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hydrofluoric acid system: Influence of fluoride ion on ThO2 dissolution
Progress in Nuclear Energy 93 (2016) 362e370
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Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Activation energy determination and kinetic modeling of thorium oxide dissolution in nitric acid/ hydrofluoric acid system: Influence of fluoride ion on ThO2 dissolution Ali Reza Keshtkar*, Saeed Abbasizadeh Nuclear Fuel Cycle School, Nuclear Science and Technology Research Institute, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 February 2016 Received in revised form 22 July 2016 Accepted 11 September 2016
The dissolution of thorium oxide (ThO2) is investigated in nitric acid/hydrofluoric acid (HNO3/HF) system as a function of several parameters such as reaction fluoride ion content, HNO3 concentration and reaction temperature using an experimental reactor. Based on results, the dissolution of ThO2 increased with increasing of HNO3 concentration and temperature. The normalized weight losses (NL) and normalized dissolution rate (RL) of ThO2 were evaluated to determine the partial order related to the proton concentration (n) and apparent activation energy (EApp). The value of EApp was found to be 21.4 (kJ/mol) for pure HNO3 system and 6.9 (kJ/mol) for HNO3/HF system over the reaction temperature range of 25 Ce85 C. The applicability of eleven different kinetic models was studied to describe ThO2 dissolution. The kinetic data was best fitted by Kabai equation and kinetic results indicated that the dissolution process is controlled by the surface chemical reaction at the liquid-solid interface. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Dissolution Thorium oxide Fluoride ion Kinetics Activation energy
1. Introduction There are many metal oxides dissolution mechanisms in aqueous acid system such as Triuranium octoxide powder (U3O8) (Inoue and Tsujino, 1984), uranium dioxide (UO2) (Taylor et al., 1963), iron oxide (hematite, Fe2O3) (Lee et al., 2007), copper oxide (CuO) (Plakhotnaya et al., 2005), and thorium oxides (ThO2) (Akabori and Shiratori, 1994; Rai et al., 2000). Applied acid systems were nitric acid, hydrochloric acid, sulfuric acid and aqua regia (Tian et al., 2008). Among them, actinide oxides are used as nuclear fuels and are commonly dissolved in aqueous nitric acids. Thoria (ThO2) is one of the most important actinide oxides in nuclear energy applications because it has particular potential in this field (Shying et al., 1970). Dissolution of pure ThO2 or highly dense ThO2 (in mixture of (Th, U)O2) in aqueous nitric acid is very low because no redox reaction exists at solid/liquid interface during dissolution (Akabori and Shiratori, 1994; Greiling and Lieser, 1984). In order to solve this problem, the adjusted amounts of hydrofluoric acid could be added into the nitric acid because the appropriate fluoride ion can increase the dissolution rates (Akabori and Shiratori, 1994; Shying et al., 1970). On the other hand, excessive use of fluoride
* Corresponding author. E-mail address: [email protected] (A.R. Keshtkar). http://dx.doi.org/10.1016/j.pnucene.2016.09.008 0149-1970/© 2016 Elsevier Ltd. All rights reserved.
ions is undesirable for the ThO2 dissolution due to the high corrosion of fluoride ions. Therefore, concentration range of fluoride ion should be reasonable. Thorium-based oxides are commonly dissolved in 13 M nitric acid containing 0.0e0.05 M sodium fluoride as a fluorine ion source (Akabori and Shiratori, 1994). In general, for dissolution of mineral ores and metal oxides, the control of some reaction factors such as dissolution temperature, solid to liquid ratio, acidic solution concentration, and stirring speed is one potential method to increase dissolution rates (Demir et al., 2004; Raza et al., 2014; Ruan and Gilkes, 1995; Shying et al., 1970). For instance, maximum percentage of dissolved ThO2 was found at higher temperature, higher acid concentration and lower solid to solvent ratio and the effect of stirring speed did not appear significant (Shying et al., 1970). In order to develop the dissolution process, information about the kinetic models and dissolution rate will be particularly essential. Recognition of the kinetic behavior of solid dissolution is necessary to optimize and control the process further. In general, there are two dissolution steps including diffusion mechanism and chemical reactions which one of them can be rate-controlling step in any solid phase reaction (Brown et al., 1980; Inoue and Tsujino, 1984). Many investigations have reported the dissolution kinetics of metal oxides, ores and other solids (Dash et al., 2002; Inoue and Tsujino, 1984; Lee et al., 2006). Lee et al. (2006) investigated the dissolution kinetics of Fe2O3 in
A.R. Keshtkar, S. Abbasizadeh / Progress in Nuclear Energy 93 (2016) 362e370
oxalic acid and concluded that the best fit was obtained by a diffusion-controlled shrinking core model. Inoue and Tsujino, 1984 showed that the dissolution of U3O8 in nitric acid proceeds through two stages. The diffusion mechanism was found rate-controlling step during the first stage and chemical reaction at the surface of U3O8 was found rate-controlling step during the second stage (Inoue and Tsujino, 1984). Up to now, the kinetics of dissolution of ThO2 in the mixture of hydrofluoric acid and nitric acid (HF/HNO3) has not been reported by the authors. In this investigation, dissolution of ThO2 in HNO3/HF system with variations in temperature, acid concentration, solid to liquid ratio and stirring speed were studied in an experimental dissolution reactor. One of the most important objects of this investigation was to study the applicability of kinetic models in clarifying the dissolution of ThO2 in aqueous acid. In addition to the kinetic data, activation energy of dissolution was also investigated.
363
the reactor vessel with thermal jacket circulated by hot water. In order to adjust the reactor temperature, a sensor and an indicator were used. For stirring of the ThO2/acid system, a mechanical PTFE mixer was used and stirring speed was adjusted by an inverter (agitation rate controller). 2.2. Dissolution tests All dissolution experiments were performed in a reactor with 600 ml of acid solution under different conditions. The effect of S/L ratio on thorium oxide dissolution efficiency was investigated by varying the S/L ratios from 0.5 to 16.5 mg/ml under conditions of fixed temperature, 65 C, stirring rate of 300 rpm and dissolution time of 180 min. The change in dissolution behavior of ThO2 sample is indicated in Fig. 2. As can be seen, in lower values of S/L ratios, dissolution of ThO2 occurs at shorter time. For S/L ratio of 0.5 mg/ ml, above 90% of ThO2 dissolution was achieved within 60 min.
2. Experimental section 2.1. Materials and dissolution reactor Thorium oxide powder (was purchased from Merck in 99% purity) was used in all our investigations. Concentrated nitric acid and hydrofluoric acid were obtained from Sigma-Aldrich. Deionized water was used throughout these dissolution experiments. Schematic of experimental reactor for dissolution of ThO2 in aqueous acid is shown in Fig. 1. This glass reactor includes different parts such as reactor vessel, circulator, hot water inlet tube, hot water return tube, thermal jacket, temperature indicator, agitation rate controller, PTFE mixer and solvent and thorium oxide entrance. The volume of reactor vessel was 2 liter. Firstly, thorium oxide powder was put in the reactor vessel through its entrance and then acid solvent was added. The thorium oxide/acid contents were heated in
Fig. 2. Dissolution curves at various solid to liquid ratios (experimental conditions: HNO3 concentration of 6.5 M, temperature of 65 C, stirring speed of 300 rpm).
Fig. 1. Schematic of experimental reactor for dissolution of ThO2 in aqueous acid.
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Lower S/L ratio was resulted in an increase of solvent agent in comparison of oxide. The dissolution time increased with increasing S/L ratio in order to achieve the same dissolution fraction. In this investigation, the S/L ratio of 8.5 mg/ml was selected to complete dissolution for 180 min.Effect of stirring speed on solid dissolution efficiency is a key factor because the formation of a stagnant product layer is possible during dissolution with insufficient mixing. This stagnant product layer can increase the resistance of mass transfer and inhibit the dissolution reaction because of possible precipitation of reaction product. However, dissolution experiments (at the temperature of 65 C, S/L of 8.5 mg/ml, and dissolution time of 180 min), were performed with different speeds in the range of 200e400 rpm and the results of which are shown in Fig. 3. As can be seen, it has no significant effect on the dissolution of ThO2 at those stirring speeds. The results indicated that sufficient mixing was induced by the controller in reactor system and reaction product was transferred into the bulk phase and there was no inhibition of the dissolution reaction. Dissolution fractions (%) of ThO2 were found to be 89.0, 93.9, 94.5, 94.8 and 94.1% for stirring speed of 200, 250, 300, 350 and 400 rpm, respectively. A small deviation was found with 200 rpm and dissolution fractions of ThO2 at four other stirring speeds were close to each other (around 94%). Consequently, all the four stirring speeds, namely 250, 300, 350 and 400 rpm yielded a more homogeneous mixing and less mass transfer resistance in comparison to stirring speed of 200 rpm. Therefore, stirring speed of 300 rpm was selected for further experiments. In order to investigate the effect of 6.5 M HNO3 acid system and 6.5 M HNO3/0.005 M HF acid system on dissolution efficiency of ThO2 powder, the experiments were performed at a temperature of 65 C, S/L ratio of 8.5 mg/ml, stirring rate of 300 rpm and contact time of 180 min. The effect of HNO3 concentration in HNO3/0.005 M HF on ThO2 dissolution efficiency was studied in the range of 0.5e9.5 M at a temperature of 65 C, stirring rate of 300 rpm, S/L ratio of 8.5 mg/ml and contact time of 180 min. As mentioned above, the concentration of HF was fixed in the HNO3/HF systems (the concentration of HF is 0.005 M). The effect of temperature on thorium oxide dissolution efficiency was investigated by varying the temperature from 25 C to 85 C at the contact time of 180 min and stirring rate of 300 rpm with an optimum HNO3 concentration. The concentration of thorium dissolved in the acid is determined by an inductivity coupled plasma atomic emission spectrophotometer (ICP-AES, Thermo Jarrel Ash, Model Trace Scan). Analytical wavelength was set at 401.9 nm for thorium ions. Dissolution fraction of solid particles (X) is ratio of concentration of dissolved Th(IV) to
initial concentration of Th(IV), in other words, X is the extent of reaction ranging from 0 to 1.
3. Theoretical section 3.1. Calculation of the normalized ThO2 dissolution rates In general, the values of normalized weight losses (NL in g/m2) were determined by the following equations (Claparede et al., 2015; Horlait et al., 2012):
NL ðiÞ ¼
mi fi S
(1)
where mi (g) is the total amount of component i measured in the solution, fi is the mass ratio of component i in the solid and S (m2) is the reactive surface area of the ThO2 powder in contact with the solution. A valid assumption in dissolution experiments for ThO2 powder is that the values of fi and S can be approximately constant in the initial period of ThO2 dissolution. Lasaga considered a general law of dissolution in which all the parameters are macroscopic. Based on the Lasaga's approach, the dissolution rate is controlled by surface reactions at the solid-solution interface with the decomposition of an activated complex. The heterogeneous reactions include adsorption of aqueous species onto the surface, reaction of adsorbed species with one another or with atoms of the surface and desorption of the product species forms at the surface (Lasaga, 1984). The normalized dissolution rate of element i, RL (i) (g/ (m2.min)), can be derived from Eq. (1) as follows:
RL ðiÞ ¼
dNL ðiÞ 1 dmi ¼ dt fi S dt
(2)
The normalized dissolution rate of the matrix is also defined as follows:
NL ¼
m X ¼ fi NL ðiÞ S i
(3)
where m is the dissolved solid mass. The normalized dissolution rate of solid can be derived from Eq. (3) as follows:
RL ¼
dNL 1 dm ¼ S dt dt
(4)
Thus, RL (g/(m2.min)) which is equal to RL(i) (g/(m2.min)) can be calculated from Eq. (2) (Dacheux et al., 2006; Heisbourg et al., 2003). This normalized dissolution rate expresses the mass loss of the dissolved solid per time and the chemical durability of the samples are normalized by the reactive surface of the solid in contact with the solution (Dacheux et al., 2010).
3.2. Effect of acidity and temperature on dissolution of ThO2 efficiency
Fig. 3. The values of ThO2 dissolution fraction in 6.5 M HNO3/0.005 M HF acid system at various stirring speeds (experimental conditions: temperature of 65 C, solid to liquid ratio of 8.5 mg/ml, dissolution time of 180 min).
In order to investigate the dissolution reactions between minerals and aqueous solutions, many studies are reported (Heisbourg et al., 2004; Thomas et al., 2000, 2001). They confirmed that the influence of pH on the normalized dissolution rate can be explained by the decomposition of an activated complex whose concentration at the surface depends on the proton concentration in the acidic solution. The values of RL (for pH < 7) were found to be proportional to a fractional power of the proton activity. Dependence of RL on the proton concentration was presented as follows:
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h in h in n RL ¼ k0 T aH3 Oþ ¼ k0 T gH3 Oþ H3 Oþ ¼ k0 T;I H3 Oþ
365
(5)
where aH3 Oþ is the proton activity, gH3 Oþ is the proton activity coefficient, k0 T and k0 T;I (The relation between k0 T and k0 T;I is k0 T;I ¼ k0 T ðgH3 Oþ Þn ) are the apparent normalized dissolution rate constants expressed in (g/(m2.min)) at eLog(H3Oþ) ¼ 0 which are temperature dependent. The n value is partial order related to the H3Oþ which is estimated from the relation between RL and H3Oþ, namely, the variation of Log(RL) versus eLog(H3Oþ). This linear relation is written as follows:
i h LogðRL Þ ¼ Log k0 T;I n Log H3 Oþ
(6)
As can be seen, n and k0 T;I can be determined from the slope and intercept of Eq. (6). The values of n parameter were commonly found between 0 and 1 for several oxides (Claparede et al., 2011; Heisbourg et al., 2003, 2004) which is indicative of the presence of surface reactions controlling the dissolution process. In order to determine the activation energy of ThO2 dissolution, the simple Arrhenius law is employed, i.e., 00
RL ¼ k
T
EApp exp RT
(7)
00
wherek is the normalized dissolution rate constant independent of temperature expressed in (g/(m2.min)), EApp is apparent activation energy of the dissolution of ThO2 expressed in kJ/mol), R is the gas universal constant (8.314 J/mol K) and T is the absolute temperature (K). EApp is estimated from the relation between RL and 1/T, namely, the variation of Ln (RL) versus 1/T. This linear relation is written as follows
00 E 1 App LnðRL Þ ¼ Ln k T R
(8) 00
As can be seen, EApp and k can be determined from the slope and intercept of Eq. (8). The values of EApp were commonly found to be lower than formation energy of chemical bonds (Eyring, 1935) because the adsorbed species were formed onto the surface of materials. Several theories showed that the decomposition of an activated complex such as adsorption of aqueous species onto the surface, reaction of adsorbed species with one another or with atoms of the surface and finally desorption of the product species formed at the solid/liquid interface was rate-controlling step of dissolution reaction (Eyring, 1935). Desorption step was usually slower than the others and consequently, the overall dissolution rate of the sample was controlled by this step. 4. Results and discussion 4.1. Effect of HF in acid system on dissolution efficiency of ThO2 In order to investigate the effect of fluoride ion on the dissolution efficiency of ThO2, two acid systems, namely, pure 6.5 M HNO3 and 6.5 M HNO3/0.005 M HF systems were employed in our experiments. Dissolution curves of ThO2 in both acid systems are shown in Fig. 4. As can be seen in Fig. 4, percentage of dissolved ThO2 in pure nitric acid is lower than 10.1% after 180 min. Therefore, dissolution of ThO2 using pure HNO3 is not a practicable method to dissolve it for a short time. Fig. 4 shows that percentage of dissolved ThO2 increases up to 94.5%. This increase can be due to the added fluoride ion in 6.5 M nitric acid system containing 0.005 M HF. This result is in good agreement with those in the previous works (Shying et al., 1970).
Fig. 4. Dissolution curves of ThO2 in both pure HNO3 and HNO3/HF acid systems.
Indeed, after addition of HF acid in the solvent system, the active centers for dissolution of ThO2 were dissociated hydroxyl sites on the surface. The first step is dissociation of surface hydroxyl to form positively charged thorium site and the second step is adsorption of fluoride ion onto these positively charged Th sites. Both of these steps are fast, therefore, they are not rate controlling step. These two steps are shown in Fig. 5. Next step of dissolution mechanism is surface reaction. In this step there is a reaction between fluoride ion in the solution and the fluorinated surface compounds. Then, a film containing thorium fluoride complex (such as ThF4) is created on the surface of ThO2 particles (Fig. 6 a). Finally, the created film is separated from the ThO2 particles into the solution (Akabori and Shiratori, 1994). The step of desorption of a thorium fluoride complex from ThO2 surface is rate controlling. In order to complete the dissolution cycle, negative charge must be associated with an oxygen atom on the ThO2 surface (Fig. 6 b) which forms the positively charged thorium site due to the reaction of negative charge with the H3Oþ in acid solution (Fig. 6 c). Indeed, after desorption of surface thorium atoms, this reaction is replaced by first step and the dissolution process continues. 4.2. Effect of concentration of HNO3 on ThO2 dissolution efficiency In order to underline the effect of nitric acid concentration on dissolution efficiency of ThO2 in HNO3/0.005 M HF system, various concentrations of HNO3 (3.5e9.5 M HNO3) were employed for dissolution experiments. Dissolution fraction (%) and the curves of the weight loss of ThO2 are shown in Fig. 7 and Fig. 8 a, respectively. As can be seen, dissolution of ThO2 and NL (Th) increases with increasing the nitric acid concentration. When concentration of nitric acid was 3.5 M, the concentration of H3Oþ in acid solution would be lower than those in higher concentration of HNO3 (6.5 and 9.5 M). When H3Oþ concentration was high, negative charge would be rapidly associated with an oxygen atom on the ThO2 surface to complete the dissolution cycle. Indeed, in order to form renewed positively charged thorium sites after desorption of surface thorium atoms, reaction of negative charge with the H3Oþ in acid solution should be performed. This reaction was easily performed in 6.5 and 9.5 M HNO3. On the other hand, both of higher HNO3 concentrations, namely, 6.5 and 9.5 M HNO3 after 180 min had high dissolution fraction (94.5% for nitric acid concentration of 6.5 M and 96.9% for nitric acid concentration of 9.5 M) and NL (Th) (0.0392 for nitric acid concentration of 6.5 M and 0.0401 for nitric acid concentration of 9.5 M). Therefore, the concentration of 6.5 M HNO3 in our mixed acid system was selected for further experiments because preparation of 6.5 M HNO3 solution is more
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Fig. 5. Dissolution mechanism of ThO2 (Part I): (a) dissociation of surface hydroxyl (b) fluoride ion adsorption.
Fig. 6. Dissolution mechanism of ThO2 (Part II: surface reaction):(a) Thorium fluoride formation on oxide surface (b) association of negative charge with a surface oxygen atom (c) formation of the positively charged thorium site.
economical than preparation of 9.5 M HNO3 solution. In general, dissolution rate was calculated by measuring the weight loss of the ThO2. The associated free proton activity was specified according to Eq. (4). The variation of Log (RL (Th)) versus eLog (H3Oþ) is plotted in Fig. 8 b. The obtained slope of this linear relation gives some information on the ThO2 dissolution mechanism occurring at the
solid/liquid interface. The results showed that n value was found to be 0.3 for ThO2 sample. This value confirms that no redox reaction was performed during the dissolution and indicated that a surfacecontrolling phenomenon, namely reaction of negatively charged oxygen on the surface with H3Oþ in acid solution was existed at the oxide/solvent interface. Several researchers indicated that n values
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4.3. Kinetic modeling of ThO2 dissolution with various concentrations of HNO3 Dissolution processes generally include solid-liquid reaction systems. Either diffusion mechanism or chemical reaction can be the rate-controlling step in any solid phase. In general, characteristic curves of reaction extent versus time (X-t) for reactions of solids are acceleratory, sigmoidal or deceleratory. Diffusion mechanism includes the transportation of reactants or products through the layer of reaction products. On the other hand, the shapes of reactant crystallites are also influenced by kinetic characteristics. If the interposition of a barrier layer diminishes the effective contact between reactants, the rate processes are often deceleratory throughout. The deceleratory kinetics based on diffusion mechanisms equations were obtained by one of the following equations in integral form (Brown et al., 1980; Cornell and Schwertmann, 2004): Fig. 7. Dissolution Fraction (%) of ThO2 in various nitric acid concentrations in HNO3/ HF systems (concentration of HF is fixed and equals 0.005 M).
ð1 XÞlnð1 XÞ þ X ¼ kt i h 1 2 1 ð1 XÞ3 ¼ kt
(10)
X 2 ¼ kt
(11)
2 1 X 3
2
ð1 XÞ3 ¼ kt
h i2 ð1 XÞð1=3Þ 1 ¼ kt
Fig. 8. (a) The curves of NL (Th) versus dissolution time in various HNO3/HF acid systems (b) The linear variation of Log RL (Th) versus the inverse Log (H3Oþ) during dissolution tests of ThO2 at 65 C.
were in the range of 0e1 for the most of the materials (Dacheux et al., 2006; Heisbourg et al., 2004; Thomas et al., 2000). For instance, Heisbourg et al. (2004) reported that n value for ThO2 sample was found to be 0.26.
(9)
(12)
(13)
where X (dimensionless) is the fraction of dissolution of solid particles (reaction extent) which is estimated as the ratio of dissolved Th(IV) concentration to concentration of primarily added Th(IV), k (min1) is the rate constant of reaction and t (min) is time. As mentioned above, the kinetic characteristics are also significantly influenced by the shapes of reactant crystallites. Variations in behavior are apparent when diffusion in the layer is heterogeneous as a consequence of cracking or because of development of more than a single product layer. The rate expression for reaction of a cylindrical particle is shown in Eq. (9) which shows twodimensional diffusion. A diffusion-limited reaction proceeding in spherical particles obeys Eq. (10) which usually called the Jander equation and shows three-dimensional diffusion. When the surface area is constant, the simplest kinetic law is Eq. (11) which is parabolic law and the reactant is in the form of a thin sheet with one-dimensional diffusion. The other equation based on threedimensional diffusion is called Ginstling-Brounshtein (Eq. (12)) which is applied for the dissolution of spherical particles. Eq. (13) assumes a spherical model and shows that the rate of interface advance under diffusion control is also proportional to the amount of unreacted material. When chemical reaction at the interface of solid-liquid is the rate-controlling step, the kinetic characteristics of the overall rate process are determined by the geometry of advance of the reaction interface from boundaries in the direction of the centers of the particles concerned. If the influence of a slow nucleation and an acceleratory period was removed by artificial initiation of reaction on all surfaces, the kinetic analysis was simplified to the consideration of a process advancing at all faces of a crystal of known size and geometry. One of the deceleratory rate equations based on geometric models which are often referred to as the contracting area is given as follows (Brown et al., 1980): 1
1 ð1 XÞ2 ¼ kt
(14)
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Eq. (14) was applied for consideration of a reaction initiated at all surfaces of a cylinder of reactant. The other deceleratory rate equations based on geometric models which are often referred to as the contracting volume is given as follows (Brown et al., 1980): 1
1 ð1 XÞ3 ¼ kt
(15)
Eq. (15) is usually referred to reactions in rectangular, cubical and spherical particles. Both of Eqs. (10) and (11) were applied for reactions occurring at all faces of the solid which is based on phase boundary movement. The other deceleratory rate equations based on order of reactions can be written as follows (Brown et al., 1980):
lnð1 XÞ ¼ kt
(16)
When dimensions of particles are small enough, reaction rate is governed by nucleation and first-order equation is obeyed. Such behavior may occur in the ultimate stages of decomposition reactions of solid phase and Eq. (16) is employed for the system of random nucleation. AvramieErofe'ev equation is one of the sigmoid rate equations and this equation is applied for a wide range of dissolution fraction (X). The Two AvramieErofe'ev equations are given as follows (Brown et al., 1980): 1
½lnð1 XÞ2 ¼ kt
(17)
1
½lnð1 XÞ3 ¼ kt
(18)
These AvramieErofe'ev equations have the same form as Eq. (16). Their difference originates from general form of equation 1 (½lnð1 XÞn ¼ kt). The denominator (n) of Eq. (16) is 1, whereas it is 2 and 3 for Eqs. (17) and (18), respectively. The difference between denominators originates from growth characteristics of crystal. When reaction continues through the development of flat and cylindrical nuclei, initiated at edges or surface cracks in the reactant solid, the applied expression is Eqs. (17) and (18), respectively. Another relationship is modified Nernst equation which is called Kabai equation. This equation considers the dissolution of metal oxides and indicates a surface reaction. A linear form of Kabai equation is given as follows (Brown et al., 1980; Ruan and Gilkes, 1995):
ln ln
1 1X
(R2 > 0.972) fitted better than the other kinetic models and this equation indicates sigmoidal dissolution-time curves. Deviations occurred only at low dissolution times (not shown), where the effective shaking period was underestimated because the filtration time was neglected. Furthermore, Eq. (16) which is the first order reaction also yielded a good fit (R2 > 0.945). The time of induction fairly is short in comparison to the equilibrium time, especially when the acidity of the solution is high. The dissolution rate constant (k(min1)) increased as nitric acid concentration increased for all three concentrations (k ¼ 0.00550, 0.01590, 0.02000 for concentration of 3.5, 6.5 and 9.5 M HNO3), respectively). When the initial stages of the dissolution enlarged, a sigmoidal trend was indeed observed further supporting the selection of the Kabai equation. Eq. (18) was found to be the least appropriate based on the R2 values for all three acid nitric concentrations. R2 values were found to be 0.487, 0.224 and 0.080 for acid nitric concentrations of 3.5, 6.5 and 9.5 M. 4.4. Effect of temperature on dissolution efficiency of ThO2 and determination of activation energy Temperature is an important parameter influencing the behavior of the ThO2 sample during dissolution process. The dissolution fraction (%) of ThO2 at four different temperatures (from 25 to 85 C) is indicated in Fig. 9, while the variation of NL (Th) versus the dissolution time for ThO2 sample is indicated in Fig. 10 a. As can be seen, dissolution percentage of ThO2 increases with increasing temperature from 25 C to 85 C. As expected from Eq. (5), RL (Th) value widely increased as the temperature rises. For instance, RL (Th) value increased from 1:41 104 to 2:24 104 (g/(m2.min)) with a rise in temperature from 25 C to
¼ alnk þ alnt
(19)
where a is phase-specific constant. The correlation coefficient of kinetic models (R2) and k values (min1) are obtained from the slopes and intercepts of the linear variation and the results are given in Table 1. By comparing the R2 values of kinetic models, it is observed that Kabai equation which is modified first order reaction Fig. 9. The dissolution fraction (%) of ThO2 at four different temperatures. Table 1 The results of kinetic models including correlation coefficients (R2) and reaction rate constants (k (min1)) for applied kinetic equations (Eqs. (9)e(19)). Equation number in the text
9 10 11 12 13 14 15 16 17 18 19
K(min1)
R2 3.5M
6.5M
9.5M
3.5M
6.5M
9.5M
0.832 0.804 0.856 0.823 0.743 0.934 0.958 0.945 0.913 0.487 0.972
0.934 0.931 0.906 0.938 0.814 0.904 0.935 0.966 0.779 0.224 0.980
0.867 0.921 0.808 0.891 0.884 0.801 0.855 0.948 0.679 0.080 0.977
0.00134 0.00039 0.00210 0.00033 0.00071 0.00235 0.00167 0.00572 0.00669 0.00716 0.00550
0.00509 0.00225 0.00613 0.00141 0.01254 0.00532 0.00418 0.01823 0.01211 0.01067 0.01590
0.00603 0.00299 0.00688 0.00174 0.02359 0.00601 0.00486 0.02293 0.01364 0.01156 0.02000
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pure HNO3 is mainly due to the strong increase of RL with the addition of fluoride ion at lower temperature. 5. Conclusion The effective parameters on the ThO2 dissolution such as fluoride ion content, HNO3 concentration and reaction temperature were investigated. Furthermore, different kinetic models were applied in order to describe the dissolution of ThO2. The results indicated that dissolution fraction of ThO2 was significantly increased from 10.1% to 94.5% after addition of HF in acid solvent system. Both of ThO2 dissolution fraction and NL(Th) increased with increasing of nitric acid concentration. The value of n is found to be 0.3003 suggesting no redox reaction was performed during the dissolution and indicated that a reaction between negatively charged oxygen on the surface with H3Oþ in acid solution was performed at the oxide/solvent interface. The results of temperature effect confirmed the better dissolution at a higher temperature. The normalized dissolution rate of ThO2 increased with increasing of HNO3 concentration and temperature. The activation energy of dissolution process was found to be 21.4 (kJ/mol) for pure HNO3 system and 6.9 (kJ/mol) for HNO3/HF system. The reaction kinetic studies indicated that the dissolution process of ThO2 in HF/ HNO3 system is controlled by surface chemical reaction. Kinetic results showed that the experimental data perfectly fitted the Kabai equation. References
Fig. 10. (a) The curves of NL (Th) versus dissolution time at different temperatures (b) The linear variation of Ln RL (Th) versus the reciprocal temperature (1/T) during dissolution tests of ThO2 at 6.5 M HNO3 and 6.5 M HNO3/0.005 M HF systems.
85 C. On the other hand, two temperatures of 65 C and 85 C had high dissolution fraction (94.5% and 97.3% for 65 C and 85 C, respectively) and NL (Th) (0.039 and 0.040 (g/m2) for 65 C and 85 C, respectively). Dissolution fraction of ThO2 at 65 C was approximately near the dissolution fraction of ThO2 at 85 C. The apparent activation energy (EApp) resulting from the contribution of the proton adsorption enthalpy in order to form the activated complex was determined by Arrhenius equation at various temperature (25e85 C). The value of the EApp was determined from the linear regression (Eq. (8)). The variation of Ln (RL (Th)) versus reciprocal of temperature (1/T) during the dissolution of ThO2 is plotted in Fig. 10 b for both 6.5 M HNO3 and 6.5 M HNO3/0.005 M HF 00 systems. The EApp andk values were determined from the slope and intercept of linear plot (Fig. 10b), respectively. For pure 6.5 M 00 HNO3 acid system, EApp andk were found to be 21.4 kJ/mol and 2 2 4.5 10 (g/(m .min)), respectively. For 6.5 M HNO3/0.005 M HF 00 system, EApp andk were found to be 6.9 kJ/mol and 2.4 103 (g/ 2 (m .min)), respectively. The same activation energy of dissolution of ThO2 (20±3ðkJ=molÞ) was obtained by Heisbourg et al. (2003) for pure HNO3 system. Indeed, adsorption energy on the ThO2 surface probably is reduced the EApp due to the existence of an activated complex. Decrease of EApp in HNO3/HF acid system compared with
Akabori, M., Shiratori, T., 1994. Dissolution of ThO2 based oxides in nitric acid solutions at elevated temperatures. J. Nucl. Sci. Technol. 31, 539e545. Brown, M., Dollimore, D., Galwey, A., 1980. Theory of solid state reaction kinetics. Compr. Chem. Kinet. 22, 41e113. Claparede, L., Clavier, N., Dacheux, N., Mesbah, A., Martinez, J., Szenknect, S., Moisy, P., 2011. Multiparametric dissolution of thoriumecerium dioxide solid solutions. Inorg. Chem. 50, 11702e11714. Claparede, L., Tocino, F., Szenknect, S., Mesbah, A., Clavier, N., Moisy, P., Dacheux, N., 2015. Dissolution of Th 1 xUxO 2: effects of chemical composition and microstructure. J. Nucl. Mater. 457, 304e316. Cornell, R.M., Schwertmann, U., 2004. Transformations, the Iron Oxides. Wiley-VCH Verlag GmbH & Co. KGaA, pp. 365e407. Dacheux, N., Clavier, N., Ritt, J., 2006. Behavior of thoriumeuranium (IV) phosphateediphosphate sintered samples during leaching tests. Part IeKinetic study. J. Nucl. Mater. 349, 291e303. Dacheux, N., De Kerdaniel, E.D.F., Clavier, N., Podor, R., Aupiais, J., Szenknect, S., 2010. Kinetics of dissolution of thorium and uranium doped britholite ceramics. J. Nucl. Mater. 404, 33e43. Dash, S., Singh, A., Ajikumar, P., Subramanian, H., Rajalakshmi, M., Tyagi, A., Arora, A., Narasimhan, S., Raj, B., 2002. Synthesis and characterization of nanocrystalline thoria obtained from thermally decomposed thorium carbonate. J. Nucl. Mater. 303, 156e168. € Demir, H., Ozmetin, C., Kocakerim, M.M., Yapıcı, S., Çopur, M., 2004. Determination of a semi empirical kinetic model for dissolution of metallic copper particles in HNO 3 solutions. Chem. Eng. Process. Process Intensif. 43, 1095e1100. Eyring, H., 1935. The activated complex in chemical reactions. J. Chem. Phys. 3, 107e115. Greiling, H.-D., Lieser, Κ., 1984. Properties of ThO2, UO2 and PuO2 as function of pretreatment and their dissolution in HNO3. Radiochim. Acta 35, 79e90. Heisbourg, G., Hubert, S., Dacheux, N., Purans, J., 2004. Kinetic and thermodynamic studies of the dissolution of thoria-urania solid solutions. J. Nucl. Mater. 335, 5e13. Heisbourg, G., Hubert, S., Dacheux, N., Ritt, J., 2003. The kinetics of dissolution of Th 1 x U x O2 solid solutions in nitric media. J. Nucl. Mater. 321, 141e151. Horlait, D., Tocino, F., Clavier, N., Dacheux, N., Szenknect, S., 2012. Multiparametric study of Th 1 xLnxO 2 x/2 mixed oxides dissolution in nitric acid media. J. Nucl. Mater. 429, 237e244. Inoue, A., Tsujino, T., 1984. Dissolution rates of uranium oxide (U3O8) powders in nitric acid. Ind. Eng. Chem. Process Des. Dev. 23, 122e125. Lasaga, A.C., 1984. Chemical kinetics of water-rock interactions. J. Geophys. Res. Solid Earth (1978e2012) 89, 4009e4025. Lee, S.O., Tran, T., Jung, B.H., Kim, S.J., Kim, M.J., 2007. Dissolution of iron oxide using oxalic acid. Hydrometallurgy 87, 91e99. Lee, S.O., Tran, T., Park, Y.Y., Kim, S.J., Kim, M.J., 2006. Study on the kinetics of iron oxide leaching by oxalic acid. Int. J. Mineral Process. 80, 144e152. Plakhotnaya, O.N., Gorichev, I.G., Batrakov, V.V., Izotov, A.D., Kutepov, A.M., 2005. Modeling of copper(II) oxide dissolution in sulfuric acid solutions in the
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presence of ammonia and complexones. Theor. Found. Chem. Eng. 39, 204e212. Rai, D., Moore, D.A., Oakes, C.S., Yui, M., 2000. Thermodynamic model for the solubility of thorium dioxide in the Naþ-CleOHeH2O system at 23 C and 90 C. Radiochimica Acta Int. J. Chem. Aspects Nucl. Sci. Technol. 88, 297. Raza, N., Zafar, Z.I., Najam-ul-Haq, M., 2014. Utilization of formic acid solutions in leaching reaction kinetics of natural magnesite ores. Hydrometallurgy 149, 183e188. Ruan, H., Gilkes, R., 1995. Acid dissolution of synthetic aluminous goethite before and after transformation to hematite by heating. Clay Miner. 30, 55e66. Shying, M., Florence, T., Carswell, D., 1970. Oxide dissolution mechanismsdI: the role of fluoride in the thoria/nitric/hydrofluoric acid system. J. Inorg. Nucl. Chem. 32, 3493e3508.
Taylor, R.F., Sharratt, E.W., De Chazal, L.E.M., Logsdail, D.H., 1963. Dissolution rates of uranium dioxide sintered pellets in nitric acid systems. J. Appl. Chem. 13, 32e40. Thomas, A.C., Dacheux, N., Le Coustumer, P., Brandel, V., Genet, M., 2000. Kinetic and thermodynamic study of the thorium phosphateediphosphate dissolution. J. Nucl. Mater. 281, 91e105. Thomas, A.C., Dacheux, N., Le Coustumer, P., Brandel, V., Genet, M., 2001. Kinetic and thermodynamic studies of the dissolution of thoriumeuranium (IV) phosphateediphosphate solid solutions. J. Nucl. Mater. 295, 249e264. Tian, M., Pell, W.G., Conway, B.E., 2008. EQCN study of anodic dissolution and surface oxide film formation at Au in the presence of Cl or Br ions: a model process for corrosion studies. Corros. Sci. 50, 2682e2690.
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Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Activation energy determination and kinetic modeling of thorium oxide dissolution in nitric acid/ hydrofluoric acid system: Influence of fluoride ion on ThO2 dissolution Ali Reza Keshtkar*, Saeed Abbasizadeh Nuclear Fuel Cycle School, Nuclear Science and Technology Research Institute, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 February 2016 Received in revised form 22 July 2016 Accepted 11 September 2016
The dissolution of thorium oxide (ThO2) is investigated in nitric acid/hydrofluoric acid (HNO3/HF) system as a function of several parameters such as reaction fluoride ion content, HNO3 concentration and reaction temperature using an experimental reactor. Based on results, the dissolution of ThO2 increased with increasing of HNO3 concentration and temperature. The normalized weight losses (NL) and normalized dissolution rate (RL) of ThO2 were evaluated to determine the partial order related to the proton concentration (n) and apparent activation energy (EApp). The value of EApp was found to be 21.4 (kJ/mol) for pure HNO3 system and 6.9 (kJ/mol) for HNO3/HF system over the reaction temperature range of 25 Ce85 C. The applicability of eleven different kinetic models was studied to describe ThO2 dissolution. The kinetic data was best fitted by Kabai equation and kinetic results indicated that the dissolution process is controlled by the surface chemical reaction at the liquid-solid interface. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Dissolution Thorium oxide Fluoride ion Kinetics Activation energy
1. Introduction There are many metal oxides dissolution mechanisms in aqueous acid system such as Triuranium octoxide powder (U3O8) (Inoue and Tsujino, 1984), uranium dioxide (UO2) (Taylor et al., 1963), iron oxide (hematite, Fe2O3) (Lee et al., 2007), copper oxide (CuO) (Plakhotnaya et al., 2005), and thorium oxides (ThO2) (Akabori and Shiratori, 1994; Rai et al., 2000). Applied acid systems were nitric acid, hydrochloric acid, sulfuric acid and aqua regia (Tian et al., 2008). Among them, actinide oxides are used as nuclear fuels and are commonly dissolved in aqueous nitric acids. Thoria (ThO2) is one of the most important actinide oxides in nuclear energy applications because it has particular potential in this field (Shying et al., 1970). Dissolution of pure ThO2 or highly dense ThO2 (in mixture of (Th, U)O2) in aqueous nitric acid is very low because no redox reaction exists at solid/liquid interface during dissolution (Akabori and Shiratori, 1994; Greiling and Lieser, 1984). In order to solve this problem, the adjusted amounts of hydrofluoric acid could be added into the nitric acid because the appropriate fluoride ion can increase the dissolution rates (Akabori and Shiratori, 1994; Shying et al., 1970). On the other hand, excessive use of fluoride
* Corresponding author. E-mail address: [email protected] (A.R. Keshtkar). http://dx.doi.org/10.1016/j.pnucene.2016.09.008 0149-1970/© 2016 Elsevier Ltd. All rights reserved.
ions is undesirable for the ThO2 dissolution due to the high corrosion of fluoride ions. Therefore, concentration range of fluoride ion should be reasonable. Thorium-based oxides are commonly dissolved in 13 M nitric acid containing 0.0e0.05 M sodium fluoride as a fluorine ion source (Akabori and Shiratori, 1994). In general, for dissolution of mineral ores and metal oxides, the control of some reaction factors such as dissolution temperature, solid to liquid ratio, acidic solution concentration, and stirring speed is one potential method to increase dissolution rates (Demir et al., 2004; Raza et al., 2014; Ruan and Gilkes, 1995; Shying et al., 1970). For instance, maximum percentage of dissolved ThO2 was found at higher temperature, higher acid concentration and lower solid to solvent ratio and the effect of stirring speed did not appear significant (Shying et al., 1970). In order to develop the dissolution process, information about the kinetic models and dissolution rate will be particularly essential. Recognition of the kinetic behavior of solid dissolution is necessary to optimize and control the process further. In general, there are two dissolution steps including diffusion mechanism and chemical reactions which one of them can be rate-controlling step in any solid phase reaction (Brown et al., 1980; Inoue and Tsujino, 1984). Many investigations have reported the dissolution kinetics of metal oxides, ores and other solids (Dash et al., 2002; Inoue and Tsujino, 1984; Lee et al., 2006). Lee et al. (2006) investigated the dissolution kinetics of Fe2O3 in
A.R. Keshtkar, S. Abbasizadeh / Progress in Nuclear Energy 93 (2016) 362e370
oxalic acid and concluded that the best fit was obtained by a diffusion-controlled shrinking core model. Inoue and Tsujino, 1984 showed that the dissolution of U3O8 in nitric acid proceeds through two stages. The diffusion mechanism was found rate-controlling step during the first stage and chemical reaction at the surface of U3O8 was found rate-controlling step during the second stage (Inoue and Tsujino, 1984). Up to now, the kinetics of dissolution of ThO2 in the mixture of hydrofluoric acid and nitric acid (HF/HNO3) has not been reported by the authors. In this investigation, dissolution of ThO2 in HNO3/HF system with variations in temperature, acid concentration, solid to liquid ratio and stirring speed were studied in an experimental dissolution reactor. One of the most important objects of this investigation was to study the applicability of kinetic models in clarifying the dissolution of ThO2 in aqueous acid. In addition to the kinetic data, activation energy of dissolution was also investigated.
363
the reactor vessel with thermal jacket circulated by hot water. In order to adjust the reactor temperature, a sensor and an indicator were used. For stirring of the ThO2/acid system, a mechanical PTFE mixer was used and stirring speed was adjusted by an inverter (agitation rate controller). 2.2. Dissolution tests All dissolution experiments were performed in a reactor with 600 ml of acid solution under different conditions. The effect of S/L ratio on thorium oxide dissolution efficiency was investigated by varying the S/L ratios from 0.5 to 16.5 mg/ml under conditions of fixed temperature, 65 C, stirring rate of 300 rpm and dissolution time of 180 min. The change in dissolution behavior of ThO2 sample is indicated in Fig. 2. As can be seen, in lower values of S/L ratios, dissolution of ThO2 occurs at shorter time. For S/L ratio of 0.5 mg/ ml, above 90% of ThO2 dissolution was achieved within 60 min.
2. Experimental section 2.1. Materials and dissolution reactor Thorium oxide powder (was purchased from Merck in 99% purity) was used in all our investigations. Concentrated nitric acid and hydrofluoric acid were obtained from Sigma-Aldrich. Deionized water was used throughout these dissolution experiments. Schematic of experimental reactor for dissolution of ThO2 in aqueous acid is shown in Fig. 1. This glass reactor includes different parts such as reactor vessel, circulator, hot water inlet tube, hot water return tube, thermal jacket, temperature indicator, agitation rate controller, PTFE mixer and solvent and thorium oxide entrance. The volume of reactor vessel was 2 liter. Firstly, thorium oxide powder was put in the reactor vessel through its entrance and then acid solvent was added. The thorium oxide/acid contents were heated in
Fig. 2. Dissolution curves at various solid to liquid ratios (experimental conditions: HNO3 concentration of 6.5 M, temperature of 65 C, stirring speed of 300 rpm).
Fig. 1. Schematic of experimental reactor for dissolution of ThO2 in aqueous acid.
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Lower S/L ratio was resulted in an increase of solvent agent in comparison of oxide. The dissolution time increased with increasing S/L ratio in order to achieve the same dissolution fraction. In this investigation, the S/L ratio of 8.5 mg/ml was selected to complete dissolution for 180 min.Effect of stirring speed on solid dissolution efficiency is a key factor because the formation of a stagnant product layer is possible during dissolution with insufficient mixing. This stagnant product layer can increase the resistance of mass transfer and inhibit the dissolution reaction because of possible precipitation of reaction product. However, dissolution experiments (at the temperature of 65 C, S/L of 8.5 mg/ml, and dissolution time of 180 min), were performed with different speeds in the range of 200e400 rpm and the results of which are shown in Fig. 3. As can be seen, it has no significant effect on the dissolution of ThO2 at those stirring speeds. The results indicated that sufficient mixing was induced by the controller in reactor system and reaction product was transferred into the bulk phase and there was no inhibition of the dissolution reaction. Dissolution fractions (%) of ThO2 were found to be 89.0, 93.9, 94.5, 94.8 and 94.1% for stirring speed of 200, 250, 300, 350 and 400 rpm, respectively. A small deviation was found with 200 rpm and dissolution fractions of ThO2 at four other stirring speeds were close to each other (around 94%). Consequently, all the four stirring speeds, namely 250, 300, 350 and 400 rpm yielded a more homogeneous mixing and less mass transfer resistance in comparison to stirring speed of 200 rpm. Therefore, stirring speed of 300 rpm was selected for further experiments. In order to investigate the effect of 6.5 M HNO3 acid system and 6.5 M HNO3/0.005 M HF acid system on dissolution efficiency of ThO2 powder, the experiments were performed at a temperature of 65 C, S/L ratio of 8.5 mg/ml, stirring rate of 300 rpm and contact time of 180 min. The effect of HNO3 concentration in HNO3/0.005 M HF on ThO2 dissolution efficiency was studied in the range of 0.5e9.5 M at a temperature of 65 C, stirring rate of 300 rpm, S/L ratio of 8.5 mg/ml and contact time of 180 min. As mentioned above, the concentration of HF was fixed in the HNO3/HF systems (the concentration of HF is 0.005 M). The effect of temperature on thorium oxide dissolution efficiency was investigated by varying the temperature from 25 C to 85 C at the contact time of 180 min and stirring rate of 300 rpm with an optimum HNO3 concentration. The concentration of thorium dissolved in the acid is determined by an inductivity coupled plasma atomic emission spectrophotometer (ICP-AES, Thermo Jarrel Ash, Model Trace Scan). Analytical wavelength was set at 401.9 nm for thorium ions. Dissolution fraction of solid particles (X) is ratio of concentration of dissolved Th(IV) to
initial concentration of Th(IV), in other words, X is the extent of reaction ranging from 0 to 1.
3. Theoretical section 3.1. Calculation of the normalized ThO2 dissolution rates In general, the values of normalized weight losses (NL in g/m2) were determined by the following equations (Claparede et al., 2015; Horlait et al., 2012):
NL ðiÞ ¼
mi fi S
(1)
where mi (g) is the total amount of component i measured in the solution, fi is the mass ratio of component i in the solid and S (m2) is the reactive surface area of the ThO2 powder in contact with the solution. A valid assumption in dissolution experiments for ThO2 powder is that the values of fi and S can be approximately constant in the initial period of ThO2 dissolution. Lasaga considered a general law of dissolution in which all the parameters are macroscopic. Based on the Lasaga's approach, the dissolution rate is controlled by surface reactions at the solid-solution interface with the decomposition of an activated complex. The heterogeneous reactions include adsorption of aqueous species onto the surface, reaction of adsorbed species with one another or with atoms of the surface and desorption of the product species forms at the surface (Lasaga, 1984). The normalized dissolution rate of element i, RL (i) (g/ (m2.min)), can be derived from Eq. (1) as follows:
RL ðiÞ ¼
dNL ðiÞ 1 dmi ¼ dt fi S dt
(2)
The normalized dissolution rate of the matrix is also defined as follows:
NL ¼
m X ¼ fi NL ðiÞ S i
(3)
where m is the dissolved solid mass. The normalized dissolution rate of solid can be derived from Eq. (3) as follows:
RL ¼
dNL 1 dm ¼ S dt dt
(4)
Thus, RL (g/(m2.min)) which is equal to RL(i) (g/(m2.min)) can be calculated from Eq. (2) (Dacheux et al., 2006; Heisbourg et al., 2003). This normalized dissolution rate expresses the mass loss of the dissolved solid per time and the chemical durability of the samples are normalized by the reactive surface of the solid in contact with the solution (Dacheux et al., 2010).
3.2. Effect of acidity and temperature on dissolution of ThO2 efficiency
Fig. 3. The values of ThO2 dissolution fraction in 6.5 M HNO3/0.005 M HF acid system at various stirring speeds (experimental conditions: temperature of 65 C, solid to liquid ratio of 8.5 mg/ml, dissolution time of 180 min).
In order to investigate the dissolution reactions between minerals and aqueous solutions, many studies are reported (Heisbourg et al., 2004; Thomas et al., 2000, 2001). They confirmed that the influence of pH on the normalized dissolution rate can be explained by the decomposition of an activated complex whose concentration at the surface depends on the proton concentration in the acidic solution. The values of RL (for pH < 7) were found to be proportional to a fractional power of the proton activity. Dependence of RL on the proton concentration was presented as follows:
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h in h in n RL ¼ k0 T aH3 Oþ ¼ k0 T gH3 Oþ H3 Oþ ¼ k0 T;I H3 Oþ
365
(5)
where aH3 Oþ is the proton activity, gH3 Oþ is the proton activity coefficient, k0 T and k0 T;I (The relation between k0 T and k0 T;I is k0 T;I ¼ k0 T ðgH3 Oþ Þn ) are the apparent normalized dissolution rate constants expressed in (g/(m2.min)) at eLog(H3Oþ) ¼ 0 which are temperature dependent. The n value is partial order related to the H3Oþ which is estimated from the relation between RL and H3Oþ, namely, the variation of Log(RL) versus eLog(H3Oþ). This linear relation is written as follows:
i h LogðRL Þ ¼ Log k0 T;I n Log H3 Oþ
(6)
As can be seen, n and k0 T;I can be determined from the slope and intercept of Eq. (6). The values of n parameter were commonly found between 0 and 1 for several oxides (Claparede et al., 2011; Heisbourg et al., 2003, 2004) which is indicative of the presence of surface reactions controlling the dissolution process. In order to determine the activation energy of ThO2 dissolution, the simple Arrhenius law is employed, i.e., 00
RL ¼ k
T
EApp exp RT
(7)
00
wherek is the normalized dissolution rate constant independent of temperature expressed in (g/(m2.min)), EApp is apparent activation energy of the dissolution of ThO2 expressed in kJ/mol), R is the gas universal constant (8.314 J/mol K) and T is the absolute temperature (K). EApp is estimated from the relation between RL and 1/T, namely, the variation of Ln (RL) versus 1/T. This linear relation is written as follows
00 E 1 App LnðRL Þ ¼ Ln k T R
(8) 00
As can be seen, EApp and k can be determined from the slope and intercept of Eq. (8). The values of EApp were commonly found to be lower than formation energy of chemical bonds (Eyring, 1935) because the adsorbed species were formed onto the surface of materials. Several theories showed that the decomposition of an activated complex such as adsorption of aqueous species onto the surface, reaction of adsorbed species with one another or with atoms of the surface and finally desorption of the product species formed at the solid/liquid interface was rate-controlling step of dissolution reaction (Eyring, 1935). Desorption step was usually slower than the others and consequently, the overall dissolution rate of the sample was controlled by this step. 4. Results and discussion 4.1. Effect of HF in acid system on dissolution efficiency of ThO2 In order to investigate the effect of fluoride ion on the dissolution efficiency of ThO2, two acid systems, namely, pure 6.5 M HNO3 and 6.5 M HNO3/0.005 M HF systems were employed in our experiments. Dissolution curves of ThO2 in both acid systems are shown in Fig. 4. As can be seen in Fig. 4, percentage of dissolved ThO2 in pure nitric acid is lower than 10.1% after 180 min. Therefore, dissolution of ThO2 using pure HNO3 is not a practicable method to dissolve it for a short time. Fig. 4 shows that percentage of dissolved ThO2 increases up to 94.5%. This increase can be due to the added fluoride ion in 6.5 M nitric acid system containing 0.005 M HF. This result is in good agreement with those in the previous works (Shying et al., 1970).
Fig. 4. Dissolution curves of ThO2 in both pure HNO3 and HNO3/HF acid systems.
Indeed, after addition of HF acid in the solvent system, the active centers for dissolution of ThO2 were dissociated hydroxyl sites on the surface. The first step is dissociation of surface hydroxyl to form positively charged thorium site and the second step is adsorption of fluoride ion onto these positively charged Th sites. Both of these steps are fast, therefore, they are not rate controlling step. These two steps are shown in Fig. 5. Next step of dissolution mechanism is surface reaction. In this step there is a reaction between fluoride ion in the solution and the fluorinated surface compounds. Then, a film containing thorium fluoride complex (such as ThF4) is created on the surface of ThO2 particles (Fig. 6 a). Finally, the created film is separated from the ThO2 particles into the solution (Akabori and Shiratori, 1994). The step of desorption of a thorium fluoride complex from ThO2 surface is rate controlling. In order to complete the dissolution cycle, negative charge must be associated with an oxygen atom on the ThO2 surface (Fig. 6 b) which forms the positively charged thorium site due to the reaction of negative charge with the H3Oþ in acid solution (Fig. 6 c). Indeed, after desorption of surface thorium atoms, this reaction is replaced by first step and the dissolution process continues. 4.2. Effect of concentration of HNO3 on ThO2 dissolution efficiency In order to underline the effect of nitric acid concentration on dissolution efficiency of ThO2 in HNO3/0.005 M HF system, various concentrations of HNO3 (3.5e9.5 M HNO3) were employed for dissolution experiments. Dissolution fraction (%) and the curves of the weight loss of ThO2 are shown in Fig. 7 and Fig. 8 a, respectively. As can be seen, dissolution of ThO2 and NL (Th) increases with increasing the nitric acid concentration. When concentration of nitric acid was 3.5 M, the concentration of H3Oþ in acid solution would be lower than those in higher concentration of HNO3 (6.5 and 9.5 M). When H3Oþ concentration was high, negative charge would be rapidly associated with an oxygen atom on the ThO2 surface to complete the dissolution cycle. Indeed, in order to form renewed positively charged thorium sites after desorption of surface thorium atoms, reaction of negative charge with the H3Oþ in acid solution should be performed. This reaction was easily performed in 6.5 and 9.5 M HNO3. On the other hand, both of higher HNO3 concentrations, namely, 6.5 and 9.5 M HNO3 after 180 min had high dissolution fraction (94.5% for nitric acid concentration of 6.5 M and 96.9% for nitric acid concentration of 9.5 M) and NL (Th) (0.0392 for nitric acid concentration of 6.5 M and 0.0401 for nitric acid concentration of 9.5 M). Therefore, the concentration of 6.5 M HNO3 in our mixed acid system was selected for further experiments because preparation of 6.5 M HNO3 solution is more
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Fig. 5. Dissolution mechanism of ThO2 (Part I): (a) dissociation of surface hydroxyl (b) fluoride ion adsorption.
Fig. 6. Dissolution mechanism of ThO2 (Part II: surface reaction):(a) Thorium fluoride formation on oxide surface (b) association of negative charge with a surface oxygen atom (c) formation of the positively charged thorium site.
economical than preparation of 9.5 M HNO3 solution. In general, dissolution rate was calculated by measuring the weight loss of the ThO2. The associated free proton activity was specified according to Eq. (4). The variation of Log (RL (Th)) versus eLog (H3Oþ) is plotted in Fig. 8 b. The obtained slope of this linear relation gives some information on the ThO2 dissolution mechanism occurring at the
solid/liquid interface. The results showed that n value was found to be 0.3 for ThO2 sample. This value confirms that no redox reaction was performed during the dissolution and indicated that a surfacecontrolling phenomenon, namely reaction of negatively charged oxygen on the surface with H3Oþ in acid solution was existed at the oxide/solvent interface. Several researchers indicated that n values
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367
4.3. Kinetic modeling of ThO2 dissolution with various concentrations of HNO3 Dissolution processes generally include solid-liquid reaction systems. Either diffusion mechanism or chemical reaction can be the rate-controlling step in any solid phase. In general, characteristic curves of reaction extent versus time (X-t) for reactions of solids are acceleratory, sigmoidal or deceleratory. Diffusion mechanism includes the transportation of reactants or products through the layer of reaction products. On the other hand, the shapes of reactant crystallites are also influenced by kinetic characteristics. If the interposition of a barrier layer diminishes the effective contact between reactants, the rate processes are often deceleratory throughout. The deceleratory kinetics based on diffusion mechanisms equations were obtained by one of the following equations in integral form (Brown et al., 1980; Cornell and Schwertmann, 2004): Fig. 7. Dissolution Fraction (%) of ThO2 in various nitric acid concentrations in HNO3/ HF systems (concentration of HF is fixed and equals 0.005 M).
ð1 XÞlnð1 XÞ þ X ¼ kt i h 1 2 1 ð1 XÞ3 ¼ kt
(10)
X 2 ¼ kt
(11)
2 1 X 3
2
ð1 XÞ3 ¼ kt
h i2 ð1 XÞð1=3Þ 1 ¼ kt
Fig. 8. (a) The curves of NL (Th) versus dissolution time in various HNO3/HF acid systems (b) The linear variation of Log RL (Th) versus the inverse Log (H3Oþ) during dissolution tests of ThO2 at 65 C.
were in the range of 0e1 for the most of the materials (Dacheux et al., 2006; Heisbourg et al., 2004; Thomas et al., 2000). For instance, Heisbourg et al. (2004) reported that n value for ThO2 sample was found to be 0.26.
(9)
(12)
(13)
where X (dimensionless) is the fraction of dissolution of solid particles (reaction extent) which is estimated as the ratio of dissolved Th(IV) concentration to concentration of primarily added Th(IV), k (min1) is the rate constant of reaction and t (min) is time. As mentioned above, the kinetic characteristics are also significantly influenced by the shapes of reactant crystallites. Variations in behavior are apparent when diffusion in the layer is heterogeneous as a consequence of cracking or because of development of more than a single product layer. The rate expression for reaction of a cylindrical particle is shown in Eq. (9) which shows twodimensional diffusion. A diffusion-limited reaction proceeding in spherical particles obeys Eq. (10) which usually called the Jander equation and shows three-dimensional diffusion. When the surface area is constant, the simplest kinetic law is Eq. (11) which is parabolic law and the reactant is in the form of a thin sheet with one-dimensional diffusion. The other equation based on threedimensional diffusion is called Ginstling-Brounshtein (Eq. (12)) which is applied for the dissolution of spherical particles. Eq. (13) assumes a spherical model and shows that the rate of interface advance under diffusion control is also proportional to the amount of unreacted material. When chemical reaction at the interface of solid-liquid is the rate-controlling step, the kinetic characteristics of the overall rate process are determined by the geometry of advance of the reaction interface from boundaries in the direction of the centers of the particles concerned. If the influence of a slow nucleation and an acceleratory period was removed by artificial initiation of reaction on all surfaces, the kinetic analysis was simplified to the consideration of a process advancing at all faces of a crystal of known size and geometry. One of the deceleratory rate equations based on geometric models which are often referred to as the contracting area is given as follows (Brown et al., 1980): 1
1 ð1 XÞ2 ¼ kt
(14)
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Eq. (14) was applied for consideration of a reaction initiated at all surfaces of a cylinder of reactant. The other deceleratory rate equations based on geometric models which are often referred to as the contracting volume is given as follows (Brown et al., 1980): 1
1 ð1 XÞ3 ¼ kt
(15)
Eq. (15) is usually referred to reactions in rectangular, cubical and spherical particles. Both of Eqs. (10) and (11) were applied for reactions occurring at all faces of the solid which is based on phase boundary movement. The other deceleratory rate equations based on order of reactions can be written as follows (Brown et al., 1980):
lnð1 XÞ ¼ kt
(16)
When dimensions of particles are small enough, reaction rate is governed by nucleation and first-order equation is obeyed. Such behavior may occur in the ultimate stages of decomposition reactions of solid phase and Eq. (16) is employed for the system of random nucleation. AvramieErofe'ev equation is one of the sigmoid rate equations and this equation is applied for a wide range of dissolution fraction (X). The Two AvramieErofe'ev equations are given as follows (Brown et al., 1980): 1
½lnð1 XÞ2 ¼ kt
(17)
1
½lnð1 XÞ3 ¼ kt
(18)
These AvramieErofe'ev equations have the same form as Eq. (16). Their difference originates from general form of equation 1 (½lnð1 XÞn ¼ kt). The denominator (n) of Eq. (16) is 1, whereas it is 2 and 3 for Eqs. (17) and (18), respectively. The difference between denominators originates from growth characteristics of crystal. When reaction continues through the development of flat and cylindrical nuclei, initiated at edges or surface cracks in the reactant solid, the applied expression is Eqs. (17) and (18), respectively. Another relationship is modified Nernst equation which is called Kabai equation. This equation considers the dissolution of metal oxides and indicates a surface reaction. A linear form of Kabai equation is given as follows (Brown et al., 1980; Ruan and Gilkes, 1995):
ln ln
1 1X
(R2 > 0.972) fitted better than the other kinetic models and this equation indicates sigmoidal dissolution-time curves. Deviations occurred only at low dissolution times (not shown), where the effective shaking period was underestimated because the filtration time was neglected. Furthermore, Eq. (16) which is the first order reaction also yielded a good fit (R2 > 0.945). The time of induction fairly is short in comparison to the equilibrium time, especially when the acidity of the solution is high. The dissolution rate constant (k(min1)) increased as nitric acid concentration increased for all three concentrations (k ¼ 0.00550, 0.01590, 0.02000 for concentration of 3.5, 6.5 and 9.5 M HNO3), respectively). When the initial stages of the dissolution enlarged, a sigmoidal trend was indeed observed further supporting the selection of the Kabai equation. Eq. (18) was found to be the least appropriate based on the R2 values for all three acid nitric concentrations. R2 values were found to be 0.487, 0.224 and 0.080 for acid nitric concentrations of 3.5, 6.5 and 9.5 M. 4.4. Effect of temperature on dissolution efficiency of ThO2 and determination of activation energy Temperature is an important parameter influencing the behavior of the ThO2 sample during dissolution process. The dissolution fraction (%) of ThO2 at four different temperatures (from 25 to 85 C) is indicated in Fig. 9, while the variation of NL (Th) versus the dissolution time for ThO2 sample is indicated in Fig. 10 a. As can be seen, dissolution percentage of ThO2 increases with increasing temperature from 25 C to 85 C. As expected from Eq. (5), RL (Th) value widely increased as the temperature rises. For instance, RL (Th) value increased from 1:41 104 to 2:24 104 (g/(m2.min)) with a rise in temperature from 25 C to
¼ alnk þ alnt
(19)
where a is phase-specific constant. The correlation coefficient of kinetic models (R2) and k values (min1) are obtained from the slopes and intercepts of the linear variation and the results are given in Table 1. By comparing the R2 values of kinetic models, it is observed that Kabai equation which is modified first order reaction Fig. 9. The dissolution fraction (%) of ThO2 at four different temperatures. Table 1 The results of kinetic models including correlation coefficients (R2) and reaction rate constants (k (min1)) for applied kinetic equations (Eqs. (9)e(19)). Equation number in the text
9 10 11 12 13 14 15 16 17 18 19
K(min1)
R2 3.5M
6.5M
9.5M
3.5M
6.5M
9.5M
0.832 0.804 0.856 0.823 0.743 0.934 0.958 0.945 0.913 0.487 0.972
0.934 0.931 0.906 0.938 0.814 0.904 0.935 0.966 0.779 0.224 0.980
0.867 0.921 0.808 0.891 0.884 0.801 0.855 0.948 0.679 0.080 0.977
0.00134 0.00039 0.00210 0.00033 0.00071 0.00235 0.00167 0.00572 0.00669 0.00716 0.00550
0.00509 0.00225 0.00613 0.00141 0.01254 0.00532 0.00418 0.01823 0.01211 0.01067 0.01590
0.00603 0.00299 0.00688 0.00174 0.02359 0.00601 0.00486 0.02293 0.01364 0.01156 0.02000
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pure HNO3 is mainly due to the strong increase of RL with the addition of fluoride ion at lower temperature. 5. Conclusion The effective parameters on the ThO2 dissolution such as fluoride ion content, HNO3 concentration and reaction temperature were investigated. Furthermore, different kinetic models were applied in order to describe the dissolution of ThO2. The results indicated that dissolution fraction of ThO2 was significantly increased from 10.1% to 94.5% after addition of HF in acid solvent system. Both of ThO2 dissolution fraction and NL(Th) increased with increasing of nitric acid concentration. The value of n is found to be 0.3003 suggesting no redox reaction was performed during the dissolution and indicated that a reaction between negatively charged oxygen on the surface with H3Oþ in acid solution was performed at the oxide/solvent interface. The results of temperature effect confirmed the better dissolution at a higher temperature. The normalized dissolution rate of ThO2 increased with increasing of HNO3 concentration and temperature. The activation energy of dissolution process was found to be 21.4 (kJ/mol) for pure HNO3 system and 6.9 (kJ/mol) for HNO3/HF system. The reaction kinetic studies indicated that the dissolution process of ThO2 in HF/ HNO3 system is controlled by surface chemical reaction. Kinetic results showed that the experimental data perfectly fitted the Kabai equation. References
Fig. 10. (a) The curves of NL (Th) versus dissolution time at different temperatures (b) The linear variation of Ln RL (Th) versus the reciprocal temperature (1/T) during dissolution tests of ThO2 at 6.5 M HNO3 and 6.5 M HNO3/0.005 M HF systems.
85 C. On the other hand, two temperatures of 65 C and 85 C had high dissolution fraction (94.5% and 97.3% for 65 C and 85 C, respectively) and NL (Th) (0.039 and 0.040 (g/m2) for 65 C and 85 C, respectively). Dissolution fraction of ThO2 at 65 C was approximately near the dissolution fraction of ThO2 at 85 C. The apparent activation energy (EApp) resulting from the contribution of the proton adsorption enthalpy in order to form the activated complex was determined by Arrhenius equation at various temperature (25e85 C). The value of the EApp was determined from the linear regression (Eq. (8)). The variation of Ln (RL (Th)) versus reciprocal of temperature (1/T) during the dissolution of ThO2 is plotted in Fig. 10 b for both 6.5 M HNO3 and 6.5 M HNO3/0.005 M HF 00 systems. The EApp andk values were determined from the slope and intercept of linear plot (Fig. 10b), respectively. For pure 6.5 M 00 HNO3 acid system, EApp andk were found to be 21.4 kJ/mol and 2 2 4.5 10 (g/(m .min)), respectively. For 6.5 M HNO3/0.005 M HF 00 system, EApp andk were found to be 6.9 kJ/mol and 2.4 103 (g/ 2 (m .min)), respectively. The same activation energy of dissolution of ThO2 (20±3ðkJ=molÞ) was obtained by Heisbourg et al. (2003) for pure HNO3 system. Indeed, adsorption energy on the ThO2 surface probably is reduced the EApp due to the existence of an activated complex. Decrease of EApp in HNO3/HF acid system compared with
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