Sorption behavior of thorium onto granite and its constituent minerals

ABSTRACT

The sorption behavior of thorium (Th) onto granite and its major constituent minerals, feldspar, quartz and mica were investigated by batch sorption experiments. Experiments were carried out under variable pH and carbonate concentrations. Distribution coefficients (K_d) decreased with increased carbonate concentrations and showed the minimal value at around pH 10. This sorption tendency was seen for all the rock and mineral samples, and it was due to the formation of aqueous hydroxo–carbonate complexes of Th in the solutions. The order of sorbability for Th was mica > feldspar > quartz ≈ granite. The sorption behaviors of Th were analyzed by the non-electrostatic surface complexation model with the Visual Minteq computer program. The K_d for granite were calculated by component additivity approaches. The model calculations were able to explain the experimental results reasonably well. It was shown that the sorption behavior of Th onto granite can be explained by the complexation with the surface sites of mainly biotite and feldspar.

KEYWORDS:

• Thorium
• sorption
• carbonate
• distribution coefficient
• surface complex

1. Introduction

For the geological disposal of radioactive waste, an implementer conducts the assessment and submits it to the regulator as a part of the application for obtaining a license to construct and operate a repository. The regulator is required to review the assessment efficiently and effectively. The Nuclear Safety Research Center of Japan Atomic Energy Agency, being responsible for supporting the regulatory activities, focuses research activities on features, events and processes that are highly correlated with the results of the safety analysis. Retardation of radionuclide migration by sorption onto a host rock in natural barrier systems is one of the important factors that influence the performance of a radioactive waste disposal system. Performance assessment calculations for hypothetical high-level radioactive waste (HLW) repositories [1] show that ²²⁹Th which is a member of the neptunium series (4n+1) is one of the radionuclides dominating the long-term radiological hazard. Thorium exists only in the tetravalent oxidation state independent of the redox conditions of groundwater [2,3] and is often considered as an analog of other tetravalent actinide elements (U, Np and Pu) [4,5]. The dominant aqueous species of Th in reference groundwaters for the performance assessment [1,6] were estimated to be hydroxo–carbonate complexes from thermodynamic calculations [7]. The carbonate concentrations in the modeled reference groundwaters are 3.4 × 10⁻³ mol dm⁻³ (fresh type) and 1.2 × 10⁻² mol dm⁻³ (saline type) [6]. In the long term, the sorption behavior of Th would change because pH and carbonate concentration of groundwater is likely to be changed [1,7–10]. Hence, it is necessary to understand the sorption behavior of Th under variable groundwater conditions for a long-term safety assessment of geological disposal of HLW.

Granitic rock is considered as one of the candidate host rocks for the geological disposal of HLW [1]. The sorption data of Th onto granitic rocks have been scarcely reported [11], and the dependence of sorption on pH and carbonate concentration cannot be evaluated. For quartz, which is the major constituent mineral in granitic rocks, several sorption data for Th have been obtained [12–14] and pH dependence of the sorption has been modeled [4,13]. However, the influence of carbonate on the sorption has not been clarified. For the other major constituent minerals of granitic rocks, feldspar and mica, sorption data of Th cannot be found.

In the present study, sorption data of Th onto granite were obtained by batch sorption experiments under variable pH and carbonate concentrations. The sorption data for major constituent minerals of granite were also obtained to discuss the sorption of Th onto granite. The sorption behaviors of Th onto the constituent minerals were analyzed by the surface complexation model (SCM) and those onto granite were analyzed by component additivity (CA) approaches [15]. The sorption behaviors of Th onto some minerals have been analyzed by several SCMs such as the constant-capacitance model [16,17], the diffuse-layer model (DLM) [13,16,18–20], the triple-layer model (TLM) [21–26] and the non-electrostatic model (NEM) [4,16,19,27–30]. However, the model parameters for the constituent minerals of granite have been scarcely reported. In this study, the NEM assuming a 1-site surface complexation which needed the simplest parameters was employed.

2. Experimental

2.1. Experimental solutions

A Th stock solution was prepared by the following procedure. Thorium nitrate hydrate (²³²Th(NO₃)₄⋅nH₂O, 4 ≤ n ≤ 5) was purchased from Fluka Chemika Co. One gram of Th(NO₃)₄⋅nH₂O was dissolved in 10 cm³ volume of 0.1 mol dm⁻³ hydrochloric acid (HCl). Diluting 0.1 cm³ volume of the solution to 10 cm³ with 0.1 mol dm⁻³ HCl, Th stock solution was prepared (the concentration of Th is approximately 2 × 10⁻³ mol dm⁻³).

Three types of solutions, 0.01, 0.05 and 0.1 mol dm⁻³ sodium hydrogen carbonate (NaHCO₃), were prepared in a controlled-atmosphere glove box under Ar to avoid dissolution of carbon dioxide gas from the atmosphere. The solubilities of Th in the NaHCO₃ solutions were calculated by the Visual Minteq computer program using the existing thermodynamic data [2,3] (Table 1) with the Davies equation for activity correction [31]. The amorphous oxide (ThO₂ (am, aged)) [3] was assumed to be the solubility limiting solid. The calculation results for 0.01 and 0.1 mol dm⁻³ NaHCO₃ solutions are shown in Figure 1. Considering the solubility of Th, experimental solutions were prepared by adding the Th stock solution into the aforementioned NaHCO₃ solutions, to get the concentration of 2 × 10⁻⁹, 4 × 10⁻⁹ and 2 × 10⁻⁸ mol dm⁻³ for the 0.01, 0.05 and 0.1 mol dm⁻³ NaHCO₃ solutions, respectively. The initial concentrations of Th in the experimental solutions were determined by inductively coupled plasma mass spectrometry (ICP-MS, ELAN DRC, PerkinElmer Inc.) to be 2.0 × 10⁻⁹, 4.3 ×10⁻⁹ and 1.9 × 10⁻⁸ mol dm⁻³ for the 0.01, 0.05 and 0.1 mol dm⁻³ NaHCO₃ solutions, respectively.

Table 1. Thermodynamic data for Th species [2,3].

Species	Reaction	log K
Th(OH)^3+	Th^4+ + H2O = Th(OH)^3+ + H^+	−2.500 ± 0.500
Th(OH)2^2+	Th^4+ + 2H2O = Th(OH)2^2+ + 2H^+	−6.200 ± 0.500
Th(OH)4(aq)	Th^4+ + 4H2O = Th(OH)4(aq) + 4H^+	−17.400 ± 0.700
Th2(OH)2^6+	2Th^4+ + 2H2O = Th2(OH)2^6+ + 2H^+	−5.900 ± 0.500
Th2(OH)3^5+	2Th^4+ + 3H2O = Th2(OH)3^5+ + 3H^+	−6.800 ± 0.200
Th4(OH)8^8+	4Th^4+ + 8H2O = Th4(OH)8^8+ + 8H^+	−20.400 ± 0.400
Th4(OH)12^4+	4Th^4+ + 12H2O = Th4(OH)12^4+ + 12H^+	−26.600 ± 0.200
Th6(OH)14^10+	6Th^4+ + 14H2O = Th6(OH)14^10+ + 14H^+	−36.800 ± 1.200
Th6(OH)15^9+	6Th^4+ + 15H2O = Th6(OH)15^9+ + 15H^+	−36.800 ± 1.500
Th(CO3)5^6−	Th^4+ + 5CO3^2− = Th(CO3)5^6−	31.000 ± 0.700
Th(OH)2(CO3)2^2−	Th^4+ + 2H2O + 2CO3^2− = Th(OH)2(CO3)2^2− + 2H^+	8.798 ± 0.501
ThOH(CO3)4^5−	Th^4+ + H2O + 4CO3^2− = ThOH(CO3)4^5− + H^+	21.599 ± 0.500
Th(OH)4CO3^2−	Th^4+ + 4H2O + CO3^2− = Th(OH)4CO3^2− + 4H^+	−15.605 ± 0.603
ThO2(am, aged)	Th^4+ + 2H2O = ThO2(am, aged) + 4H^+	−8.504 ± 0.900

Figure 1. Solubility of Th in 0.01 mol dm⁻³ NaHCO₃ solution (a) and 0.1 mol dm⁻³ NaHCO₃ solution (b) calculated with existing thermodynamic data [2,3].

Prior to the sorption runs, blank tests were carried out to check for precipitation and colloid formation of Th at pH 8.5–11. A 10 cm³ volume of the Th solution was poured into a polypropylene test tube with a screw cap. After 2 weeks, a 2 cm³ aliquot was sampled and filtered through a 10,000 nominal molecular weight limit (NMWL) ultrafilter (USY-1, Toyo Roshi Kaisha, Ltd.) preconditioned with a small amount of the sample solution. The filtrate was sampled (0.5 cm³ for 0.01 and 0.05 mol dm⁻³ NaHCO₃, or 0.2 cm³ for 0.1 mol dm⁻³ NaHCO₃) and diluted to 3 cm³ with 5% HNO₃. The concentrations of Th were determined by ICP-MS. It was confirmed that the Th concentration did not decrease from the initial concentration, indicating that precipitation and colloid formation [25,32] of Th were negligible.

2.2. Rock and mineral samples

The main constituent minerals of granite, such as feldspar, quartz and mica, were selected for sorption experiments. Feldspar and quartz were represented by commercially available samples of albite (NaAlSi₃O₈, Iwamoto Co., Ltd.) and quartz form silica (SiO₂, Kanto Chemical Co., Inc.), respectively. The mica group minerals were represented by biotite (K(Mg, Fe(II))₃(Al, Fe(III))Si₃O₁₀(OH, F)₂, Nichika Inc.). These mineral samples were in powdered form (<100 μm). Inada granite sample in granulated form (a few hundred μm) was purchased from Nichika Inc. All of the solid samples were used without pretreatment. Scanning electron microscope images (JSM-6010, JEOL Ltd.) of these solids are shown in Figure 2. Their specific surface areas were measured by the Brunauer–Emmett–Teller (BET) N₂ gas adsorption method (NOVA 1200e, Quantachrome Instruments) [33]. The measured specific surface areas were 1.0 m² g⁻¹ (albite), 0.7 m² g⁻¹ (quartz), 4.3 m² g⁻¹ (biotite) and 0.5 m² g⁻¹ (granite).

Figure 2. Scanning electron microscope images of the employed solids (×100 magnification).

2.3. Sorption experiments

Sorption experiments were performed in a controlled-atmosphere glove box under Ar. The experimental runs were made following the procedure of the ‘measurement method of the distribution coefficient on the sorption process’ compiled by the Atomic Energy Society of Japan [34]. One week is recommended as the standard sorption period in this literature, and sorption runs were performed for longer period (2 weeks) in this study. The rock and mineral samples (0.1 g) were immersed in a 10 cm³ volume of the Th experimental solutions in polypropylene test tubes with a screw cap. The pH of the sample suspension was adjusted to 8.5–11 with NaOH solution. The pH of ground water generally ranges between 5 and 10 [35], but it is difficult to adjust the pH to lower values because carbon dioxide is released from the solution by adding acid. The sample suspensions were agitated once a day. After two weeks, the pH and the concentration of Th were measured. The pH was measured with a Sure–Flow combination glass electrode (ROSS 8172BNWP, Thermo Fisher Scientific Inc.). The electrode was calibrated with standard pH buffer solutions of 7.00, 10.01 and 12.46.

A 1 cm³ aliquot was sampled and filtered through a 10,000 NMWL ultrafilter. The filtrate was sampled (0.5 cm³ for 0.01 and 0.05 mol dm⁻³ NaHCO₃, or 0.2 cm³ for 0.1 mol dm⁻³ NaHCO₃) and diluted to 3 cm³ with 5% HNO₃. The concentrations of Th were determined by ICP-MS.

3. Results and discussion

3.1. Experimental results

The distribution coefficient, K_d (m³ kg⁻¹), was calculated using the following equation:(1) $$K_{\mathrm{d}}=\frac{c_{\mathrm{ini}}-c_{\mathrm{eq}}}{c_{\mathrm{eq}}}\frac{V_{\mathrm{ini}}}{M}$$(1) where c_ini is the initial concentration of Th (mol dm⁻³), c_eq the equilibrated concentration of Th (mol dm⁻³), V_ini the initial volume of the solution (m³) and M the weight of the solid phase (kg). The obtained pH and K_d values are summarized in Tables 2–5. For the data obtained from the lower equilibrated concentrations than the lower limit of quantitation (2×10⁻¹¹ mol dm⁻³ for 0.01 and 0.05 mol dm⁻³, and 5×10⁻¹¹ mol dm⁻³ for 0.1 mol dm⁻³ NaHCO₃ conditions, considering the dilution ratio), the lowest K_d values were shown in the tables.

Table 2. Experimental variables and data for Th sorption on albite.

NaHCO3
0.01 mol dm^−3		0.05 mol dm^−3		0.1 mol dm^−3
pH	Kd (m^3 kg^−1)	pH	Kd (m^3 kg^−1)	pH	Kd (m^3 kg^−1)
8.70	>9.9 × 10^0	8.71	(3.0 ± 0.3) × 10^0	8.67	(7.3 ± 0.4) × 10^−1
8.80	>9.9 × 10^0	8.95	(1.9 ± 0.1) × 10^0	8.77	(4.8 ± 0.1) × 10^−1
9.21	>9.9 × 10^0	9.24	(1.2 ± 0.1) × 10^0	8.89	(3.3 ± 0.1) × 10^−1
9.50	>9.9 × 10^0	9.64	(7.6 ± 0.8) × 10^−1	9.00	(2.9 ± 0.1) × 10^−1
10.16	>9.9 × 10^0	9.95	(5.6 ± 0.3) × 10^−1	9.10	(2.2 ± 0.1) × 10^−1
10.82	>9.9 × 10^0	10.05	(4.6 ± 0.3) × 10^−1	9.20	(1.9 ± 0.1) × 10^−1
		10.59	(1.1 ± 0.1) × 10^0	9.45	(1.2 ± 0.1) × 10^−1
				9.74	(8.7 ± 0.3) × 10^−2
				10.39	(1.7 ± 0.1) × 10^−1

Table 3. Experimental variables and data for Th sorption on quartz.

NaHCO3
0.01 mol dm^−3		0.05 mol dm^−3		0.1 mol dm^−3
pH	Kd (m^3 kg^−1)	pH	Kd (m^3 kg^−1)	pH	Kd (m^3 kg^−1)
8.63	(9.5 ± 1.2) × 10^0	8.68	(1.3 ± 0.1) × 10^−1	8.53	(5.1 ± 1.2) × 10^−2
8.85	(8.0 ± 0.8) × 10^0	9.01	(1.3 ± 0.1) × 10^−1	8.82	(4.2 ± 0.2) × 10^−2
8.99	(2.9 ± 0.3) × 10^0	9.24	(1.1 ± 0.1) × 10^−1	8.96	(3.0 ± 0.3) × 10^−2
9.19	(4.4 ± 0.7) × 10^0	9.56	(1.0 ± 0.1) × 10^−1	9.07	(2.1 ± 0.2) × 10^−2
9.51	(3.6 ± 0.5) × 10^0	9.96	(1.4 ± 0.1) × 10^−1	9.18	(2.4 ± 0.2) × 10^−2
10.18	(7.8 ± 1.3) × 10^0	10.31	(1.6 ± 0.1) × 10^−1	9.21	(3.2 ± 0.2) × 10^−2
10.67	>9.9 × 10^0	10.82	(2.1 ± 0.4) × 10^0	9.71	(2.5 ± 0.2) × 10^−2
				10.39	(5.5 ± 0.3) × 10^−2

Table 4. Experimental variables and data for Th sorption on biotite.

NaHCO3
0.01 mol dm^−3		0.05 mol dm^−3		0.1 mol dm^−3
pH	Kd (m^3 kg^−1)	pH	Kd (m^3 kg^−1)	pH	Kd (m^3 kg^−1)
8.96	>9.9 × 10^0	8.70	>2.1 × 10^1	8.76	(2.8 ± 0.4) × 10^1
9.07	>9.9 × 10^0	8.98	>2.1 × 10^1	8.90	(1.9 ± 0.1) × 10^1
9.30	>9.9 × 10^0	9.25	(2.1 ± 0.8) × 10^1	8.96	(9.6 ± 0.9) × 10^0
9.54	>9.9 × 10^0	9.39	(1.2 ± 0.2) × 10^1	9.06	(1.5 ± 0.1) × 10^1
10.16	>9.9 × 10^0	9.55	(1.0 ± 0.1) × 10^1	9.21	(8.6 ± 0.7) × 10^0
10.67	>9.9 × 10^0	9.93	(1.0 ± 0.2) × 10^1	9.48	(5.9 ± 0.2) × 10^0
		10.13	(2.0 ± 0.9) × 10^1	9.76	(3.9 ± 0.3) × 10^0
		10.46	(2.1 ± 0.5) × 10^1	10.26	(3.3 ± 0.3) × 10^0
		10.52	>2.1 × 10^1	10.37	(7.1 ± 0.6) × 10^0

Table 5. Experimental variables and data for Th sorption on granite.

NaHCO3
0.01 mol dm^−3		0.05 mol dm^−3		0.1 mol dm^−3
pH	Kd (m^3 kg^−1)	pH	Kd (m^3 kg^−1)	pH	Kd (m^3 kg^−1)
8.61	(4.3 ± 0.5) × 10^0	8.84	(1.9 ± 0.1) × 10^−1	8.70	(6.9 ± 0.3) × 10^−2
8.81	(5.9 ± 0.9) × 10^0	8.99	(7.2 ± 0.4) × 10^−2	8.77	(4.6 ± 0.2) × 10^−2
9.21	(4.7 ± 0.5) × 10^0	9.07	(1.4 ± 0.1) × 10^−1	8.90	(7.0 ± 0.3) × 10^−2
9.32	(8.9 ± 0.1) × 10^0	9.25	(6.7 ± 0.4) × 10^−2	9.00	(4.2 ± 0.2) × 10^−2
9.57	(3.9 ± 0.6) × 10^0	9.31	(1.2 ± 0.1) × 10^−1	9.03	(3.9 ± 0.2) × 10^−2
9.59	(7.9 ± 0.5) × 10^0	9.47	(1.1 ± 0.1) × 10^−1	9.11	(3.9 ± 0.2) × 10^−2
9.78	(7.6 ± 1.4) × 10^0	9.56	(5.3 ± 0.4) × 10^−2	9.17	(9.2 ± 0.3) × 10^−2
10.17	(7.2 ± 1.6) × 10^0	9.59	(8.9 ± 0.4) × 10^−2	9.20	(4.2 ± 0.3) × 10^−2
10.23	(9.4 ± 0.9) × 10^0	9.80	(8.5 ± 0.3) × 10^−2	9.22	(1.7 ± 0.2) × 10^−2
10.55	>9.9 × 10^0	9.96	(5.2 ± 0.3) × 10^−2	9.59	(1.7 ± 0.2) × 10^−2
10.63	>9.9 × 10^0	9.97	(9.2 ± 0.4) × 10^−2	9.75	(3.4 ± 0.2) × 10^−2
		10.08	(6.9 ± 0.4) × 10^−2	9.81	(1.5 ± 0.2) × 10^−2
		10.55	(2.5 ± 0.1) × 10^−1	10.06	(1.5 ± 0.3) × 10^−2
		10.56	(2.0 ± 0.1) × 10^−1	10.30	(1.9 ± 0.2) × 10^−2
				10.59	(4.3 ± 0.2) × 10^−2

The obtained K_d values for albite are plotted versus pH in Figure 3(a). All the K_d values for 0.01 mol dm⁻³ NaHCO₃ were higher than 9.9 m³ kg⁻¹ at pH 8.70–10.82. The K_d values for 0.05 mol dm⁻³ NaHCO₃ were from 4.6 × 10⁻¹ to 3.0 m³ kg⁻¹ at pH 8.71–10.59. The K_d values for 0.1 mol dm⁻³ NaHCO₃ were from 8.7 × 10⁻² to 7.3 × 10⁻¹ m³ kg⁻¹ at pH 8.67–10.39. The K_d values decreased with increasing NaHCO₃ concentration and the local minimal value was seen at around pH 10.

Figure 3. Comparison of K_d values for Th obtained in this study and previously reported ones: (a) albite, (b) quartz [12,14], (c) biotite, and (d) granite [11]. ‘0.01 M’ represents the 0.01 mol dm⁻³ NaHCO₃ concentration. Previous data for albite and biotite are not available.

The obtained K_d values for quartz are plotted versus pH in Figure 3(b). The K_d values for 0.01 mol dm⁻³ NaHCO₃ were from 2.9 to 9.5 m³ kg⁻¹ at pH 8.63–10.18. The values are almost the same as the literature values obtained under the conditions of 0.01 mol dm⁻³ NaClO₄ by Allard et al. [12] and slightly higher than the values obtained under the conditions of 0.02 mol dm⁻³ KNO₃ by Chen and Wang [14]. The K_d decreased with increasing NaHCO₃ concentration, the values for 0.1 mol dm⁻³ NaHCO₃ were about two orders of magnitude lower than those for 0.01 mol dm⁻³ NaHCO₃ (from 2.1 × 10⁻² to 5.5 × 10⁻² m³ kg⁻¹). The K_d values for quartz were lower than those for albite, and the pH dependences of K_d for quartz showed the same tendency as those for albite.

The obtained K_d values for biotite are plotted versus pH in Figure 3(c). All the K_d values for 0.01 mol dm⁻³ NaHCO₃ were higher than 9.9 m³ kg⁻¹ at pH 8.96–10.67. The K_d values decreased with increasing NaHCO₃ concentration, the K_d values for 0.1 mol dm⁻³ NaHCO₃ were from 3.3 to 28 m³ kg⁻¹ at pH 8.76–10.37. The K_d values for biotite were higher than those for albite and quartz, and the pH dependences of K_d for biotite showed the same tendency as those for albite and quartz.

The obtained K_d values for granite are plotted versus pH in Figure 3(d). The K_d values for 0.01 mol dm⁻³ NaHCO₃ were from 3.9 to 9.4 m³ kg⁻¹ at pH 8.61–10.23 and higher than 9.9 m³ kg⁻¹ at the higher pH region. The values are almost the same as the literature values obtained under the conditions of 3.3 × 10⁻³ mol dm⁻³ HCO₃⁻ [11]. The K_d decreased with increasing NaHCO₃ concentration, the values for 0.1 mol dm⁻³ NaHCO₃ were about two orders of magnitude lower than those for 0.01 mol dm⁻³ NaHCO₃ (from 1.5 × 10⁻² to 9.2 × 10⁻² m³ kg⁻¹). The pH dependences of K_d for granite were almost the same as those for the constituent minerals.

The dominant sorption mechanism of Th on the constituent minerals is considered to be surface complexation [4,18,36]. Quartz has silanol sites (≡SiOH) on the edge surfaces. Albite, which is sodium aluminosilicate includes aluminol sites (≡AlOH) and ≡SiOH on the edge surfaces. Biotite that has Fe in its mineral structure has a possibility of including ferrol sites (≡FeOH) [37] in addition to ≡AlOH and ≡SiOH. By considering the surface complexation of Th with such surface hydroxyl groups, the sorption behaviors were analyzed by the SCM [38].

3.2. Analysis of the sorption behavior by the SCM

The sorption behaviors of Th were analyzed by the NEM with the Visual Minteq computer program using the thermodynamic data of all solution species summarized in Table 1. The NEM neglects the possible formation of outer-sphere complexes involving the background electrolytes such as ≡SO⁻_Na⁺ or ≡SOH₂⁺_CO₃²⁻ [37–41]. The protonation and deprotonation reactions of surface hydroxyl groups (≡SOH) can be expressed by (2) $$\equiv \mathrm{SOH}+{\mathrm{H}}^{+}=\equiv {\mathrm{SOH}}_2^{+}{K}_{\mathrm{a}1}$$(2) (3) $$\equiv \mathrm{SOH}=\equiv \mathrm{S}{\mathrm{O}}^{-}+{\mathrm{H}}^{+}{K}_{\mathrm{a}2}$$(3)

Based on the dominant aqueous Th species (Figure 1), the surface species were assumed as follows [27–30,36,39]: (4) $$\equiv \mathrm{SOH}+\mathrm{Th}{\left(\mathrm{OH}\right)}_4\left(\mathrm{aq}\right)=\equiv \mathrm{SOTh}{\left(\mathrm{OH}\right)}_3^0+{\mathrm{H}}_2\mathrm{O}$$(4) (5) $$\equiv \mathrm{SOH}+\mathrm{Th}{\left(\mathrm{OH}\right)}_2{\left(\mathrm{C}{\mathrm{O}}_3\right)}_2^{2-}=\equiv \mathrm{SOThOH}{\left(\mathrm{C}{\mathrm{O}}_3\right)}_2^{2-}+{\mathrm{H}}_2\mathrm{O}$$(5) (6) $$\equiv \mathrm{SOH}+\mathrm{ThOH}{\left(\mathrm{C}{\mathrm{O}}_3\right)}_4^{5-}=\equiv \mathrm{SOTh}{\left(\mathrm{C}{\mathrm{O}}_3\right)}_4^{5-}+{\mathrm{H}}_2\mathrm{O}$$(6)

In addition, the formation of ≡SOTh(OH)₄⁻ species was also considered because the ≡SO⁻ site was stable in the high pH regions [4]. The reactions between ≡SOH sites and Th⁴⁺ which is the master species of Th(IV) for calculations were as follows: (7) $$\begin{array}{ccc}& \equiv & \mathrm{SOH}+\mathrm{T}{\mathrm{h}}^{4+}+3{\mathrm{H}}_2\mathrm{O}=\equiv \mathrm{SOTh}{\left(\mathrm{OH}\right)}_3^0\hfill \\ & & +4{\mathrm{H}}^{+}{K}_1\hfill \end{array}$$(7) (8) $$\begin{array}{ccc}& \equiv & \mathrm{SOH}+\mathrm{T}{\mathrm{h}}^{4+}+4{\mathrm{H}}_2\mathrm{O}=\equiv \mathrm{SOTh}{\left(\mathrm{OH}\right)}_4^{-}\hfill \\ & & +5{\mathrm{H}}^{+}{K}_2\hfill \end{array}$$(8) (9) $$\begin{array}{ccc}& \equiv & \mathrm{SOH}+\mathrm{T}{\mathrm{h}}^{4+}+{\mathrm{H}}_2\mathrm{O}+2{\mathrm{CO}}_3^{2-}\hfill \\ \hfill =& \equiv & \mathrm{SOThOH}{\left(\mathrm{C}{\mathrm{O}}_3\right)}_2^{2-}+2{\mathrm{H}}^{+}{K}_3\hfill \end{array}$$(9) (10) $$\begin{array}{ccc}& \equiv & \mathrm{SOH}+\mathrm{T}{\mathrm{h}}^{4+}+4{\mathrm{CO}}_3^{2-}=\equiv \mathrm{SOTh}{\left(\mathrm{C}{\mathrm{O}}_3\right)}_4^{5-}\hfill \\ & & +{\mathrm{H}}^{+}{K}_4\hfill \end{array}$$(10)

The K_d values were calculated as (11) $$K_d=\frac{\Sigma [\mathrm{surface}\mathrm{Th}\mathrm{species}]}{\Sigma [\mathrm{aqueous}\mathrm{Th}\mathrm{species}]}\frac{V_{\mathrm{ini}}}{M}$$(11)

Nuclear Energy Agency (NEA) [15] reported the indicative values for SCM parameters of important minerals. In the calculations for albite, the surface site density (n_s = 4.05 sites nm⁻²) and the surface acidity constants (log K_a1 = 4.13 and log K_a2 = −8.46) of feldspar reported by the NEA [15] were adopted. The measured surface area (S = 1.0 m² g⁻¹) by BET was adopted. The existing literature values of the equilibrium constants for surface complexation of Th are summarized in Table 6. The values for albite are not available. Instead, the model calculation was performed by using K₁ and K₂ values for the NEM for montmorillonite ((Na,Ca)_0.33(Al,Mg)₂Si₄O₁₀(OH)₂·nH₂O) [27] and kaolinite (Al₄Si₄O₁₀(OH)₈) [30] (Table 6). These minerals are aluminosilicate minerals formed by weathering or alteration of plagioclase [42] and have ≡SiOH and ≡AlOH; similar sorption property to albite can be expected. The equilibrium constants of surface carbonato-complex species (K₃ and K₄) were tried to be estimated by linear free energy relationships (LFERs) which is based on the analogy of hydrolysis in solution to sorption onto surface hydroxyl groups. Bradbury and Baeyens [27,28] formulate the interrelation between the formation constants of aqueous hydroxo-complex species of metal ions (Me^z) (12) $$\mathrm{M}{\mathrm{e}}^z+x{\mathrm{H}}_2\mathrm{O}=\mathrm{Me}{\left(\mathrm{OH}\right)}_x^{z-x}+x{\mathrm{H}}^{+\mathrm{aq}}{K}_x$$(12) and that of surface species (13) $$\begin{array}{ccc}& \equiv & \mathrm{SOH}+\mathrm{M}{\mathrm{e}}^z+\left(x-1\right){\mathrm{H}}_2\mathrm{O}=\equiv \mathrm{SOMe}{\left(\mathrm{OH}\right)}_{(x-1)}^{z-x}\hfill \\ & & +x{\mathrm{H}}^{+}{}^{\mathrm{sur}}{K}_{x-1}\hfill \end{array}$$(13) as (14) $$\mathrm{lo}{\mathrm{g}}^{\mathrm{sur}}{K}_{x-1}=8.1\pm 0.3+\left(0.90\pm 0.02\right)\mathrm{lo}{\mathrm{g}}^{\mathrm{aq}}{\mathrm{K}}_x$$(14) and (15) $$\mathrm{lo}{\mathrm{g}}^{\mathrm{sur}}{K_x}_{-1}=7.9\pm 0.4+\left(0.83\pm 0.02\right)\mathrm{lo}{\mathrm{g}}^{\mathrm{aq}}{K}_x$$(15) for montmorillonite and illite, respectively. Figure 4 shows the correlation of log ^surK_x−1 with log ^aqK_x for montmorillonite and illite reported by Bradbury and Baeyens [27,28]. The formation constants of surface carbonato-complex species of Th were only reported by Ervanne et al. [30] (Table 6). The formation of ≡SOTh(OH)₂CO₃⁻(16) $$\begin{array}{ccc}& \equiv & \mathrm{SOH}+\mathrm{T}{\mathrm{h}}^{4+}+2{\mathrm{H}}_2\mathrm{O}+{\mathrm{CO}}_3^{2-}\hfill \\ \hfill =& \equiv & \mathrm{SOTh}{\left(\mathrm{OH}\right)}_2{\mathrm{CO}}_3^{-}+3{\mathrm{H}}^{+}\hfill \end{array}$$(16) was estimated from the aqueous carbonato-complex species (17) $$\begin{array}{ccc}& & \mathrm{T}{\mathrm{h}}^{4+}+3{\mathrm{H}}_2\mathrm{O}+{\mathrm{CO}}_3^{2-}=\mathrm{Th}{\left(\mathrm{OH}\right)}_3{\mathrm{CO}}_3^{-}+3{\mathrm{H}}^{+}\hfill \\ & & \log K=-3.5\hfill \end{array}$$(17)

Table 6. Existing literature values of equilibrium constants for surface complexation of Th.

Reaction	log K
	NEM					DLM	TLM
	Kaolinite	Montmorillonite	Illite	Illite	Hematite	Hematite	Kaolinite	Quartz	Goetite	Goetite
≡SOH + H^+ = ≡SOH2^+	4.55	4.5	4	4.0	5.9	7.43	1.75	−0.8	–	5.57
≡SOH = ≡SO^− + H^+	−9.01	−7.9	−6.2	−6.2	−8.5	−8.17	−6.25	−6.8	–	−9.52
≡SOH + Th^4+ = ≡SOTh^3+ + H^+	–	7.2	–	7.4	5.6	–	–	–	1.0	3.5
≡SOH + Th^4+ + H2O = ≡SOThOH^2+ + 2H^+	–	2.7	–	2.3	–	–	0.2	0.6	−0.75	0.2
≡SOH + Th^4+ + 2H2O = ≡SOTh(OH)2^+ + 3H^+	−4.5	−2.6	−3.0	−2.4	−3.5	−2	−4.6	−3.7	−2.38	−6.38
≡SOH + Th^4+ + 3H2O = ≡SOTh(OH)3^0 + 4H^+	−9.8	−9.1	−8.0	−8.8	−9.2	–	−10.1	−9.8	−9.85	−10.6
≡SOH + Th^4+ + 4H2O = ≡SOTh(OH)4^− + 5H^+	−17.8	−16.9	−13.4	−15.3	−17.3	−16.7	–	−15.5	−16.75	−16.3
≡SOH + Th^4+ + 2H2O + CO3^2^−
= ≡SOTh(OH)2CO3^2^− + 3H^+	5.1	–	5.3	–	–	–	–	–	–	–
References	[30]	[27]	[30]	[28]	[19]	[19]	[22]	[22]	[21]	[23]

Figure 4. Correlation of surface complexation constants of metal species sorbing on the mineral surface with the corresponding aqueous hydrolysis constants (blue and green marks) summarized in Bradbury and Baeyens [27,28]. The blue line shows LFER for montmorillonite and the green dotted line for illite. Red marks are the data reported by Ervanne et al. [30].

The formation constants of ≡SOTh(OH)₂CO₃⁻, ≡SOTh(OH)₂⁺ and ≡SOTh(OH)₂° for kaolinite and illite reported by Ervanne et al. [30] were plotted in Figure 4. The data points of surface hydroxo-carbonato complex species, ≡SOTh(OH)₂CO₃⁻, can be explained by the LFER. The log K₃ and log K₄ values were estimated from the formation constants of aqueous carbonate complex species (^aqK'_x) listed in Table 1 as (18) $$\begin{array}{ccc}\hfill \mathrm{T}{\mathrm{h}}^{4+}& +& x{\mathrm{H}}_2\mathrm{O}+y{\mathrm{CO}}_3^{2-}=\mathrm{Th}{\left(\mathrm{OH}\right)}_x{\left(\mathrm{C}{\mathrm{O}}_3\right)}_y^{4-x-2y}\hfill \\ & & +x{\mathrm{H}}^{+}{}^{\mathrm{aq}}{K}_x^{\text{'}}\hfill \end{array}$$(18) (19) $$\begin{array}{ccc}& \equiv & \mathrm{SOH}+\mathrm{T}{\mathrm{h}}^{4+}+\left(x-1\right){\mathrm{H}}_2\mathrm{O}+y{\mathrm{CO}}_3^{2-}\hfill \\ \hfill =& \equiv & \mathrm{SOTh}{\left(\mathrm{OH}\right)}_{(x-1)}{\left(\mathrm{C}{\mathrm{O}}_3\right)}_y^{4-x-2y}+x{\mathrm{H}}^{+}{}^{\mathrm{sur}}{K}_{x-1}^{\text{'}}\hfill \end{array}$$(19) (20) $$\mathrm{lo}{\mathrm{g}}^{\mathrm{sur}}{K}_{x-1}^{\text{'}}=8.1+0.90\log {}^{\mathrm{aq}}{K}_x^{\text{'}}$$(20) to be log K₃ = -16.0 and log K₄ = 27.5. Figure 5(a) shows the comparison of the predicted K_d values for albite with the experimentally measured ones. The model calculations with the values of log K₁ = −9.8 and log K₂ = −17.8 predicted the sorption tendency well. The employed SCM parameters are summarized in Table 7. Figure 6(a) shows the calculated mole fractions of Th species under 0.05 mol dm⁻³ NaHCO₃ conditions. It is shown that the ≡SOThOH(CO₃)₂²⁻ and ≡SOTh(OH)₄⁻ are dominant sorption species. The mole fractions of aqueous species, ThOH(CO₃)₄⁵⁻ and Th(OH)₂(CO₃)₂²⁻, are shown at around pH10. The local minimal K_d value at around pH 10 was due to the stabilization of aqueous species by hydroxo–carbonate complexation.

Figure 5. Comparison of K_d values of Th predicted using the NEM (lines) with experimentally measured ones (marks).

Table 7. Model parameters and equilibrium constants for the NEM calculation.

			Albite	Quartz	Biotite
Surface area	S	m^2 g^−1	1	0.7	4.3
Site density	ns	sites nm^−2	4.05	5.67	3.81
Surface acidity constant	log Ka1		4.13	−1.26	4.6
	log Ka2		−8.46	−7.28	−6.4
Formation constant	log K1		−9.8	–	−8.8
	log K2		−17.8	−17.5	−15.3
	log K3		16.0	15.5	18.5
	log K4		27.5	–	–

Figure 6. Calculated mole fraction of Th species under 0.05 mol dm⁻³ NaHCO₃ condition. (a) Albite, (b) quartz, (c) biotite, (d) granite and (e) granite calculated using one order of magnitude lower K₁–K₇ values for feldspar. (F), feldspar; (Q), quartz; (B), biotite.

In the calculations for quartz, the measured surface area (0.7 m² g⁻¹), the surface acidity constants (log K_a1 = −1.26 and log K_a2 = −7.28) [15] and the surface site density (5.67 sites nm⁻²) [15] were adopted. For the formation constants of surface sorption species onto quartz, only the values for the TLM [22] are available. In the TLM, the electrostatic terms are included in the set of components in order to correct for the effects of surface charge on equilibrium constants [15]. On the other hand, the electrostatic terms are incorporated within equilibrium constants for sorption reactions in the NEM, it is difficult to adopt the equilibrium constants for the TLM to the NEM. The formation constants of surface species for quartz were estimated by optical fitting. The dominant surface species were assumed to be ≡SOThOH(CO₃)₂²⁻ and ≡SOTh(OH)₄⁻ from the calculated mole fractions of Th species for albite (Figure 6(a)), and the K₂ and K₃ values were estimated. Calculation results are shown in Figure 5(b). The log K₂ value can be estimated from −18 to −17 and the log K₃ can be from 15 to 16. The calculation results with the intermediate values (log K₂ = −17.5 and log K₃ = 15.5) explain the experimental results reasonably well (Figure 5(c)), and these values are similar to those for albite. Figure 6(b) shows the calculation results of Th species under 0.05 mol dm⁻³ NaHCO₃ conditions. The mole fractions of ≡SOThOH(CO₃)₂²⁻ are smaller than the case for albite, which causes the lower K_d values than those for albite. It is due to the lower pK_a2 value of quartz (7.28) than albite (8.46), and the concentration of ≡SOH for quartz is lower than that for albite at pH > 8.

In the calculations for biotite, the measured surface area (4.3 m² g⁻¹), the surface acidity constants (log K_a1 = 4.6 and log K_a2 = −6.4) [43,44] and the surface site density (3.81 sites nm⁻²) for mica [15] were adopted. The formation constants of surface species for biotite are not available. Instead, the values for illite (K(Al,Mg,Fe)₂(Si,Al)₄O₁₀(OH)₂) [28,30] which belongs to the mica group [45] and contains ≡SiOH, ≡AlOH and ≡FeOH were adopted. The formation constants of surface carbonato-complex species were estimated by LFER (Equation (15)(15) $$\mathrm{lo}{\mathrm{g}}^{\mathrm{sur}}{K_x}_{-1}=7.9\pm 0.4+\left(0.83\pm 0.02\right)\mathrm{lo}{\mathrm{g}}^{\mathrm{aq}}{K}_x$$(15) ). The values of K₃ and K₄ were calculated from the formation constants of aqueous carbonate complex species (Table 1) as (21) $$\mathrm{lo}{\mathrm{g}}^{\mathrm{sur}}{K}_{x-1}^{\text{'}}=7.9+0.83\mathrm{lo}{\mathrm{g}}^{\mathrm{aq}}{K}_x^{\text{'}}$$(21) to be log K₃ = −15.2 and log K₄ = 25.8. Figure 5(d) shows the comparison of the predicted K_d values for biotite with the experimentally measured ones. The calculation results using the values (log K₁ = −8.0 and log K₂ = 13.4) reported by Ervanne et al. [30] overestimated the K_d values by about one order of magnitude. On the other hand, the model calculations using the values (log K₁ = −8.8 and log K₂ = 15.3) reported by Bradbury and Baeyens [28] can explain the experimental results reasonably well at pH > 10, but underestimated the K_d values at lower pH and higher concentrations of carbonate. This is likely due to the underestimation of the formation constant of ≡SOThOH(CO₃)₂²⁻ species (log K₃ = 15.2) which was expected to dominate the sorption at low pH and high carbonate concentration. The slope in the interrelation between ^aqK'_x and ^surK'_x-1 is expected to be nearly 1 by assuming simple exchange of ≡SO⁻ and OH⁻ in the surface complexation reaction as (22) $$\equiv \mathrm{S}{\mathrm{O}}^{-}+\mathrm{Me}{\left(\mathrm{OH}\right)}_x^{z-x}=\equiv \mathrm{SOMe}{\left(\mathrm{OH}\right)}_{(x-1)}^{z-x}+\mathrm{O}{\mathrm{H}}^{-},$$(22) the slope of 0.83 might be too low. The log K₃ value estimated by the extrapolation of data for some metal species [28] using Equation (21)(21) $$\mathrm{lo}{\mathrm{g}}^{\mathrm{sur}}{K}_{x-1}^{\text{'}}=7.9+0.83\mathrm{lo}{\mathrm{g}}^{\mathrm{aq}}{K}_x^{\text{'}}$$(21) would be also too low. Using least-squares fitting, with a slope of 1, to the data for illite shown in Figure 4, the relationship between log ^surK'_x-1 and log ^aqK'_x was formulated as (23) $$\log {}^{\mathrm{sur}}{K}_{x-1}^{\text{'}}=10.4+\mathrm{lo}{\mathrm{g}}^{\mathrm{aq}}{K}_x^{\text{'}},$$(23) which gave the log K₃ value to be nearly 19.2 (^aqK'_x = 8.798). Figure 5(e) shows that the recalculation results with log K₅ = 18.5 (the formation of ≡SOTh(CO₃)₄⁵⁻was ignored) explain the experimental results reasonably well. Figure 6(c) shows the calculated mole fractions of Th species under 0.05 mol dm⁻³ NaHCO₃ conditions. The dominant surface species for biotite were the same as those for albite and quartz. The mole fractions of aqueous Th species are lower than the case for albite and quartz, which causes the higher K_d values.

Sorption behaviors of Th onto granite were analyzed by the CA approaches [15]. The composition of granite was assumed as 45% feldspar, 50% quartz and 5% biotite [46]. The specific surface area of granite was measured as 0.5 m² g⁻¹. However, surface areas below 1 m² g⁻¹ cannot be measured accurately by the N₂–BET method [47] and the particle size of the granite samples (a few hundred μm) was much larger than the powdered mineral samples (Figure 2); the value of measured specific surface area is unreliable. André et al. [48] reported the interaction between the particle size and specific surface area for crushed granite, and the particle size of 250–500 μm corresponds to the specific surface area of 0.111 m² g⁻¹. In this calculation, the specific surface area of 0.1 m² g⁻¹ was adopted. The surface area of each mineral was assumed to be proportional to its content. For the surface acidity constants (K_a1, K_a2) and the formation constants of the surface species (K₁–K₄), the values summarized in Table 7 were adopted. Figure 5(f) shows the calculated K_d values for granite compared with the experimentally measured ones. The calculation results can explain the experimental results well. André et al. [48] also reported that the K_d values for intact drill core of granite were about one order of magnitude lower than those for the crushed granite with the particle size of 250–500 μm. Byegård et al. [49] reported the dependence of K_d on the particle diameter of granite and it supports the results of André et al. [48]. In addition, Hakanen et al. [50] reported that K_d values for crushed crystalline rocks were up to 30 times higher than those for intact rocks. Therefore, the K_d values for the intact granite rocks are expected to be about one order of magnitude lower than the experimental results. Figure 6(d) shows the mole fractions of Th species for granite under 0.05 mol dm⁻³ NaHCO₃ conditions. It was suggested that biotite and feldspar dominate the sorption of Th in granite at near neutral pH and feldspar dominates at higher pH. Although the surface areas of the constituent minerals were assumed to be proportional to its content in this study, the sorption behavior of Th in granite is affected by the effective surface areas of the constituent minerals. Further studies are necessary to understand the effective surface area of each mineral in granite.

4. Conclusion

The K_d values of Th for granite and its major constituent minerals (albite, quartz and biotite) were obtained at pH 8.5–11 under 0.01, 0.05 and 0.1 mol dm⁻³ NaHCO₃ conditions. The K_d values for granite under 0.01 mol dm⁻³ NaHCO₃ conditions were from 3.9 to 9.4 m³ kg⁻¹ at pH 8.61–10.23 and higher than 9.9 m³ kg⁻¹ at higher pH regions. The K_d decreased with increased carbonate concentrations, the K_d values for 0.1 mol dm⁻³ NaHCO₃ were from 1.5 × 10⁻² to 9.2 × 10⁻² m³ kg⁻¹, and the local minimal value was shown at around pH10. These sorption tendencies were also shown for the constituent minerals.

The NEM calculations for the sorption of Th onto the constituent minerals were able to explain the experimental results well. The local minimal K_d value was due to the stabilization of aqueous species by hydroxo–carbonate complexations. Sorption behaviors of Th onto granite were analyzed by the CA approaches, and the calculation results agreed with the experimental results well. The calculation results for mol fractions of Th suggest that biotite and feldspar can be acting as the dominant sorbent minerals in granite.

Acknowledgments

The authors acknowledge Mr. M. Kamoshida and Mr. N. Terunuma for experimental measurements; Dr. L. Barr for reviewing the language. Part of this research is funded by the Secretariat of Nuclear Regulation Authority (NRA), Japan (formerly the Nuclear and Industrial Safety Agency, Ministry of Economy, Trade and Industry, Japan).

Disclosure statement

No potential conflict of interest was reported by the authors.