over the corresponding values of H₃PO₄ (K₁ = 7.51 × 10^–3, K₂ = 6.33 × 10^–8 and K₃ = 4.73 ×10^–13).^[5]

Fig. 5.  The aqueous pH and the aqueous concentrations of elements after the solid solution–aqueous solution (SSAS) interaction for 2880 h.

It is also obvious that there was a steep increase in the amount of dissolved calcium, phosphate and arsenate and the accompanying decrease in solution pH between x = 0.43 (AsPHA-4) and x = 0.71 (AsPHA-7) with peak values at x = 0.54 (AsPHA-5) or x = 0.63 (AsPHA-6) for the aqueous dissolution of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions. This phenomenon was also observed by other researchers.^[11] The XRD analysis indicated that the unit cell a and c parameters did not vary completely linearly with the degree of substitution as expected by the Vegard’s Law. The solids with the mole fraction of Ca₅(AsO₄)₃(OH) between 0.46 and 1.0 were typically fine crystals; those with the mole fraction of Ca₅(AsO₄)₃(OH) between 0 and 0.46 large tabular.^[20] The expansion of the unit cell in response to AsO₄ substitution is primarily a result of an average expansion of the (As,P)O₄ tetrahedra. The individual (As,P)–O distances in the averaged (As,P)O₄ tetrahedra increase with increasing As content in the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions, as expected.^[9] However, the (As,P)–O1 distance increases more rapidly with increasing As content until ~2/3 occupancy, after which no further change is observed, indicating a greater distortion in the averaged tetrahedra for intermediate compositions.^[9] Expansion of the average size of (As,P)O₄ tetrahedra is also reflected in the widely considered metaprism twist angle, giving the rotation of the two triangular faces formed by O1 and O2 about Ca1.^[30] The trend of increasing twist with increasing As content up to As fraction 0.66 is consistent with the distortion between the (As,P)–O distances, where the (As,P)–O1 distance increases more rapidly than the (As,P)–O2 distance over the intermediate concentration range, which would serve to accentuate the metaprism twist in this same range.^[9] This distortion or twist could result in the increasing of the aqueous solubility of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions in this same range.

The concentrations of aqueous phosphate and arsenate species for the dissolution results are plotted in Fig. 6. The lines shown represent the pathways of stoichiometric dissolution and the arrows indicate the experimental dissolution pathways. The solid solution samples of AsPHA-1 [Ca₅(P_0.12As_0.88O₄)₃(OH)], AsPHA-2 [Ca₅(P_0.22As_0.78O₄)₃(OH)], AsPHA-5 [Ca₅(P_0.54As_0.46O₄)₃(OH)] and AsPHA-9 [Ca₅(P_0.92As_0.08O₄)₃(OH)] dissolved stoichiometrically at 25°C before the first samples were taken at 1 h. For the solid solutions of AsPHA-3, AsPHA-4, AsPHA-6, AsPHA-7 and AsPHA-8, the region of stoichiometric dissolution was over before the first samples were taken at 1h. Following the stoichiometric dissolution, the concentrations of aqueous phosphate species decreased and the concentrations of aqueous arsenate species increased for the duration of the experiment. The experimental results indicated that the dissolution was stoichiometric only at the very beginning of the process, and then dissolution became non-stoichiometric and the system underwent a dissolution–recrystallisation process that affects the ratio of the substituting ions in both the solid and the aqueous solution. During the SSAS interaction, the aqueous solution enriched in the more soluble component of the solid solutions, i.e. the endmember Ca₅(AsO₄)₃(OH). On the contrary, the solid enriched in the less soluble component, i.e. the endmember Ca₅(PO₄)₃(OH).

Fig. 6.  The relationship between the aqueous arsenate concentration and the aqueous phosphate concentration for the solid solution dissolution at 25°C. The lines represent theoretical stoichiometric dissolution pathways for the Ca₅(P_xAs_1–xO₄)₃OH solid solutions. The arrows indicate the experimental dissolution pathway.

At the fundamental level, reactions between solids and liquids involve a coupled sequence of mass transport, adsorption and desorption phenomena, heterogeneous reaction, chemical transformations of intermediates, and coupled dissolution–recrystallisation processes, etc.^[25,31,32] Accompanying the early release of Ca, PO₄^3– and AsO₄^3– was a rapid increase in reacted solution pH from 2.0 to 4.3–5.9 in the first hour of the dissolution experiment. A complete description of the protons consumed during the dissolution must take account of the following reactions: stoichiometric dissolution of the bulk solid; stoichiometric exchange of 2H⁺ for one Ca; H⁺ adsorption and desorption on the apatite surface; protonation and complexation of aqueous phosphate and arsenate species in solution.^[31,32] The adsorption of protons onto negatively charged oxygen ions of phosphate or arsenate groups of the apatitic Ca₅(P_xAs_1–xO₄)₃(OH) solid solution could result in transformation of surface PO₄^3– groups into HPO₄^2– or AsO₄^3– groups into HAsO₄^2– and catalyse the dissolution process.^[31] Based on the sequence of ionic detachment from the surface to a solution, it is suggested that dissolution of apatite is always non-stoichiometric at the atomic level.^[31] When an initial portion of the apatitic Ca₅(P_xAs_1–xO₄)₃(OH) solid solution had been dissolved, some amount of phosphate was returned from the solution back and adsorbed onto the surface of the solid. As a result, the aqueous phosphate concentration after 1-h dissolution at 25°C started to decrease with time slowly. The adsorption and re-precipitation of arsenate onto the solid surface was significantly weaker than phosphate.

Because of the non-stoichiometric dissolution and secondary dissolution of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solution (note the increasing calcium and arsenate concentration and the decreasing phosphate concentration in Fig. 4), the possibility exists that the chemical composition at the surface of the solid phase is not directly related to the bulk composition. The surface material is also the material most likely to be in equilibrium with the aqueous phase.^[33] The more insoluble Ca₅(PO₄)₃(OH) tended to be removed first in the precipitation process, with the more soluble Ca₅(AsO₄)₃(OH) preferentially concentrated in the later-formed material. This later-formed material was concentrated at the surface of the precipitates. As the initial material equilibrates, the Ca₅(PO₄)₃(OH) fraction increased as a result of non-stoichiometric dissolution.

The thermodynamic analysis could be initiated by assuming the possible pure-phase equilibrium relations.^[33] The Pure-phase equilibrium was assessed by calculating the saturation index (SI), defined by SI = log IAP/K_sp, where IAP is the ion activity product (i.e. [Ca²⁺]⁵[PO₄^3–]³[OH^–] or [Ca²⁺]⁵[AsO₄^3–]³[OH^–]) and the solubility product K_sp is the thermodynamic-equilibrium constant for the dissolution reaction. If the SI is equal to zero, the aqueous phase is in equilibrium with the solid phase. An SI greater than zero indicates supersaturation, and an SI less than zero indicates undersaturation.

Phosphate minerals are known to be sparingly soluble and HAP is less soluble than arsenate hydroxylapatite (AsHAP). The mean K_sp values were calculated for Ca₅(PO₄)₃(OH) of 10^–53.28 (10^–53.02–10^–53.51) at 25°C and 10^–55.73 (10^–54.85–10^–56.85) at 45°C.^[21] The K_sp values 10^–53.28 for Ca₅(PO₄)₃(OH) was ~3.72 log units lower than 10^–57 reported by Stumm and Morgan.^[34] The thermodynamic solubility product for HAP was K_sp =10^{–58.3 [35]} and 10^–53.9.^[5] Inconsistency in data presented in literature could be due to the failure to achieve equilibrium,^[21,31] even though some mineral suspensions were equilibrated for as long as 6 weeks^[36] or 120 h^[37] before being analysed. Apatite is known to be often non-stoichiometric, specifically Ca deficient. Both the stoichiometric (Ca : P = 1.67) and any non-stoichiometric hydroxylapatite (Ca : P ratio within 1.50–1.67) might be described as the same substance. Values for the log K_sp for HAP with Ca : P = 1.67 have been reported to be approximately –59^[38] whereas a value of –42.5 was reported for HAP with Ca : P = 1.5.^[39] From the result of a batch dissolution for 6 weeks, the log K_sp = –58 ± 1 for synthetic HAP was obtained by Valsami-Jones et al.^[36]

There are few experimental data on the thermodynamic properties of arsenate hydroxylapatite in literature. The mean K_sp value of 10^–39.2 was calculated for Ca₅(AsO₄)₃(OH) from the results of the precipitation experiment or 10^–41.6 from the results of the dissolution experiment.^[17] This value is ~2.08 log units lower than 10^–38.04 reported by Bothe and Brown,^[27] but it is obviously higher than 10^–47.25.^[5] The thermodynamic solubility products for Ca₅(AsO₄)₃(OH) were 10^–45.20 at 35°C, 10^–45.28 at 40°C, 10^–45.34 at 45°C and 10^–45.46 at 50°C.^[18]

Therefore, the K_sp values of 10^–57 for HAP^[34] and 10^–41.68 for AsHAP^[17] were used in the calculation using the program PHREEQC in the present study. The calculated saturation indices for Ca₅(AsO₄)₃(OH) show a trend of increasing values as the composition of the solid phases approaches that of the pure-phase endmember, Ca₅(AsO₄)₃(OH), thereby indicating that Ca₅(AsO₄)₃(OH) is not the equilibrium phase at low Ca₅(AsO₄)₃(OH) mole fraction and high Ca₅(PO₄)₃(OH) mole fraction (Fig. 7). After 480 h of dissolution, the saturation indices for Ca₅(AsO₄)₃(OH) showed steady-state behaviour, and at lower Ca₅(AsO₄)₃(OH) mole fractions the SI values were still significantly below the values for pure Ca₅(AsO₄)₃(OH), showing that pure Ca₅(AsO₄)₃(OH) did not control the concentrations of aqueous arsenate species in these samples. This result was consistent with the dissolution of the (Ba,Sr)SO₄ precipitates^[33] and the Ca₅(P_xAs_1–xO₄)₃F solid solution.^[22]

Fig. 7.  Calculated saturation indices for hydroxylapatite (HAP) and arsenate hydroxylapatite (AsHAP).

The calculated saturation indices for Ca₅(PO₄)₃(OH) show a distinctly different trend than those for Ca₅(AsO₄)₃(OH) (Fig. 7). Generally, the Ca₅(PO₄)₃(OH) saturated index (SI) values decreased as the Ca₅(PO₄)₃(OH) mole fraction increased and show slight oversaturation with respect to pure Ca₅(PO₄)₃(OH) at the end of the dissolution experiment. The results indicated that the concentrations of aqueous arsenate species could not be explained by pure-phase equilibrium with Ca₅(AsO₄)₃(OH) and the concentrations of aqueous phosphate species appeared to be in equilibrium or close to equilibrium with Ca₅(PO₄)₃(OH).

The saturation indexes were also calculated using PHREEQC with respect to calcium phosphates and arsenates other than HAP and AsHAP. The results indicated that all aqueous solutions were always undersaturated with respect to calcium phosphates and arsenates, such as Ca₈(HPO₄)₂(PO₄)₄·5H₂O, Ca₃(AsO₄)₂, Ca₃(AsO₄)₂·4H₂O, Ca₄(OH)₂(AsO₄)₂·4H₂O, Ca(H₂AsO₄)₂, CaHAsO₄ and portlandite, with the SI of –15.41 to –2.24, –16.49 to –4.64, –15.79 to –3.94, –27.39 to –10.73, –11.28 to –9.04, –9.90 to –6.38 and –16.71 to –11.90 respectively. For all aqueous solution samples, the saturation indexes with respect to CaHPO₄·2H₂O were calculated to be –1.29 to –0.26. But the dissolution of the solid solution lead to an increase of supersaturation with respect to Ca₃(PO₄)₂ with the SI of 0.23–4.14. In such a case the dissolution of the solid solution with a Ca/(P+As) ratio of 1.67 would be followed by precipitation of solids with Ca/P ratios of 1.50–1.67. This would lead to a subsequent increase of the Ca/(P+As) ratio in the aqueous solution. The dramatic decay (after the initial rise) in the concentration of phosphate shown in Fig. 4 could be due to the precipitation of minor amounts of calcium phosphate phases with a Ca/P ratio smaller than 1.67.

Understanding SSAS processes is of fundamental importance. However, in spite of the numerous studies, the availability of thermodynamic data for SSAS systems is still scarce.^[25,40] Lippmann extended the solubility product concept to solid solutions by developing the concept of ‘total activity product’ ΣΠ_SS, which is defined as the sum of the partial activity products contributed by the individual endmembers of the solid solution.^[25,40–42] At thermodynamic equilibrium, the total activity product ΣΠ_eq, expressed as a function of the solid composition, yields Lippmann’s ‘solidus’ relationship. In the same way, the ‘solutus’ relationship expresses ΣΠ_eq as a function of the aqueous solution composition. The graphical representation of solidus and solutus yields a phase diagram, usually known as a Lippmann diagram.^[25,40,42] A comprehensive methodology for describing reaction paths and equilibrium end points in solid-solution aqueous solution systems had been presented and discussed in the literature.^[25,40–50]

When there are several sites per formula unit for the substituting ions, the relationship between the activities of the components and the molar fractions of the substitution ions can be simplified by considering the chemical formula on a ‘one-substituting-ion’ basis. In the case of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solution (AsPHA), the formula units of the components are redefined as Ca_5/3(PO₄)(OH)_1/3 (HAP_1/3) and Ca_5/3(AsO₄)(OH)_1/3 (AsHAP_1/3), which is equivalent to consider the formula unit of the solid solution as Ca_5/3(P_xAs_1–xO₄)(OH)_1/3 (AsPHA_1/3). A Lippmann diagram is based on the total solubility product, ΣΠ, which for the Ca_5/3(P_xAs_1–xO₄)(OH)_1/3 solid solution (AsPHA_1/3) can be written as:

where brackets designate aqueous activity. K_HAP1/3 and K_AsHAP1/3, X_HAP1/3 and X_AsHAP1/3, γ_HAP1/3 and γ_AsHAP1/3 are the thermodynamic solubility products, the mole fractions (x, 1–x) and the activity coefficients of the Ca_5/3(PO₄)(OH)_1/3 and Ca_5/3(AsO₄) (OH)_1/3 components in the Ca_5/3(P_xAs_1–xO₄)(OH)_1/3 solid solution. The term [Ca²⁺]^5/3([PO₄^3–]+[AsO₄^3–])[OH^–]^1/3 is the ‘total solubility product’ ΣΠ_AsPHA1/3 at equilibrium.^[42] This relationship, called the solidus, defines all possible thermodynamic saturation states for the two-component solid solution series in terms of the solid phase composition.^[43]

As given by Glynn and Reardon,^[42] the equation of the solutus can be given by:

where X_PO4^3–,aq and X_AsO4^3–,aq are the activity fractions for [PO₄^3–] and [AsO₄^3–] in the aqueous phase respectively. This relationship defines all possible thermodynamic saturation states for the two-component solid solution series in terms of the aqueous phase composition.^[43]

Identical to the equation for the solid solution curves given by Glynn and Reardon,^[42] the total solubility product for the Ca_5/3(P_xAs_1–xO₄)(OH)_1/3 solid solution at stoichiometric saturation, ΣΠ_ss, can be expressed as:

where K_SS, [Ca²⁺]^5/3[PO₄^3–]^x[AsO₄^3–]^(1–x)[OH^–]^1/3, is the stoichiometric saturation constant for the Ca_5/3(P_xAs_1–xO₄)(OH)_1/3 solid solution.

The total solubility products for the stoichiometric saturation with respect to both pure endmembers, ΣΠ_HAP1/3 and ΣΠ_AsHAP1/3, can be described in terms of the endmember solubility products K_HAP1/3 and K_AsHAP1/3 respectively:

According to the definition of the total solubility product, the ‘total solubility product’ ΣΠ_AsPHA’ for the formula unit of the solid solution as Ca₅(P_xAs_1–xO₄)₃(OH) can be calculated from the ‘total solubility product’ ΣΠ_AsPHA1/3 by

A Lippmann phase diagram for the solid solution as Ca₅(P_xAs_1–xO₄)₃(OH) is a plot of the solidus and solutus as log ΣΠ_AsPHA (or log{ΣΠ_AsPHA1/3}³) on the ordinate versus two superimposed aqueous and solid phase mole fraction scales on the abscissa.

A Lippmann diagram for the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions for the ideal case when a₀ = 0.0 is shown in Fig. 8. It was constructed using thermodynamic solubility products for Ca₅(PO₄)₃(OH) of 10^–57 and Ca₅(AsO₄)₃(OH) of 10^–41.6 reported in the previous researches.^[17,34] The diagrams contain the solidus (log ΣΠ_AsPHA v. X_HAP1/3 or X_HAP) and the solutus (log ΣΠ_AsPHA v. X_PO4^3–,aq) for the Ca₅(P_xAs_1–xO₄)₃(OH) solid solution series, and the total solubility product curves at stoichiometric saturation for the nine different members of the arsenate–phosphate hydroxylapatite solid solution (ΣΠ_SS v. X_PO4^3–,aq; x = 0.12, 0.22, …, 0.92). In addition to the solutus and the solidus, we have plotted the saturation curves for pure endmembers HAP (x = 1.00) and AsHAP (x = 0.00). Also included are the data from our study, plotted as [Ca²⁺]⁵([PO₄^3–]+[AsO₄^3–])³[OH^–] v. X_PO4^3–,aq.

Fig. 8.  Lippmann diagrams for dissolution of the Ca₅(P_xAs_1–xO₄)₃OH solid solutions showing possible stoichiometric dissolution pathway. (a) Hypothetical partial-equilibrium reaction paths for the dissolution of three solid phases Ca₅(P_xAs_1–xO₄)₃OH (x = 0.22, 0.54 and 0.82) are drawn in short-dashed and arrowed lines. Solid arrows show primary saturation states. The triangle, square and circle symbols represent equilibrium end-points for the three solid phases respectively. Long-dashed curves depict the series of possible stoichiometric saturation states for the Ca₅(P_xAs_1–xO₄)₃OH solid solutions. (b) and (c) Plotting of the experimental data on Lippmann diagrams with different abscissa.

In Fig. 8a, the curve for pure endmember HAP (x = 1.00) is very close to the solutus curve over the entire range of X_PO4^3–,aq. The position of the Lippmann solutus curve is insensitive to the actual thermodynamic mixing properties of the solid-solutions, only the solidus curve is affected in all SSAS systems with large differences in endmember solubility products.^[44] The greater the difference in solubility products, the lesser the influence of the excess thermodynamic mixing properties on the position of the solutus curve.^[42] Lippmann diagrams resulting from the application of variable solid phase activity coefficients are rather similar to the one depicting ideal solid solution. The only difference is a slight upward convexity of the solidus.^[45]

Several hypothetical reaction paths are shown in Fig. 8a, in relation to Lippmann solutus and solidus curves for the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions. The reaction path of a stoichiometrically dissolving solid solution moves vertically from the abscissa of a Lippmann diagram, originating at the mole fraction corresponding to the initial solid solution composition.^[43] The pathways show initial stoichiometric dissolution up to the solutus curve, followed by non-stoichiometric dissolution along the solutus, towards the more soluble endmember.^[44] Paths x = 0.22, x = 0.54 and x = 0.82 illustrate hypothetical reaction paths for the solid solutions Ca₅(P_0.22As_0.78O₄)₃(OH), Ca₅(P_0.54As_0.46O₄)₃(OH) and Ca₅(P_0.82As_0.18O₄)₃(OH) respectively.^[44]

The experimental data plotted on Lippmann phase diagrams show that the precipitates either follow or slightly overshoot the Lippmann solutus curve, then approach the solutus curve (Fig. 8b,c), indicating the dissolution path for these precipitates may involve stoichiometric dissolution to the Lippmann solutus curve followed by a possible exchange reaction.^[33,44] In general, the location of data points on a Lippmann diagram will depend on the aqueous speciation, degree to which secondary phases are formed, and the relative rates of dissolution and precipitation.^[46] As Ca₅(P_xAs_1–xO₄)₃(OH) dissolves in solution with pH < 7, aqueous P^V and As^V are converted primarily into HPO₄^2– and HAsO₄^2– and only a small fractions remain as PO₄^3– and AsO₄^3–. The small values of the activity fractions are a consequence of the P^V and As^V speciation and the fractions of total P^V and As^V would be orders of magnitude greater. For the plot of the experimental data on the Lippmann diagram, the effect of the aqueous P^V and As^V speciation was considered by calculating the activity of PO₄^3– and AsO₄^3– with the program PHREEQC. Our dissolution data indicate a persistent enrichment in the HAP component in the solid phase and a persistent enrichment in the arsenate component in the aqueous phase (Table 1 and Fig. 6). The possibility of formation of a phase close in composition to pure HAP seems unavoidable, given the extremely low solubility of HAP and the large oversaturation with respect to HAP, the relatively high solubility of AsHAP and the undersaturation with respect to AsHAP (Fig. 7).

The large difference between the solubility products of the endmembers involves a strong preferential partitioning of the less soluble endmember towards the solid phase,^[40] which explains AsHAP-poor solid solutions are in equilibrium with arsenate-rich aqueous solutions. Therefore, from the point of view of the equilibrium thermodynamics, in solidification–stabilisation of As-containing hazardous wastes and As-contaminated soil using phosphates (apatite), large amount of phosphates (apatite) must be applied in the process to avoid the leaching of arsenic.^[22] Although johnbaumite [Ca₅(AsO₄)₃OH] and other calcium arsenates have been considered for safe arsenic disposal, in treating industry and mineral processing wastes with lime, it has been assumed that these solids are extremely insoluble and stable.^[11,14,23] The experimental results indicated that johnbaumite [Ca₅(AsO₄)₃OH] is stable under alkaline conditions, and in moderately soluble when compared with hydroxylapatite [Ca₅(PO₄)₃OH]. The use of hydroxylapatite to decrease the arsenate content of contaminated waters is not effective as johnbaumite is much more soluble than the phosphate analogue and substitution of phosphate by arsenate in the apatite lattice can occur only for very high concentrations of arsenate.^[23] As a soil amendment, apatite removes many priority metals from solution phase. An exception was arsenate, an oxyanion, which demonstrated slightly reduced retention within the apatite-amended soil.^[47] Arsenic typically exists in anionic forms under environmental conditions and apatite is not very effective on arsenic.

During the dissolution of the synthetic Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions (0–2880 h) at 25°C and initial pH = 2, the concentrations profiles of aqueous calcium, phosphate species and arsenate showed a rapid initial release of constituent ions to solution followed by a decreasing rate of dissolution and eventually, steady-state. The aqueous pH values and the concentrations of aqueous arsenate species increased rapidly at the beginning of the dissolution and reached a steady-state after 1 and 480 h respectively. The aqueous Ca concentrations increased rapidly at the beginning of the dissolution and reached a peak value in 3–6 h, and then declined. After 48–72-h dissolution, the aqueous Ca concentrations increased slowly once again and achieved an equilibrium state after 240 h. The concentrations of aqueous phosphate species increased very fast at the beginning of dissolution and reached a peak value in 1 h and then declined slowly with time and remained constant after 240–360-h dissolution. Generally, the aqueous OH^– concentrations increased with the increase in the concentrations of aqueous arsenate species and the decrease in the concentrations of aqueous phosphate species.

The aqueous element concentrations were significantly affected by the mole fraction of Ca₅(PO₄)₃(OH) in the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions. There was a steep increase in the amount of dissolved calcium, phosphate and arsenate and the accompanying decrease in solution pH between x = 0.43 and x = 0.71 with peak values at x = 0.54 or x = 0.63 for the aqueous dissolution of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions. The dissolution of the Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions into an initially dilute aqueous solution was often stoichiometric and followed by the non-stoichiometric dissolution. During the non-stoichiometric dissolution, the concentrations of aqueous phosphate species decreased and the concentrations of aqueous arsenate species increased.

The SSAS reaction paths for the dissolution of the synthetic Ca₅(P_xAs_1–xO₄)₃(OH) solid solutions were plotted on Lippmann diagrams. Solid phase activity coefficients used in the construction of the Lippmann diagram were calculated with the Guggenheim coefficient of a₀ = 0 for an ideal solid solution. It can readily be seen in the Lippmann diagram that the experimental data followed or slightly overshot the Lippmann solutus curve, then approach the solutus curve. According to the Lippmann diagram, AsHAP-poor solid solutions are in equilibrium with arsenate-rich aqueous solutions.