Solubility of FeSe2(cr) at 318 K in the presence of iron

ABSTRACT The concentration of Se equilibrated with FeSe2(cr) was determined by solubility experiments under reducing conditions and 318 ± 1 K. Agreement between the solubility data obtained from the oversaturation and undersaturation directions suggested the attainment of equilibrium. X-ray diffraction analyses revealed the formation of the FeSe2(cr) phase only. The log10 K 0 values of −5.0 ± 1.4 and −14.9 ± 1.5 for the FeSe2(cr) solubility reactions of FeSe2(cr) ⇄ Fe2+ +0.5 Se4 2− + e− and FeSe2(cr) +2 H+ +2 e− ⇄ Fe2+ +2 HSe−, respectively were determined . Moreover, the selenium solubility in the presence of selenide and Fe under anoxic conditions was discussed with the results of our experiments and previous experimental work performed at 348 K. Under the experimental conditions corresponding to the typical pH and Eh of anoxic groundwater and equilibrium with stable FeSe2(cr), the Se solubilities were reduced and remained as constant values from 6.3 × 10−8 to 9.0 × 10−7 mol dm−3　over the pH range from 6.5 to 9.5, even in spite of the linear relationship between iron concentrations with pH. This indicated that Se was consumed before the formation of FeSe2(cr) and implied that consideration of reaction paths to equilibrium with FeSe2(cr) was necessary for an estimation of Se solubility for performance assessment in geological disposal system.


Introduction
Selenium is a trace nutrient, but it is toxic at high concentrations. Thus, in the past few decades, comprehensive studies on environmental behaviors of selenium have been conducted [1]. Additionally, selenium-79 has received worldwide attention because it is present in high-level radioactive glass wastes (HLW) from reprocessing spent fuels as a long-lived fission product with a half-life of 2.95 × 10 5 years [2]. The storage of high-level radioactive glass wastes in geological disposal is based on the concept of confinement by a multibarrier system in order to deal with radioactive waste in a manner that protects human health and the environment now and in the future without imposing undue burdens on future generations [3,4]. To isolate the waste from the biosphere until most of the radioactivity has decayed multibarrier design consists of vitrified waste package, steel canister, bentonite backfill, and geological barriers [3,4]. In these systems selenium can be released by the dissolution of vitrified waste, which are components of HLW disposal system [3]. Once released selenium reaches an overpack, it is preferentially adsorbed to a surface of a corrosion product of iron [5][6][7][8]. Moreover, selenium reaches bentonite in the buffer region through the overpack region. Selenium is absorbed into bentonite [9] and reacts with pyrite (an accessory mineral) in bentonite by substitution of sulfur [10][11][12][13][14]. If selenium is released into host rocks through the engineered barrier, it is absorbed into minerals [5,15,16] and incorporated into solids by substitution of sulfur [10][11][12][13][14]. The reaction process of absorption into surface of a corrosion product of iron, clay minerals, and sand stone reached equilibrium within several minutes to a few months [5][6][7][8][9]16]. For the reaction of substitution of sulfur on pyrite, the state of equilibrium was observed within 5 days [11][12][13][14]. Although selenium is incorporated into solids by the above-mentioned kinetically rapid reactions, a thermodynamically stable phase is expected to finally form in the environment [17,18]. Selenide minerals are encountered in telethermal selenide veins, unconformity-related and sandstone-hosted uranium deposits, and epithermal Au-Ag deposit [19]. The process of formation for such selenide minerals is often associated with the chemical property of sulfur. Selenium, which is a thousand times less abundant than sulfur in the earth's crust, often substitutes for sulfur in sulfide minerals due to the similarity of their crystallochemical properties [19]. Under the condition of HLW, sulfide mineral is mainly stable as pyrite (FeSe 2 ) because iron ions are ubiquitous. Therefore, it is expected that the dominating phase was found to be FeSe 2 (cr) via a substitution of reduced S by Se. Thus, for the safety assessment of HLW, it is necessary to elucidate the selenium concentration that considers equilibrium with FeSe 2 (cr). The accurate solubility of a solid phase under determined conditions is typically obtained from both oversaturation and undersaturation directions solubility experiments.
There were only two studies that reported the solubility of selenium in the presence of iron. Iida et al. [20] performed solubility experiments, which determined the solubility-limiting solid phase of selenium solid (Se(s)) in the presence of iron under anoxic conditions. They concluded that the solubility of selenium was controlled by a minor amount of amorphous selenium solid (Se(am)) because low concentrations expected as FeSe 2 (cr) equilibrated were not obtained. In the solubility experiments of Doi et al. [21], the solubility product for ferroselite (FeSe 2 (cr)) from both oversaturation and undersaturation directions was determined. The precipitate was aged at 348 K because elevated temperature such as that used in the study of Doi et al. [21] was expected to promote the formation of FeSe 2 (cr) and allow deep underground temperature to be realistically simulated [21]. They predicted and observed a very low solubility of selenium. Additionally, they identified ferroselite (FeSe 2 (cr)) that formed upon aging at 348 K by X-ray powder diffraction. They concluded that equilibrium was re-established in all samples at the time of pH and Eh measurements at 298 K and an accurate solubility product for the ferroselite dissolution reaction was obtained. We note that compared with long aging periods ranging from 29 to 217 days at 348 K, the 5 h used for pH and Eh measurements at room temperature (298 K) were too short for equilibration with a solid. Much shorter to be equilibrated with a solid, obtained solubility was expected to be the solubility equilibrated at 348 K.
In this study, we investigated the solubility of selenium equilibrated with FeSe 2 (cr) at the temperatures expected in deep geological disposals. With respect to the geothermal gradient in most part of Japan with exception of volcanic regions, the geothermal gradient is generally reported to be approximately 3 K per 100 m [22,23]. The temperature at the ground surface is assumed to be 288 K. The assumed ambient temperature at a depth of 1,000 m could be estimated to be 318 K [24]. Therefore, the temperature was maintained at 318 K in the present solubility experiment. The reaction mechanism that controls the selenium concentration in the presence of FeSe 2 (cr) was assumed to be a key concern in estimating the expected solubility of selenium in an HLW repository. Thus, the relevant reaction paths of equilibrium with FeSe 2 (cr) with respect to selenium concentration were discussed using the results of this study as well as previous studies [21].

Solubility experiments
The solubility experiments were conducted under anaerobic conditions in a glovebox with an oxygen content of < 1 ppm. The dissolved oxygen in all liquids was removed by purging with nitrogen (N 2 ) gas. The chemicals used for the preparation of starting solutions of Fe and Se and adjustment of pH and Eh were of reagent grade. A metallic Se sample (Wako Pure Chemical Industries, Tokyo, Japan) was washed with 0.01 mol dm −3 sodium hydroxide (NaOH) (Kanto Kagaku, Tokyo, Japan) several times to remove soluble impurities such as SeO 2 . The washed metallic Se was solubilized in 1.8 mol dm −3 NaOH at 393 K. The resulting solution was filtered through a 0.45 μm membrane filter to remove excess solid material. A 7 g sample of metallic Fe was washed three times with 0.05 mol dm −3 hydrochloric acid (HCl), followed by distilled water to remove organic substances. The washed metallic Fe was dissolved in 12 mol dm −3 HCl. The resulting solution was filtered through a 0.45 μm membrane filter.
For solubility experiments from oversaturation direction, aliquots of Se and Fe filtrates were added to deionized water. The initial concentrations of Se and Fe (adjusted to pH 8 and 9.5) were 2.3 × 10 −3 and 5.9 × 10 −3 mol dm −3 , respectively. Meanwhile, the initial concentration of Se and Fe solutions adjusted to pH 6.5 were 2.1 × 10 −2 and 1.0 × 10 −2 mol dm −3 , respectively. Samples were stored in an oven at 318 ± 1 K.
For solubility experiments from undersaturation directions, the synthetic solid of FeSe 2 (cr) was obtained by mixing 1.8 × 10 −2 mol dm −3 Fe and 3.7 × 10 −2 mol dm −3 Se. The mixture was stored in an oven at 348 K. Aging period was approximately 3 months based on the aging time of solubility experiment in Doi et al. [21]. The precipitated solids were filtrated through 0.45 μm membrane filter and washed with 0.2 mol dm −3 HNO 3 (Kanto Kagaku) and deionized water. After drying, outside of the globe box, the crystalline structure of FeSe 2 (cr) in the synthesized solids was obtained via X-ray diffraction patterns analysis (SmartLab, Rigaku Corporation, Japan). The synthesized FeSe 2 (cr) was added to deionized water and the pH values were adjusted to 6.5, 8, and 9.5 using HCl and NaOH solutions. The resulting samples were stored in an oven at 318 ± 1 K. Moderately reducing conditions were maintained using 1 ml and 0.5 ml of 98% hydrazine monohydrate for samples in 100 ml and 50 ml glass vials, respectively. All samples were stored in tempered hard-glass vials with a screw cap (100 ml : series of sample of 1-1 to 1-7, 7-1 to 7-7, 13-1 to 13-4, 19-1 to 19-4, 24-1 to 24-6, and 30-1 to 30-4, 50 ml : others). The contents of the glass vials were stirred periodically until they were analyzed. Values of solution pH and Eh were measured at room temperature (298 ± 1 K) with a combination glass electrode, which was calibrated against pH buffers and an oxidation-reduction potential electrode. Aliquots of the sample aqueous phase were withdrawn and filtered through ultrafilters with an effective 10,000 molecular weight cutoff. Filtrates used for the determination of aqueous Fe and Se concentrations were acidified with 0.2 mol dm −3 HNO 3 (to prevent the precipitation of iron oxide) and oxidized by hydrogen peroxide (to prevent volatilization of Se), respectively. The aqueous concentration of Fe and Se was determined via inductively coupled plasma (ICP) mass spectrometry (NexION 300×, PerkinElmer, USA) with limits of detection (LODs) of 1.3 × 10 −9 and 1.8 × 10 −9 mol dm −3 for Se and Fe, respectively. The concentration of Na was determined via ICP-atomic emission spectroscopy (ICPE-9820, SHIMADZU, Japan) with an LOD of 1.0 × 10 −5 mol dm −3 . The precipitate was separated using a 0.45 μm membrane filter, dried in the glove box, and finally analyzed using by X-ray diffraction (SmartLab, Rigaku Corporation, Japan).

Determination of pH and Eh
The observed pH (pH obs ) measured with the combination glass electrode can be different from the correct pH corresponding to the negative logarithm of the activity of H + ion (a H + ). This was because of the difference in the ionic strength between the calibration buffer and samples used. Thus, the calculated values of −log 10 [H + ] were used to analyze the solubility data. Hydrogen ion concentrations for all samples were determined using the method developed by Rai and Yui [25]. Briefly, hydrogen ion concentrations were estimated with the correction factor 'B' as described in Equation (1).
The value of B was converted to pH obs by obtaining a −log 10 [H + ] from a titration procedure, which plotted 10 −pHobs against the moles of added free acid per liter. This titration procedure resulted in values of B against ionic strengths that were measured for experimental solutions ( Table 1). As shown in Table 1, the values of B varied from −0.050 to −0.0024. These were negligibly small in comparison with the accuracy of a combination glass electrode (±0.1).
Moreover, the influence of temperature on the values of pH and Eh must be elucidated. Although the samples were aged at 318 K, the values of pH and Eh were measured at 298 K; thus, the values of pH and Eh at 318 K were estimated. Values of pH and Eh at 318 K can be calculated based on measured values at 298 K by some estimation methods, such as equilibrium calculation with the dissolution constant of water as a function of temperature [26]. However, in the experiment with more complex aqueous chemistry influenced by the presence of electrolytes and/or reactions with aqueous species, estimated values derived by the simple equilibrium calculation and those measured values should also have shown more pronounced differences [27]. If accurate values can not be estimated by calculation, it is effective that the estimation using differences of values at each temperature were derived by measurement [28]. Then, in the present study, the values of pH and Eh at 298 and 318 K were measured for samples of oversaturation and undersaturation directions at pH 6.5, 8, and 9.5, and values of pH and Eh derived at 318 K were estimated by subtracting the difference between each temperature from measured values at 298 K. Tables 2 and 3 present the results of the measurements. As the temperature was increased from 298 to 318 K, values of pH and Eh decreased. The calculated difference of pH and Eh was 0.54 ± 0.07 and 53 ± 21 mV, respectively. Thus, all values of pH and Eh derived in this study were corrected by subtracting 0.54 and 53 mV, respectively.

Attainment of equilibrium
To confirm the attainment of equilibrium, consecutive measurement of pH and Eh and determination of aqueous Fe and Se concentrations were performed for the series of samples shown in Table S4 (Supplemental Online Material) (Nos. 1-1 to 1-7, 7-1 to 7-7, 13-1 to 13-4, 19-1 to 19-4, 24-1 to 24-6, and 30-1 to . Figure 1 shows the Fe and Se concentrations from both the oversaturation and undersaturation directions against aging periods. For expected to be similar value which can be seen for the Fe concentration of no. 19-3. Therefore, by considering the similarity of Fe and Se concentration from both oversaturation and undersaturation, which were expected when equilibrium was attained. The measured concentration of Fe decreased with the increase in pH. Meanwhile, the Se concentration was nearly constant at pH from 6.5 to 9.5. The equilibrium constants were determined from experimental results obtained between 132 and 918 days, because of the high variability of the data obtained with <100 days. Figure 2 shows the typical XRD patterns for solids derived from oversaturation and undersaturation directions in the solubility experiments. Relatively broad and sharp peaks were observed for the solids from oversaturation and undersaturation, respectively. For all samples, the patterns for FeSe 2 (cr) (ICDD No.: 01-074-0247 [29]) were observed. Meanwhile, the patterns of solids such as Se(cr) (ICDD No.: 00-006-0362 [29]) and FeSe(cr) (ICDD No.: 01-077-9511 [29]) were not observed. Thus, the dominating phase in the samples was FeSe 2 (cr). Solubilities of Se and Fe were calculated by geochemical calculation using PHREEQC code [30] with thermodynamic database of JAEA-TDB (201203c0.tdb) which is Thermodynamic Data Base developed by Japan Atomic Energy Agency [31,32]. Se(cr) and magnetite were considered as solubility limiting solids. Values of solubility of Se was calculated to be 8.9 × 10 −12 , 7.0 × 10 −9 , and 3.9 × 10 −5 mol kg-water −1 at pH 6.5, 8 and 9.5, respectively, under the conditions that Se(cr) equilibrated with a solution. Values of Se solubilities decreased with increase in values of pH. Such increase against values of pH were not seen in experimental results. Values of solubility of Fe was calculated to be 7.6 × 10 −5 , 2.0 × 10 −7 , and 1.4 × 10 −9 mol kgwater −1 at pH 6.5, 8 and 9.5, respectively, under the conditions that magnetite equilibrated. Values of Fe solubility decreased with increase in values of pH. Although the manner of the behavior of decrease in Fe solubilities against values of pH was similar, values in experiment were over one orders of magnitude higher than those calculated. Therefore, compared to the results of calculation, it was shown that Se and Fe concentrations were not determined by equilibrium with Se(cr) and magnetite. In addition, since Se and  Fe concentration at pH 6.5 and 8 and pH 6.5, 8 and 9.5 were lower than those of experimental results, it can be indicated that the possibility that the system did not reach equilibrium state and finally Se(cr) and magnetite control Se and Fe concentrations such as those derived by thermodynamic calculation. It is, however, expected that Se(cr) does not form under the condition where iron ions are ubiquitous. It is known that behavior of selenium is primarily controlled by adsorption reaction to a surface of corrosion product of iron and minerals containing iron [5][6][7][8][9][10][11][12][13][14]. Afterward, it is expected that iron-selenide minerals form. Because of this property, Se(cr) is assumed not to be a solubility limiting solid, although low values of concentration is calculated by thermodynamic calculation. Moreover, the possibility that Se(cr) does not attain to the equilibrium state is discussed further. The solubility experiment of Se(cr) was performed by Iida et al. [33] under conditions which are similar to that of the present study but does not include iron. During the 40 days of the experiment only crystalline selenium (trigonal) could be identified by XRD [33], while the formation of Se(cr) is not found in the present experiment despite longer aging period (from 100 to 918 days). Difference of these experimental results indicated that the precipitation behavior of selenium was affected by the presence of iron and Se(cr) did not precipitate if iron was abundant and ubiquitous in the system. On the other hand, there is a possibility that magnetite precipitates as solubility limiting solid for iron. In that case, it is expected that FeSe 2 (cr) coexists as the stable phase in reducing condition, resulting in controlling the Se concentration. In the present study, since magnetite was not detected in not only oversaturation but also undersaturation direction condition, the equilibrium constant of FeSe 2 (cr) was determined without the reaction in which magnetite formed.
On the other hand, there was the discrepancy of mass balance for Fe and Se concentrations in solution. Concentrations of Fe in solution are over a few order of magnitude higher than those of Se at pH 6.5 and 8. It indicated that Se so as to be more than twice of the stoichiometric molar of Fe in solution remained in solid phase without forming FeSe 2 (cr). Since minerals such as iron oxides which demonstrate a strong preferential Se adsorption were not detected by XRD, it is expected that accessory minerals which contains Se precipitated and/or Se were sorbed to FeSe 2 (cr). In the present study, very limited data for investigating the behavior of Se on the surface of solid were derived since the objective in this study is to examine the thermodynamic property considering concentration of Se and Fe in equilibrium state. Investigating the incorporation of Se into the solid phase thus needs to be explored by more detailed surface analysis.  ( Figure 3). This diagram of dissolved Se with stable solid phases removed indicated that the dominating species were Se 4 2− and HSe − . This was dependent on the sample pH and Eh values. The Pourbaix diagram was plotted at 298 K; thus, it was strictly not an accurate diagram for the species stability area that corresponded to the experimental temperature conditions. Nevertheless, the generally expected manner of occurrence and behavior of Se species were depicted in the diagram. Based on the plots of the experimental data in Figure 3, the aqueous species of HSe − was present as a dominant species at pH > 8. Thus, the equilibrium constant for equation (2) was determined with the derived experimental data at pH > 8. This was except for one sample with an Eh value of > −300 mV (No. 22), because not only HSe-but also Se 4 2exists as a dominant species in the sample.

Equilibrium constants
Furthermore, the aqueous species of Se 4 2− and HSe − coexisted as dominant species at pH < 8. The equilibrium constants for Equations (3) and (4) were determined using the derived data at pH < 8.
Note that the activities of Fe 2+ are a prerequisite for the determination of the equilibrium constants. The speciation of iron in the form of Fe 2+ and FeOH + at pH > 9 was obtained using Equation (5) and the value of log 10 K at 318 K.
The value of log 10 K was calculated using TDB (Thermodynamic Data Base) (PHREEQC19v12.dat [32]) of Walker et al. [35]. The activity coefficients for H + , HSe − , Se 4 2− , Fe 2+ , and FeOH + were calculated using the specific ion interaction theory (SIT) procedure (values of epsilon are listed in Table 5) using Equation (6) [37], since correction methods with respect to a dilute solution (i.e. Debye-Hückel theory) are not appropriate for calculations on the correction of activity coefficient for high ionic strength (>0.1 mol kg −1 ) of most samples.
The A value of 0.521 was derived from the interpolation of the Debye-Huckel constant (A) as a function of temperature (Table B-2 in [36]), and the Ba value of 1.5 was referred from Scatchard [38].
The calculated value of log 10 K for equation (2) was −14.9 ± 1.5 (Table 6). Since Se 4 2− and HSe − were present as dominant species at pH < 8, the relationship between Se 4 2− and HSe − in equilibrium with FeSe 2 (cr) should be elucidated. The equilibrium constant of equation (4) that showed the distribution of Se 4 2− and HSe − against the values of pH was derived by subtracting the value of log 10 K of equation (3) from equation (2). If log 10 K in equation (3) was a 0 , the distribution of HSe − and Se 4 2− with determined log 10 K of −14.9 for equation (2) was calculated using equation (8). . Stability diagram using GWB [33] for modeling the expected thermodynamically stable species using JAEA-TDB [31] regarding Se (〇 is for samples at pH < 8. ▲is for samples at pH > 8. An activity of HSe-= 1 × 10 −8 mol dm −3 ). The measured concentration of Se is shown by Equation (9).
Thus, a 0 values of Equation (3) were determined to satisfy Equations (8) and (9) for each data set in the experiments at pH < 8. Table 7 shows the results. The calculated values for log 10 K in Equations (3) and (4) were −5.0 ± 1.4 and 4.9 ± 1.0, respectively.
A value of Δ f G 0 m for FeSe 2 (cr) was calculated using the equation of Δ f G 0 m = Δ f H 0 m − TS 0 m , which was reported by Lemire et al. [36]. The Δ f H 0 was derived from Grønvold's measured enthalpy [39] for the peritectoid decomposition of FeSe 2 . The enthalpy change for decomposition of FeSe 1.95 to Fe 0.65 Se (Fe 2.6 Se 4 ) was obtained by Svendsen [40], using a Gibbs-Duhem integration and third-law calculation. The value of S 0 m has been determined by Grønvold [39] using the measurements of low-temperature heat capacity on FeSe 2 , which were derived by Grønvold and Westrum [41] after considering the phase composition of a FeSe 2 specimen. With the values Δ f G 0 m of FeSe 2 (cr) and both Fe 2+ and Se 4 2− from [36], the calculated equilibrium constant at 298 K for Equation (3) was −11.9 ± 1.8. This value was significantly different from that obtained in the present study, which could be explained by the different solution chemistries involved.
We note that HSe − and Se 4 2− coexisted as dominant species in our samples. The low estimated thermodynamic stability of the FeSe 2 (cr) phase was attributed to the other forms of aqueous Se species, which enhanced the solubility and was neglected in our calculations. The calculated log 10 K from Equation (4) was 3.3 ± 0.6 with Δ f G 0 m data (Δ f G 0 Se 4 2− = 97.580 kJ mol −1 and Δ f G 0 HSe − = 43.471 kJ mol −1 ) from Olin et al. [42]. This calculated log 10 K value was similar to that obtained in the present study (4.9 ± 1.0). This indicated that the distribution of Se species was dependent on pH and Eh and there were no contributions from the other species that increased the solubility. The involvement of amorphous or nanocrystalline materials in our solubility equilibria may also be present. Nevertheless, similar concentrations of Se and Fe in aqueous solution were measured at both saturation directions and only FeSe 2 (cr) was identified in the XRD analysis. Thus, it was expected that solutions in the present system were equilibrated with FeSe 2 (cr).
The significant difference in the equilibrium constant obtained from the Δ f H 0 m and S 0 m from Lemire et al. [36], and this study was attributed to the intrinsic property of iron selenide solids. In the heat capacity measurements, the solids were heated from 300 to 1000 K [39]. The heat capacity change caused by a solid-state transformation in the Fe 1-x Se phase against temperature was then obtained. Therefore, the heat properties of a freshly prepared and aged solid in aqueous solution were expected to be different.

Mechanism for FeSe 2 (cr) formation under strongly reduced environments such as deep geological disposal
The mechanism for FeSe 2 (cr) formation will be discussed on the basis of the results of the present solubility experiment performed at 318 K and that  conducted by Doi et al. [21] at 348 K. Figure 4 summarizes the concentrations of Se and Fe in equilibrium with FeSe 2 (cr), which were obtained in both studies [21]. The Se concentrations remained stable at both 318 and 348 K. The Fe concentrations increased with the decrease in pH. The Fe concentrations at 318 K were approximately 10 times larger than at 348 K. The slope of Fe concentrations as a function of pH at 318 and 348 K after linear regression were around −1.2 ± 0.1 and −1.1 ± 0.3, respectively. If the solubility limiting solid was FeSe 2 (cr) and aqueous species of Se 4 2− were dominantly present, the reaction is expressed by Equation (3). Based on the measured values, the relationship between pH and pe is expressed by Equation (10) ( Figure 5).
The error of slope in Equation (10) was calculated to be ± 0.1. Thus, the application of Equation (10) to (3) yielded a general expression for the pH dependence of Fe 2+ concentration as shown in Equations (11) and (12).
The a 1 is constant if the measured Se concentration is constant. The slope of Equation (11) was −1.4 ± 0.1, which was similar to that estimated in Figure 4 within the margin of error. Hence, the Fe concentration in Doi et al. [21] and this study were equilibrated with FeSe 2 (cr).  Although both Fe and Se were equilibrated with FeSe 2 (cr), the Fe concentrations varied depending on the pH, whereas the Se concentration remained stable at low values. This indicated that the controlling factors that determined the concentrations of Fe and Se were different. After only 34 days of reaction, the Se concentration was <1 × 10 −6 mol dm −3 , as shown in Figure 1. This also suggested that the Se was consumed before attainment of equilibrium with FeSe 2 (cr). Therefore, it was expected that the precipitation of FeSe 2 (cr) in the presence of a large amount of iron ions can proceed via its reaction paths and Se was consumed in the initial step of the reaction.
The amorphous FeO(OH) and Fe(OH) 2 are readily formed under the conditions of supersaturated iron oxides. It was considered that the possible reason for consumption was by adsorption to amorphous iron oxides [5,6]. However, XRD analysis only confirmed the presence of FeSe 2 (cr), and a similar manner of consumption was also observed with Se in an undersaturated condition. Iron oxides were poorly precipitated because of a low solubility of initially added FeSe 2 (cr); thus, the adsorption effect was expected to be limited.
The other possibility for the removal of Se from a solution was the formation of FeSe(s). Sulfur which has similar chemical properties and can play a similar geochemical role of Se precipitate initially as an iron monosulfide precursor under environments of coexisting with Fe, then finally FeS 2 (pyrite) forms via sulfidation or iron-loss of the precursor FeS(s) [43,44]. Considering the formation of FeS 2 (pyrite) from FeS precursor and similarity in the chemical properties of Se and S, it was expected that the same geochemical behavior and occurrence of the solid can be found for Se coexisting with Fe. Hence, the mechanisms for FeSe 2 (cr) formation involved the metastable precursor iron monoselenide phase (FeSe(s)), which initially precipitated causing the consumption of Se in solutions. Thereafter, via selenidation or iron loss reactions, a stable FeSe 2 (cr) was finally formed. However, the identification of initially precipitated solid via XRD analyses was not performed; thus, it was not possible to elucidate the clear influence of FeSe(s).
Although the reaction that determined the Se concentration was not identified, our experimental results indicated that Se was consumed during the first reaction step in the reaction paths to equilibrium with FeSe 2 (cr). These findings have important implications for the determination of Se solubility for the performance assessments of deep geological repositories. The values of solubility which is applied in the performance assessment of deep geological repositories have been evaluated previously by the method of simple equilibrium calculation using log 10 K 0 of solubility limiting solid (FeSe 2 (cr)) and compositions of groundwater. Consequently, such a method could not treat the rapid consumption of Se at the early stage of the reaction. The Se solubility should be evaluated with the consideration of the reaction paths to equilibrium with FeSe 2 (cr). Hence, as a first step, consumption of Se in aqueous solution is considered and then the equilibrium calculation with FeSe 2 (cr) should be performed. Otherwise if reasonable calculation model considering such reaction path is not able to be established, the measured solubility values of 6.3 × 10 −8 to 9.0 × 10 −7 mol dm −3 obtained over the pH range from 6.5 to 9.5 could be applied instead.

Conclusion
FeSe 2 (cr) solubility experiments were performed at 318 K from both the oversaturation and undersaturation directions. Experimental measurements showed that over 100 days, the concentrations of Fe and Se from both directions remained similar and equilibrium conditions were expected to be attained. The pH-independent selenium concentrations varied from 6.3 × 10 −8 to 9.0 × 10 −7 mol dm −3 . XRD analyses revealed that the formation of FeSe 2 (cr) in all samples was confirmed. The equilibrium constants were derived from the measured concentrations of Fe and Se, pH, and Eh. The log 10 K 318 K values of −5.0 ± 1.4 and −14.9 ± 1.5 for the FeSe 2 (cr) solubility reactions of FeSe 2 (cr) ⇄ Fe 2+ +0.5 Se 4 2− + e− and FeSe 2 (cr) +2 H+ +2 e− ⇄Fe 2+ +2 HSe−, respectively, were determined using the SIT model. The derived values of log 10 K for the above reactions were not consistent with those calculated with Δ f G 0 m estimated by Lemire et al. [36]. It was thought that the major cause of the significant difference in equilibrium constants was the intrinsic nature of a solid. The values of Δ f H 0 m and S 0 m for FeSe 2 , which were used to calculate Δ f G 0 m [36], were obtained by the heat capacity measurements under the conditions of solids heated at 300-1000 K and without a liquid phase [39]; thus, such drying procedure was expected to cause the difference in the chemical properties of solids with respect to that obtained in the solubility experiment.
Additionally, we considered the behavior of Fe and Se concentrations against pH for discussing the mechanisms for FeSe 2 (cr) formation under strongly reduced environments. Under stable conditions in the solubility experiments, Fe concentrations varied against pH, whereas Se concentrations remained stable at low values. This indicated that Se was consumed at the first reaction step toward the formation of and equilibrium with FeSe 2 (cr). These findings have important implications for the determination of Se solubility for the performance assessments of nuclear waste repositories. The solubility of Se has to be evaluated by the model considering two reaction steps, namely, a first step of Se consumption and a second step of the equilibrium with FeSe 2 (cr). Otherwise if a reasonable calculation model cannot be established, the measured solubility values of 6.3 × 10 −8 to 9.0 × 10 −7 mol dm −3 obtained over the pH range from 6.5 to 9.5 could be used instead.