3. Results and discussion

#### 3.1. Nd(U)-(Ga-Al)/3LiCl-2KCl system

Potentiometry method at zero current was used for determination of the apparent standard potentials of the alloys. The potential-time dependences were recorded at various temperatures and of the horizontal part of the curve corresponded to the equilibrium potential of the alloy [13–15]. In molten salts the activity coefficients of the solute species Men+ are constant at concentrations below (3–5) � <sup>10</sup>�<sup>2</sup> mole fraction [12]. For the dilute solutions of Me in the alloys, the activity coefficients are also constant [5]. To characterize the electrochemical behavior of the alloy, an apparent standard potential of the alloy, E∗∗ Me Ga ð Þ �Al , was used [5]:

$$\mathbf{E}\_{\text{Me(Ga-Al)}} = \mathbf{E}\_{\text{Me(Ga-Al)}}^{\*\*} + \frac{\mathbf{RT}}{\mathbf{nF}} \ln{\frac{\mathbf{C}\_{\text{Me(III)}}}{\mathbf{x}\_{\text{Me(Ga-Al)}}}} \,\tag{2}$$

where Me = Nd or U, EMe Ga ð Þ �Al is the equilibrium potential of the alloy (V), E∗∗ Me Ga ð Þ �Al is the apparent standard potential of the alloy (V), n is the number of electrons exchanged, CMe III ð Þ is the concentration of the metal ions in the solvent (mole fraction), and xMe Ga ð Þ �Al is the concentration of the metal in the alloy (atomic fraction).

The apparent standard potentials of the alloys Me(Ga-Al) as a function of temperature were fitted to the following equations using OriginPro version 7.5 Software, Eqs. (3)–(8):

$$E\_{\text{Nd(Ga-Al)}}^{\*\*} = -(2.987 \pm 0.007) + (5.2 \pm 0.5) \cdot 10^{-4} \cdot \text{T} \pm 0.005 \text{ V} \quad 1.5 \text{ wt.}\% \text{Al} \tag{3}$$

$$E\_{\text{Nd(Ga}-\text{Al)}}^{\*\*} = -(3.068 \pm 0.004) + (6.0 \pm 0.2) \cdot 10^{-4} \cdot \text{T} \pm 0.003 \text{ V} \quad \text{5.0 wt.}\% \text{Al} \tag{4}$$

$$E\_{\text{Nd(Ga-Al)}}^{\*\*} = -(3.143 \pm 0.006) + (6.8 \pm 0.2) \cdot 10^{-4} \cdot \text{T} \pm 0.004 \text{ V} \quad 20.0 \text{ wt.}\% \text{Al} \tag{5}$$

$$E\_{\rm U(Ga-Al)}^{\*\*} = -(2.715 \pm 0.006) + (5.1 \pm 0.1) \cdot 10^{-4} \cdot \text{T} \pm 0.003 \text{ V} \quad 1.5 \text{ wt.}\% \text{Al} \tag{6}$$

Figure 1. Apparent standard electrode potentials of Nd-Ga-Al alloys in fused Nd(Ga-Al)/3LiCl-2KCl system as a function

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Figure 2. Apparent standard electrode potentials of U-Ga-Al alloy in the fused U(Ga-Al)/3LiCl-2KCl system as a function

of temperature and composition of Ga-Al alloy (3D diagram). Reference electrode: Cl/Cl2.

of temperature and composition of Ga-Al alloy (3D diagram). Reference electrode: Cl/Cl2.

$$E\_{\rm U(Ga-Al)}^{\*\*} = -(2.758 \pm 0.004) + (5.3 \pm 0.1) \cdot 10^{-4} \cdot \text{T} \pm 0.002 \text{ V} \quad 5.0 \text{ wt.}\% \text{Al} \tag{7}$$

$$E\_{\rm U(Ga-Al)}^{\*\*} = -(2.791 \pm 0.005) + (5.5 \pm 0.1) \cdot 10^{-4} \cdot \text{T} \pm 0.003 \text{ V} \quad \text{20.0 wt.}\% \text{Al} \tag{8}$$

Newton interpolation polynomial expressions were obtained to construct three-dimensional E∗∗ Me Ga ð Þ �Al � <sup>C</sup>ð Þ Ga�Al � T graphs on the basis of the functional dependencies of the apparent standard electrode potentials of the alloys, Ga-Al mixture compositions, and temperature. Universal mathematical Maple 11 software was used for this purpose. Three-dimensional E∗∗ Me Ga ð Þ �Al � <sup>C</sup>ð Þ Ga�Al � T plots for Nd-(Ga-Al) and U-(Ga-Al) alloys and 3LiCl-2KCl eutecticbased melts are presented in Figures 1 and 2, respectively. The following expressions describe the three-dimensional graphs:

$$\rm{E\_{Nd(Ga-Al)}^{\*\*}} = \left(4.8 \cdot 10^{-4} + 2.9 \cdot 10^{-5} \cdot \rm{C} - 9.5 \cdot 10^{-7} \cdot \rm{C}^2\right) \cdot \rm{T} - 2.9 - 0.03 \cdot \rm{C} + 9.8 \cdot 10^{-4} \cdot \rm{C}^2 \text{ V} \tag{9}$$

$$\mathbf{E}\_{\mathrm{U(Ca-Al)}}^{\*\*} = \left(5 \cdot 10^{-4} + 7.2 \cdot 10^{-6} \cdot \mathbb{C} - 2.4 \cdot 10^{-7} \cdot \mathbb{C}^2\right) \cdot \mathrm{T} - 2.7 - 0.02 \cdot \mathbb{C} + 5.4 \cdot 10^{-4} \cdot \mathbb{C}^2 \quad \mathrm{V} \tag{10}$$

where C is the concentration of Al in Ga-Al alloy (wt. %).

The activity coefficients of Nd and U in liquid Ga-Al metallic alloys were determined from the following expression [5]:

$$\log \gamma\_{\text{Me(Ga-Al)}} = \frac{\text{\AA}}{2.303} \left( \mathbf{E}\_{\text{Me(III)/Me}}^{\*} - \mathbf{E}\_{\text{Me(Ga-Al)}}^{\*\*} \right) \tag{11}$$

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EMe Ga ð Þ �Al <sup>¼</sup> <sup>E</sup>∗∗

tration of the metal in the alloy (atomic fraction).

112 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

E∗∗

E∗∗

E∗∗

E∗∗

E∗∗

E∗∗

the three-dimensional graphs:

following expression [5]:

where C is the concentration of Al in Ga-Al alloy (wt. %).

logγMe Ga ð Þ �Al <sup>¼</sup> 3F

E∗∗

E∗∗

E∗∗

E∗∗

Me Ga ð Þ �Al þ

apparent standard potential of the alloy (V), n is the number of electrons exchanged, CMe III ð Þ is the concentration of the metal ions in the solvent (mole fraction), and xMe Ga ð Þ �Al is the concen-

The apparent standard potentials of the alloys Me(Ga-Al) as a function of temperature were

Nd Ga ð Þ �Al ¼ �ð2:<sup>987</sup> � <sup>0</sup>:007Þ þ ð Þ� <sup>5</sup>:<sup>2</sup> � <sup>0</sup>:<sup>5</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:005 V 1:5 wt:%Al (3)

Nd Ga ð Þ �Al ¼ �ð3:<sup>068</sup> � <sup>0</sup>:004Þ þ ð Þ� <sup>6</sup>:<sup>0</sup> � <sup>0</sup>:<sup>2</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:003 V 5:0 wt:%Al (4)

Nd Ga ð Þ �Al ¼ �ð3:<sup>143</sup> � <sup>0</sup>:006Þ þ ð Þ� <sup>6</sup>:<sup>8</sup> � <sup>0</sup>:<sup>2</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:004 V 20:0 wt:%Al (5)

U Ga ð Þ �Al ¼ �ð2:<sup>715</sup> � <sup>0</sup>:006Þ þ ð Þ� <sup>5</sup>:<sup>1</sup> � <sup>0</sup>:<sup>1</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:003 V 1:5 wt:%Al (6)

U Ga ð Þ �Al ¼ �ð2:<sup>758</sup> � <sup>0</sup>:004Þ þ ð Þ� <sup>5</sup>:<sup>3</sup> � <sup>0</sup>:<sup>1</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:002 V 5:0 wt:%Al (7)

U Ga ð Þ �Al ¼ �ð2:<sup>791</sup> � <sup>0</sup>:005Þ þ ð Þ� <sup>5</sup>:<sup>5</sup> � <sup>0</sup>:<sup>1</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:003 V 20:0 wt:%Al (8)

Newton interpolation polynomial expressions were obtained to construct three-dimensional

Me Ga ð Þ �Al � <sup>C</sup>ð Þ Ga�Al � T graphs on the basis of the functional dependencies of the apparent standard electrode potentials of the alloys, Ga-Al mixture compositions, and temperature. Universal mathematical Maple 11 software was used for this purpose. Three-dimensional

Me Ga ð Þ �Al � <sup>C</sup>ð Þ Ga�Al � T plots for Nd-(Ga-Al) and U-(Ga-Al) alloys and 3LiCl-2KCl eutecticbased melts are presented in Figures 1 and 2, respectively. The following expressions describe

Nd Ga ð Þ �Al <sup>¼</sup> <sup>4</sup>:<sup>8</sup> � <sup>10</sup>�<sup>4</sup> <sup>þ</sup> <sup>2</sup>:<sup>9</sup> � <sup>10</sup>�<sup>5</sup> � <sup>C</sup> � <sup>9</sup>:<sup>5</sup> � <sup>10</sup>�<sup>7</sup> � <sup>C</sup><sup>2</sup> � <sup>T</sup> � <sup>2</sup>:<sup>9</sup> � <sup>0</sup>:<sup>03</sup> � <sup>C</sup> <sup>þ</sup> <sup>9</sup>:<sup>8</sup> � <sup>10</sup>�<sup>4</sup> � <sup>C</sup><sup>2</sup> <sup>V</sup>

U Ga ð Þ �Al <sup>¼</sup> <sup>5</sup> � <sup>10</sup>�<sup>4</sup> <sup>þ</sup> <sup>7</sup>:<sup>2</sup> � <sup>10</sup>�<sup>6</sup> � <sup>C</sup> � <sup>2</sup>:<sup>4</sup> � <sup>10</sup>�<sup>7</sup> � <sup>C</sup><sup>2</sup> � <sup>T</sup> � <sup>2</sup>:<sup>7</sup> � <sup>0</sup>:<sup>02</sup> � <sup>C</sup> <sup>þ</sup> <sup>5</sup>:<sup>4</sup> � <sup>10</sup>�<sup>4</sup> � <sup>C</sup><sup>2</sup> <sup>V</sup>

The activity coefficients of Nd and U in liquid Ga-Al metallic alloys were determined from the

Me III ð Þ=Me � <sup>E</sup>∗∗

Me Ga ð Þ �Al

<sup>2</sup>:<sup>303</sup> <sup>E</sup><sup>∗</sup>

where Me = Nd or U, EMe Ga ð Þ �Al is the equilibrium potential of the alloy (V), E∗∗

fitted to the following equations using OriginPro version 7.5 Software, Eqs. (3)–(8):

RT nF ln

CMe III ð Þ xMe Ga ð Þ �Al

, (2)

Me Ga ð Þ �Al is the

(9)

(10)

(11)

Figure 1. Apparent standard electrode potentials of Nd-Ga-Al alloys in fused Nd(Ga-Al)/3LiCl-2KCl system as a function of temperature and composition of Ga-Al alloy (3D diagram). Reference electrode: Cl/Cl2.

Figure 2. Apparent standard electrode potentials of U-Ga-Al alloy in the fused U(Ga-Al)/3LiCl-2KCl system as a function of temperature and composition of Ga-Al alloy (3D diagram). Reference electrode: Cl/Cl2.

The data on Nd3+/Nd and U3+/U apparent standard electrode potentials in 3LiCl-2KCl eutectic were taken from the literature [7]. Temperature dependencies of Nd and U activity coefficients in liquid Ga-Al alloys were fitted to the Eqs. (12)–(17):

$$
\log \gamma\_{\text{Nd(Ga-Al)}} = 5.12 - \frac{11260}{\text{T}} \pm 0.06 \quad 1.5 \text{ wt.} \% \text{Al} \tag{12}
$$

ΔGex

ΔGex

diagram).

diagram).

U Ga ð Þ �Al ¼ �78:<sup>9</sup> <sup>þ</sup> <sup>27</sup>:<sup>1</sup> � <sup>10</sup>�<sup>3</sup>

Thermodynamics and Separation Factor of Uranium from Fission Products in "Liquid Metal-Molten Salt" System

U Ga ð Þ �Al ¼ �70:<sup>7</sup> <sup>þ</sup> <sup>23</sup>:<sup>2</sup> � <sup>10</sup>�<sup>3</sup>

Figure 3. The activity coefficients of Nd in Ga-Al alloys as a function of temperature and composition of Ga-Al alloy (3D

Figure 4. The activity coefficients of U in Ga-Al alloys as a function of temperature and composition of Ga-Al alloy (3D

T � 3:2 kJ=mol 5:0 wt:%Al (26)

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T � 3:5 kJ=mol 20:0 wt:%Al (27)

$$
\log \gamma\_{\text{Nd(Ga-Al)}} = 5.07 - \frac{11006}{\text{T}} \pm 0.04 \quad \text{5.0 wt.} \% \text{Al} \tag{13}
$$

$$
\lambda \log \gamma\_{\text{Nd(Ga-Al)}} = 4.94 - \frac{10713}{\text{T}} \pm 0.05 \quad \text{20.0 wt.} \% \text{Al} \tag{14}
$$

$$
\log \gamma\_{\text{U(Ga-Al)}} = 1.21 - \frac{4393}{\text{T}} \pm 0.05 \quad 1.5 \text{ wt.} \% \text{ Al} \tag{15}
$$

$$
\log \gamma\_{\text{U(Ga-Al)}} = 1.17 - \frac{3935}{\text{T}} \pm 0.05 \quad \text{5.0 wt.} \% \text{Al} \tag{16}
$$

$$
\log \gamma\_{\text{U(Ga-Al)}} = 1.11 - \frac{3619}{\text{T}} \pm 0.06 \quad \text{20.0 wt.} \% \text{Al} \tag{17}
$$

Three-dimensional logγNd Ga ð Þ �Al � <sup>C</sup>ð Þ Ga�Al � T and logγU Ga ð Þ �Al � <sup>C</sup>ð Þ Ga�Al � T plots for fused Nd-(Ga-Al)/3LiCl-2KCl and U-(Ga-Al)/3LiCl-2KCl systems were presented in Figures 3 and 4, respectively. The following expressions describe these three-dimensional graphs:

$$\log \,\,\gamma\_{\text{Nd(Ga-Al)}} = \left(-11390 + 91.2 \cdot \text{C} - 2.8 \cdot \text{C}^2\right) / \text{T} + 5.14 - 0.016 \cdot \text{C} + 3 \cdot 10^{-4} \cdot \text{C}^2 \tag{18}$$

$$\log \gamma\_{\mathrm{U(Ca-Al)}} = \left(-4638 + 169.4 \cdot \mathbb{C} - 5.9 \cdot \mathbb{C}^2\right) / \mathrm{T} + 1.23 - 0.014 \cdot \mathbb{C} + 4 \cdot 10^{-4} \cdot \mathbb{C}^2 \tag{19}$$

where C is the concentration of Al in Ga-Al alloy (wt. %).

Low values of the activity coefficients show strong interaction between Ln (An) and the liquid alloy. Increasing temperature shifts the system toward more ideal behavior, in agreement with the literature.

Partial excess Gibbs free energy change of Nd and U in liquid Ga-Al-based alloys was calculated using Eq. (21) and previously obtained in expressions (12)–(17):

$$
\Delta G\_{\text{Me(Ga}-Al)}^{\text{ex.}} = \Delta H\_{\text{Me(Ga}-Al)} - T\Delta S\_{\text{Me(Ga}-Al)}^{\text{ex.}} \tag{20}
$$

$$
\Delta G\_{Me(Ga-Al)}^{ex.} = 2.303RT\log\gamma\_{Me(Ga-Al)}\tag{21}
$$

$$
\Delta G\_{\text{Nd(Ga-Al)}}^{\text{ex}} = -229.1 + 115.0 \cdot 10^{-3} T \pm 3.7 \text{ kJ/mol} \quad 1.5 \text{ wt.}\% \text{Al} \tag{22}
$$

$$
\Delta G\_{\text{Nd(Ga-Al)}}^{\text{ex}} = -211.7 + 100.1 \cdot 10^{-3} T \pm 3.6 \text{ kJ/mol} \quad 5.0 \text{ wt.}\% \text{Al} \tag{23}
$$

$$
\Delta G\_{\text{Nd(Gt-Al)}}^{\text{ex}} = -175.8 + 57.9 \cdot 10^{-3} T \pm 3.4 \text{ kJ/mol} \quad \text{20.0 wt.} \% \text{Al} \tag{24}
$$

$$
\Delta G\_{\text{L(Gt-Al)}}^{\text{ex}} = -83.9 + 23.2 \cdot 10^{-3} T \pm 3.6 \text{ kJ/mol} \quad 1.5 \text{ wt.} \% \text{Al} \tag{25}
$$

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The data on Nd3+/Nd and U3+/U apparent standard electrode potentials in 3LiCl-2KCl eutectic were taken from the literature [7]. Temperature dependencies of Nd and U activity coefficients

T

Three-dimensional logγNd Ga ð Þ �Al � <sup>C</sup>ð Þ Ga�Al � T and logγU Ga ð Þ �Al � <sup>C</sup>ð Þ Ga�Al � T plots for fused Nd-(Ga-Al)/3LiCl-2KCl and U-(Ga-Al)/3LiCl-2KCl systems were presented in Figures 3 and 4,

log <sup>γ</sup>Nd Ga ð Þ �Al ¼ �<sup>11390</sup> <sup>þ</sup> <sup>91</sup>:<sup>2</sup> � <sup>C</sup> � <sup>2</sup>:<sup>8</sup> � C2 <sup>=</sup><sup>T</sup> <sup>þ</sup> <sup>5</sup>:<sup>14</sup> � <sup>0</sup>:<sup>016</sup> � <sup>C</sup> <sup>þ</sup> <sup>3</sup> � <sup>10</sup>�<sup>4</sup> � <sup>C</sup><sup>2</sup> (18)

log <sup>γ</sup>U Ga ð Þ �Al ¼ �<sup>4638</sup> <sup>þ</sup> <sup>169</sup>:<sup>4</sup> � <sup>С</sup> � <sup>5</sup>:<sup>9</sup> � <sup>С</sup><sup>2</sup> <sup>=</sup><sup>T</sup> <sup>þ</sup> <sup>1</sup>:<sup>23</sup> � <sup>0</sup>:<sup>014</sup> � <sup>C</sup> <sup>þ</sup> <sup>4</sup> � <sup>10</sup>�<sup>4</sup> � <sup>C</sup><sup>2</sup> (19)

Low values of the activity coefficients show strong interaction between Ln (An) and the liquid alloy. Increasing temperature shifts the system toward more ideal behavior, in agreement with

Partial excess Gibbs free energy change of Nd and U in liquid Ga-Al-based alloys was calcu-

Me Ga ð Þ �Al <sup>¼</sup> <sup>Δ</sup>HMe Ga ð Þ �Al � <sup>T</sup>ΔSex:

<sup>T</sup> � <sup>0</sup>:06 1:5 wt:%Al (12)

<sup>T</sup> � <sup>0</sup>:04 5:0 wt:%Al (13)

<sup>T</sup> � <sup>0</sup>:05 20:0 wt:%Al (14)

<sup>T</sup> � <sup>0</sup>:05 1:5 wt:% Al (15)

<sup>T</sup> � <sup>0</sup>:06 20:0 wt:%Al (17)

� 0:05 5:0 wt:%Al (16)

Me Ga ð Þ �Al (20)

T � 3:7 kJ=mol 1:5 wt:%Al (22)

T � 3:6 kJ=mol 5:0 wt:%Al (23)

T � 3:4 kJ=mol 20:0 wt:%Al (24)

T � 3:6 kJ=mol 1:5 wt:%Al (25)

Me Ga ð Þ �Al <sup>¼</sup> <sup>2</sup>:303RT log <sup>γ</sup>Me Ga ð Þ �Al (21)

in liquid Ga-Al alloys were fitted to the Eqs. (12)–(17):

114 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

logγNd Ga ð Þ �Al <sup>¼</sup> <sup>5</sup>:<sup>12</sup> � <sup>11260</sup>

logγNd Ga ð Þ �Al <sup>¼</sup> <sup>5</sup>:<sup>07</sup> � <sup>11006</sup>

logγNd Ga ð Þ �Al <sup>¼</sup> <sup>4</sup>:<sup>94</sup> � <sup>10713</sup>

logγU Ga ð Þ �Al <sup>¼</sup> <sup>1</sup>:<sup>21</sup> � <sup>4393</sup>

logγU Ga ð Þ �Al <sup>¼</sup> <sup>1</sup>:<sup>17</sup> � <sup>3935</sup>

logγU Ga ð Þ �Al <sup>¼</sup> <sup>1</sup>:<sup>11</sup> � <sup>3619</sup>

where C is the concentration of Al in Ga-Al alloy (wt. %).

ΔGex:

ΔGex

ΔGex

ΔGex

ΔGex

ΔGex:

lated using Eq. (21) and previously obtained in expressions (12)–(17):

Nd Ga ð Þ �Al ¼ �229:<sup>1</sup> <sup>þ</sup> <sup>115</sup>:<sup>0</sup> � <sup>10</sup>�<sup>3</sup>

Nd Ga ð Þ �Al ¼ �211:<sup>7</sup> <sup>þ</sup> <sup>100</sup>:<sup>1</sup> � <sup>10</sup>�<sup>3</sup>

Nd Ga ð Þ �Al ¼ �175:<sup>8</sup> <sup>þ</sup> <sup>57</sup>:<sup>9</sup> � <sup>10</sup>�<sup>3</sup>

U Ga ð Þ �Al ¼ �83:<sup>9</sup> <sup>þ</sup> <sup>23</sup>:<sup>2</sup> � <sup>10</sup>�<sup>3</sup>

the literature.

respectively. The following expressions describe these three-dimensional graphs:

$$
\Delta G\_{U(Ga-Al)}^{ex} = -78.9 + 27.1 \cdot 10^{-3} T \pm 3.2 \text{ kJ/mol} \quad 5.0 \text{ wt.}\% \text{Al} \tag{26}
$$

$$
\Delta G\_{\text{U(Gd-Al)}}^{\text{ex}} = -70.7 + 23.2 \cdot 10^{-3} T \pm 3.5 \text{ kJ/mol} \quad \text{20.0 wt.} \% \text{Al} \tag{27}
$$

Figure 3. The activity coefficients of Nd in Ga-Al alloys as a function of temperature and composition of Ga-Al alloy (3D diagram).

Figure 4. The activity coefficients of U in Ga-Al alloys as a function of temperature and composition of Ga-Al alloy (3D diagram).

where ΔGex: is the partial excess Gibbs free energy change (kJ/mol), ΔH is the partial enthalpy change of mixing (kJ/mol), <sup>Δ</sup>Sex: is the partial excess entropy change (J/mol�K), and <sup>γ</sup> is the activity coefficient.

The general alloy formation reaction can be written in the following way:

$$\left[\text{MeCl}\_6\right]^{3-} + 3\bar{\text{e}} + \text{n(Ga} - \text{Al}\right) = \text{Me}(\text{Ga} - \text{In})\_\text{n} + \text{6Cl}^-\tag{28}$$

The efficiency of the electrochemical separation of metals in molten salts during their deposition is characterized by the value of the separation factor:

$$
\Theta = \frac{\mathbb{C}\_2 \mathbb{x}\_1}{\mathbb{C}\_1 \mathbb{x}\_2} \tag{29}
$$

SF for fused Nd/U(Ga-Al)/3LiCl-2KCl system show the high values of partitioning. For this technique the effect of lower temperatures should be preferred. Separation factor of Nd/U

Figure 5. The separation factor of U/Nd couple as a function of temperature and composition of Ga-Al alloy (3D

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Potentiometry method at zero current was used for determination of the apparent standard potentials of the alloys. The dependencies of the apparent standard potential of Me(Ga-Al) alloys versus the temperature were fitted by the following equations using OriginPro version 7.5 Software:

La Ga ð Þ ¼ �2:<sup>851</sup> <sup>þ</sup> <sup>5</sup>:<sup>18</sup> � <sup>10</sup>�<sup>4</sup> � TV 5½ � (35)

La Inð Þ ¼ �3:<sup>081</sup> <sup>þ</sup> <sup>6</sup>:<sup>25</sup> � <sup>10</sup>�<sup>4</sup> � TV 5½ � (39)

U Ga ð Þ ¼ �2:<sup>723</sup> <sup>þ</sup> <sup>6</sup>:<sup>72</sup> � <sup>10</sup>�<sup>4</sup> � TV 5½ � (40)

La Ga ð Þ �20wt:%In ¼ �ð2:<sup>906</sup> � <sup>0</sup>:003Þ þ ð Þ� <sup>5</sup>:<sup>7</sup> � <sup>0</sup>:<sup>6</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:002 V (36)

La Ga ð Þ �40wt:%In ¼ �ð3:<sup>357</sup> � <sup>0</sup>:005Þ þ ð Þ� <sup>10</sup>:<sup>9</sup> � <sup>0</sup>:<sup>1</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:002 V (37)

La Ga ð Þ �70wt:%In ¼ �ð3:<sup>401</sup> � <sup>0</sup>:004Þ þ ð Þ� <sup>10</sup>:<sup>8</sup> � <sup>0</sup>:<sup>1</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:004 V (38)

U Ga ð Þ �20wt:%In ¼ �ð2:<sup>508</sup> � <sup>0</sup>:006Þ þ ð Þ� <sup>3</sup>:<sup>8</sup> � <sup>0</sup>:<sup>1</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:003 V (41)

U Ga ð Þ �40wt:%In ¼ �ð2:<sup>934</sup> � <sup>0</sup>:006Þ þ ð Þ� <sup>8</sup>:<sup>3</sup> � <sup>0</sup>:<sup>1</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:005 V (42)

decreases by increasing the temperature due to the entropy factor.

E∗∗

E∗∗

E∗∗

3.2. La(U)-(Ga-In)/3LiCl-2KCl system

diagram).

E∗∗

E∗∗

E∗∗

E∗∗

E∗∗

where C<sup>1</sup> and C<sup>2</sup> are the concentrations of separated metals M1 and M2 in electrolyte in mole fraction and x<sup>1</sup> and x<sup>2</sup> are the quantity of separated metals M1 and M2 in alloy in atomic fraction.

The expression for calculation of the separation factor (SF) of uranium and neodymium in gallium-aluminum alloys can be written as follows [5]:

$$\log \Theta = \frac{3F}{2.303RT} \left( E^{\*\*}\_{\mathrm{II}(Ga-Al)} - E^{\*\*}\_{\mathrm{Nd(Ga-Al)}} \right) \tag{30}$$

where E∗∗ U Ga ð Þ �Al is the apparent standard potential of U-Ga-Al alloy (V) and <sup>E</sup>∗∗ Nd Ga ð Þ �Al is the apparent standard potential of Nd-Ga-Al alloy (V).

The following expressions for separation factor of uranium and neodymium were obtained in Eqs. (31)–(33):

$$
\log \Theta\_{\text{U/Nd}} = 1.18 + \frac{3088}{T} \pm 0.03 \quad \text{1.5 wt.} \% \text{Al} \tag{31}
$$

$$1\log\Theta\_{\text{U/Nd}} = 1.05 + \frac{\text{3003}}{T} \pm 0.02 \quad \text{5.0 wt.} \% \text{Al} \tag{32}$$

$$
\log \Theta\_{\text{U/Nd}} = 1.01 + \frac{3004}{T} \pm 0.02 \quad \text{20.0 wt.} \% \text{Al} \tag{33}
$$

A three-dimensional log ΘMe Ga ð Þ �Al � Cð Þ Ga�Al � T graph showing the relationship between Nd/U separation factor, Al concentration in the Ga-Al solvent alloy, and temperature, for molten Me-(Ga-Al)/3LiCl-2KCl system, is presented in Figure 5 and is described by the following equation:

$$\log \Theta\_{\text{U/Nd}} = \left( 3134.3 - 32.84 \cdot \text{C} + 1.32 \cdot \text{C}^2 \right) / \text{T} + 1.25 - 0.05 \cdot \text{C} + 0.0019 \cdot \text{C}^2 \tag{34}$$

The separation of neodymium from uranium in molten chloride salts shows that uranium will be concentrated in the alloy phase, while neodymium will stay in the salt phase. The calculations of

Thermodynamics and Separation Factor of Uranium from Fission Products in "Liquid Metal-Molten Salt" System http://dx.doi.org/10.5772/intechopen.72451 117

Figure 5. The separation factor of U/Nd couple as a function of temperature and composition of Ga-Al alloy (3D diagram).

SF for fused Nd/U(Ga-Al)/3LiCl-2KCl system show the high values of partitioning. For this technique the effect of lower temperatures should be preferred. Separation factor of Nd/U decreases by increasing the temperature due to the entropy factor.

#### 3.2. La(U)-(Ga-In)/3LiCl-2KCl system

where ΔGex: is the partial excess Gibbs free energy change (kJ/mol), ΔH is the partial enthalpy change of mixing (kJ/mol), <sup>Δ</sup>Sex: is the partial excess entropy change (J/mol�K), and <sup>γ</sup> is the

The efficiency of the electrochemical separation of metals in molten salts during their deposi-

<sup>Θ</sup> <sup>¼</sup> <sup>C</sup>2x<sup>1</sup> C1x<sup>2</sup>

where C<sup>1</sup> and C<sup>2</sup> are the concentrations of separated metals M1 and M2 in electrolyte in mole fraction and x<sup>1</sup> and x<sup>2</sup> are the quantity of separated metals M1 and M2 in alloy in atomic

The expression for calculation of the separation factor (SF) of uranium and neodymium in

U Ga ð Þ �Al � <sup>E</sup>∗∗

Nd Ga ð Þ �Al

<sup>T</sup> � <sup>0</sup>:03 1:5 wt:%Al (31)

<sup>T</sup> � <sup>0</sup>:02 20:0 wt:%Al (33)

� 0:02 5:0 wt:%Al (32)

<sup>2</sup>:303RT <sup>E</sup>∗∗

U Ga ð Þ �Al is the apparent standard potential of U-Ga-Al alloy (V) and <sup>E</sup>∗∗

The following expressions for separation factor of uranium and neodymium were obtained in

3088

3003 T

3004

A three-dimensional log ΘMe Ga ð Þ �Al � Cð Þ Ga�Al � T graph showing the relationship between Nd/U separation factor, Al concentration in the Ga-Al solvent alloy, and temperature, for molten Me-(Ga-Al)/3LiCl-2KCl system, is presented in Figure 5 and is described by the fol-

The separation of neodymium from uranium in molten chloride salts shows that uranium will be concentrated in the alloy phase, while neodymium will stay in the salt phase. The calculations of

log <sup>Θ</sup><sup>U</sup>=Nd <sup>¼</sup> <sup>3134</sup>:<sup>3</sup> � <sup>32</sup>:<sup>84</sup> � <sup>С</sup> <sup>þ</sup> <sup>1</sup>:<sup>32</sup> � <sup>С</sup><sup>2</sup> <sup>=</sup><sup>T</sup> <sup>þ</sup> <sup>1</sup>:<sup>25</sup> � <sup>0</sup>:<sup>05</sup> � <sup>C</sup> <sup>þ</sup> <sup>0</sup>:<sup>0019</sup> � C2 (34)

<sup>3</sup>� <sup>þ</sup> <sup>3</sup><sup>ē</sup> <sup>þ</sup> n Ga ð Þ¼ � Al Me Ga ð Þ � In <sup>n</sup> <sup>þ</sup> 6Cl� (28)

(29)

(30)

Nd Ga ð Þ �Al is the

The general alloy formation reaction can be written in the following way:

½ � MeCl6

116 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

tion is characterized by the value of the separation factor:

gallium-aluminum alloys can be written as follows [5]:

apparent standard potential of Nd-Ga-Al alloy (V).

log <sup>Θ</sup> <sup>¼</sup> <sup>3</sup><sup>F</sup>

log Θ<sup>U</sup>=Nd ¼ 1:18 þ

log Θ<sup>U</sup>=Nd ¼ 1:05 þ

log Θ<sup>U</sup>=Nd ¼ 1:01 þ

activity coefficient.

fraction.

where E∗∗

Eqs. (31)–(33):

lowing equation:

Potentiometry method at zero current was used for determination of the apparent standard potentials of the alloys. The dependencies of the apparent standard potential of Me(Ga-Al) alloys versus the temperature were fitted by the following equations using OriginPro version 7.5 Software:

$$E\_{\rm La(Ga)}^{\*\*} = -2.851 + 5.18 \cdot 10^{-4} \cdot \text{T V} \quad [5] \tag{35}$$

$$E\_{\rm La(Ga-20wt.\%In)}^{\*\*} = -(2.906 \pm 0.003) + (5.7 \pm 0.6) \cdot 10^{-4} \cdot \text{T} \pm 0.002 \text{ V} \tag{36}$$

$$E\_{\rm La(Ga-40wt.\%ln)}^{\*\*} = -(3.357 \pm 0.005) + (10.9 \pm 0.1) \cdot 10^{-4} \cdot \text{T} \pm 0.002 \text{ V} \tag{37}$$

$$E\_{\rm La(Ga-70wt.\%ln)}^{\*\*} = -(3.401 \pm 0.004) + (10.8 \pm 0.1) \cdot 10^{-4} \cdot \text{T} \pm 0.004 \text{ V} \tag{38}$$

$$E\_{\rm La(ln)}^{\*\*} = -3.081 + 6.25 \cdot 10^{-4} \cdot \text{T V} \quad [5] \tag{39}$$

$$E\_{\rm U(Ga)}^{\*\*} = -2.723 + 6.72 \cdot 10^{-4} \cdot \text{T} \text{ V} \quad [5] \tag{40}$$

$$E\_{\rm U(Ga-20wt.\%In)}^{\*\*} = -(2.508 \pm 0.006) + (3.8 \pm 0.1) \cdot 10^{-4} \cdot \text{T} \pm 0.003 \text{ V} \tag{41}$$

$$E\_{\rm U(Ga-40wt.\%In)}^{\*\*} = -(2.934 \pm 0.006) + (8.3 \pm 0.1) \cdot 10^{-4} \cdot \text{T} \pm 0.005 \text{ V} \tag{42}$$

$$E\_{\rm U(Ga-70wt.\%In)}^{\*\*} = -(2.950 \pm 0.008) + (7.3 \pm 0.1) \cdot 10^{-4} \cdot \text{T} \pm 0.006 \text{ V} \tag{43}$$

$$E\_{\mathbb{U}(\text{In})}^{\*\*} = -2.921 + 6.12 \cdot 10^{-4} \cdot \text{T} \text{ V} \quad [5] \tag{44}$$

The following expressions describe these three-dimensional graphs:

temperature shifts the system toward more ideal behavior.

ΔGex

ΔGex

ΔGex

ΔGex

ΔGex

ΔGex

ΔGex

ΔGex

ΔGex

ΔGex

and lanthanum were obtained:

logγβ�La Ga ð Þ �In ¼ �<sup>13333</sup> <sup>þ</sup> <sup>59</sup> � <sup>C</sup> � <sup>0</sup>:<sup>24</sup> � <sup>С</sup><sup>2</sup> <sup>=</sup><sup>T</sup> <sup>þ</sup> <sup>4</sup>:<sup>72</sup> � <sup>0</sup>:<sup>04</sup> � <sup>С</sup> <sup>þ</sup> <sup>0</sup>, <sup>0025</sup> � <sup>С</sup><sup>2</sup> (45)

Thermodynamics and Separation Factor of Uranium from Fission Products in "Liquid Metal-Molten Salt" System

where C is the concentration of In in Ga-In alloy (wt.%). The small values of activity coefficients show strong interaction of lanthanide and actinide with the liquid alloy. Increasing

Partial excess Gibbs free energy change of La and U in liquid Ga-In alloys was calculated:

La Ga ð Þ ¼ �254:<sup>8</sup> <sup>þ</sup> <sup>90</sup>:<sup>2</sup> � <sup>10</sup>�<sup>3</sup>

La Ga ð Þ �20wt:%In ¼ �233:<sup>6</sup> <sup>þ</sup> <sup>68</sup>:<sup>6</sup> � <sup>10</sup>�<sup>3</sup>

La Ga ð Þ �40wt:%In ¼ �217:<sup>1</sup> <sup>þ</sup> <sup>66</sup>:<sup>5</sup> � <sup>10</sup>�<sup>3</sup>

La Ga ð Þ �70wt:% ¼ �201:<sup>2</sup> <sup>þ</sup> <sup>55</sup>:<sup>0</sup> � <sup>10</sup>�<sup>3</sup>

U Ga ð Þ �20wt:%In ¼ �143:<sup>3</sup> <sup>þ</sup> <sup>56</sup>:<sup>8</sup> � <sup>10</sup>�<sup>3</sup>

U Ga ð Þ �40wt:%In ¼ �90:<sup>9</sup> <sup>þ</sup> <sup>46</sup>:<sup>3</sup> � <sup>10</sup>�<sup>3</sup>

U Ga ð Þ �70wt:%In ¼ �73:<sup>8</sup> <sup>þ</sup> <sup>40</sup>:<sup>5</sup> � <sup>10</sup>�<sup>3</sup>

U Inð Þ ¼ �38:<sup>9</sup> <sup>þ</sup> <sup>44</sup>:<sup>7</sup> � <sup>10</sup>�<sup>3</sup>

logθLa-U Ga ð Þ <sup>¼</sup> <sup>2</sup>:<sup>33</sup> <sup>þ</sup>

logθLa-U Ga ð Þ �20wt:%In ¼ �2:<sup>85</sup> <sup>þ</sup>

logθLa-U Ga ð Þ �40wt:%In ¼ �3:<sup>97</sup> <sup>þ</sup>

logθLa-U Ga ð Þ �70wt:%In ¼ �5:<sup>25</sup> <sup>þ</sup>

logθLa�U In ð Þ ¼ �0:<sup>20</sup> <sup>þ</sup>

Using the temperature dependencies of the apparent standard potentials of lanthanum (35)– (39) and uranium (40)–(44) alloys, the following expressions for separation factor of uranium

1935

6006 T

6421

6818

2419

La Inð Þ ¼ �188:<sup>1</sup> <sup>þ</sup> <sup>59</sup>:<sup>3</sup> � <sup>10</sup>�<sup>3</sup>

U Ga ð Þ ¼ �95:<sup>1</sup> <sup>þ</sup> <sup>26</sup>:<sup>4</sup> � <sup>10</sup>�<sup>3</sup>

logγγ�U Ga ð Þ �In ¼ �<sup>4977</sup> � <sup>10</sup> � <sup>C</sup> <sup>þ</sup> <sup>0</sup>:<sup>4</sup> � C2 <sup>=</sup><sup>T</sup> <sup>þ</sup> <sup>1</sup>:<sup>38</sup> <sup>þ</sup> <sup>0</sup>:<sup>037</sup> � <sup>C</sup> � <sup>0</sup>:<sup>0003</sup> � C2 (46)

T kJ=mol (47)

http://dx.doi.org/10.5772/intechopen.72451

119

T � 3:2 kJ=mol (48)

T � 2:9 kJ=mol (49)

T � 3:2 kJ=mol (50)

T kJ=mol (51)

T kJ=mol (52)

T � 3:9 kJ=mol (53)

T � 3:8 kJ=mol (54)

T � 3:8 kJ=mol (55)

T kJ=mol (56)

<sup>T</sup> (57)

� 0:02 (58)

<sup>T</sup> � <sup>0</sup>:<sup>02</sup> (59)

<sup>T</sup> � <sup>0</sup>:<sup>02</sup> (60)

<sup>T</sup> (61)

Newton interpolation polynomial expressions were obtained to develop three-dimensional <sup>γ</sup>Me Ga ð Þ �In � <sup>C</sup>ð Þ Ga�In � <sup>1</sup>=T graphs on the basis of the functional dependencies of the apparent standard electrode potentials of the alloys, Ga-In mixture composition, and temperature (Figures 6 and 7).

Figure 6. The activity coefficients of La in Ga-In alloys as a function of temperature and composition of Ga-In alloy (3D diagram).

Figure 7. The activity coefficients of U in Ga-In alloys as a function of temperature and composition of Ga-In alloy (3D diagram).

The following expressions describe these three-dimensional graphs:

E∗∗

(Figures 6 and 7).

diagram).

diagram).

E∗∗

118 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

U Ga ð Þ �70wt:%In ¼ �ð2:<sup>950</sup> � <sup>0</sup>:008Þ þ ð Þ� <sup>7</sup>:<sup>3</sup> � <sup>0</sup>:<sup>1</sup> <sup>10</sup>�<sup>4</sup> � <sup>T</sup> � <sup>0</sup>:006 V (43)

Newton interpolation polynomial expressions were obtained to develop three-dimensional <sup>γ</sup>Me Ga ð Þ �In � <sup>C</sup>ð Þ Ga�In � <sup>1</sup>=T graphs on the basis of the functional dependencies of the apparent standard electrode potentials of the alloys, Ga-In mixture composition, and temperature

Figure 6. The activity coefficients of La in Ga-In alloys as a function of temperature and composition of Ga-In alloy (3D

Figure 7. The activity coefficients of U in Ga-In alloys as a function of temperature and composition of Ga-In alloy (3D

U In ð Þ ¼ �2:<sup>921</sup> <sup>þ</sup> <sup>6</sup>:<sup>12</sup> � <sup>10</sup>�<sup>4</sup> � TV 5½ � (44)

$$\log \gamma\_{\beta - \text{La(Ga} - \text{In)}} = \left(-13333 + 59 \cdot \text{C} - 0.24 \cdot \text{C}^2\right) / \text{T} + 4.72 - 0.04 \cdot \text{C} + 0,0025 \cdot \text{C}^2 \tag{45}$$

$$\log \mathbf{y}\_{\uparrow - \mathrm{U}(\mathrm{Ga} - \mathrm{In})} = \left( -4977 - 10 \cdot \mathbf{C} + 0.4 \cdot \mathbf{C}^2 \right) / \mathrm{T} + 1.38 + 0.037 \cdot \mathbf{C} - 0.0003 \cdot \mathbf{C}^2 \tag{46}$$

where C is the concentration of In in Ga-In alloy (wt.%). The small values of activity coefficients show strong interaction of lanthanide and actinide with the liquid alloy. Increasing temperature shifts the system toward more ideal behavior.

Partial excess Gibbs free energy change of La and U in liquid Ga-In alloys was calculated:

$$
\Delta G\_{\text{La(Ga)}}^{\text{ex}} = -254.8 + 90.2 \cdot 10^{-3} \text{T} \text{ kJ/mol} \tag{47}
$$

$$
\Delta G\_{\text{La(Ga-20wt.\%In)}}^{\text{ex}} = -233.6 + 68.6 \cdot 10^{-3} \text{T} \pm 3.2 \text{ kJ/mol} \tag{48}
$$

$$
\Delta G\_{\text{La(Ga-40wt.\%In)}}^{\text{ex}} = -217.1 + 66.5 \cdot 10^{-3} \text{T} \pm 2.9 \text{ kJ/mol} \tag{49}
$$

$$
\Delta G\_{\text{La(Ga}-70\text{wt.}\%)}^{\text{ex}} = -201.2 + 55.0 \cdot 10^{-3} \text{T} \pm 3.2 \text{ kJ/mol} \tag{50}
$$

$$
\Delta G\_{\text{La(In)}}^{\text{ex}} = -188.1 + 59.3 \cdot 10^{-3} \text{T kJ/mol} \tag{51}
$$

$$
\Delta G\_{\text{U(Ga)}}^{\text{ex}} = -95.1 + 26.4 \cdot 10^{-3} \text{T} \text{ kJ/mol} \tag{52}
$$

$$
\Delta G\_{\text{U(Ga-20wt.\%In)}}^{\text{ex}} = -143.3 + 56.8 \cdot 10^{-3} \text{T} \pm 3.9 \text{ kJ/mol} \tag{53}
$$

$$
\Delta G\_{\text{U(Ga -40wt.\%In)}}^{\text{ex}} = -90.9 + 46.3 \cdot 10^{-3} \text{T} \pm 3.8 \text{ kJ/mol} \tag{54}
$$

$$
\Delta G\_{\text{U(Ca-70wt,\%ln)}}^{\text{ex}} = -73.8 + 40.5 \cdot 10^{-3} \text{T} \pm 3.8 \text{ kJ/mol} \tag{55}
$$

$$
\Delta \mathbf{G}\_{\mathrm{U(ln)}}^{\mathrm{ex}} = -38.9 + 44.7 \cdot 10^{-3} \,\mathrm{T} \text{ kJ/mol} \tag{56}
$$

Using the temperature dependencies of the apparent standard potentials of lanthanum (35)– (39) and uranium (40)–(44) alloys, the following expressions for separation factor of uranium and lanthanum were obtained:

$$
\log \Theta\_{\text{La-U(Ga)}} = 2.33 + \frac{1935}{\text{T}} \tag{57}
$$

$$
\log \Theta\_{\text{La-U(Ga-20wt,\%In)}} = -2.85 + \frac{6006}{\text{T}} \pm 0.02 \tag{58}
$$

$$
\log \Theta\_{\text{La-U(Ga-40wt,\%In)}} = -3.97 + \frac{6421}{\text{T}} \pm 0.02 \tag{59}
$$

$$
\log \Theta\_{\text{La-U(Ga-70\text{wt}\%In)}} = -5.25 + \frac{6818}{\text{T}} \pm 0.02 \tag{60}
$$

$$
\log \Theta\_{\rm La-U(ln)} = -0.20 + \frac{2419}{T} \tag{61}
$$

The results obtained show the shift of the partial enthalpy change of mixing toward more positive values with increasing concentration of indium in the binary alloys. A threedimensional logΘLa=<sup>U</sup> � Cð Þ Ga�In � 1=Tgraph showing the relationship between La/U separation factor, In concentration in Ga-In solvent alloy, and temperature for molten Me-(Ga-In)/ 3LiCl-2KCl system is presented in Figure 8 and is described by the following equation:

$$\log \Theta\_{\rm IL/La} = \left(1935 + 184 \cdot \mathbb{C} - 2 \cdot \mathbb{C}^2\right) / T + 2.33 - 0.246 \cdot \mathbb{C} + 0.002 \cdot \mathbb{C}^2 \tag{62}$$

Author details

Harbin, P.R. China

References

00166-2

Metallurgiya; 1993. 342 p

Valeri Smolenski1,2\*, Alena Novoselova1,2, Alexander Bychkov3

\*Address all correspondence to: smolenski.valeri@gmail.com

3 National Research Nuclear University - MEPhI, Moscow, Russia

1 Institute of High-Temperature Electrochemistry UB RAS, Ekaterinburg, Russia

2 College of Materials Science and Chemical Engineering, Harbin Engineering University,

Thermodynamics and Separation Factor of Uranium from Fission Products in "Liquid Metal-Molten Salt" System

4 Department of Rare Metals and Nanomaterials, Institute of Physics and Technology, Ural

5 JSC "State Scientific Centre-Research Institute of Atomic Reactors", Dimitrovgrad, Russia

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[2] Sakamura Y, Hijikata T, Kinoshita K, Inoue T, Storvick TS, Krueger CL, Roy JJ, Grimmett DL, Fusselman SP, Gay RL. Measurement of standard potentials of actinides (U, Np, Pu, Am) in LiCl-KCl eutectic salt and separation of actinides from rare earths by electrorefining. Journal of Alloys and Compounds. 1998;271–273:592-596. DOI: 10.1016/S0925-8388(98)

[3] Sakamura Y, Inoue T, Shirai O, Iwai T, Arai Y, Suzuki Y. Studies on pyrochemical reprocessing for metallic and nitride fuels; behavior of transuranium elements in LiCl– KCl/liquid metal systems. In: Proceedings of the International Conference on Future

[4] Kinoshita K, Kurata M, Inoue T. Estimation of material balance in pyrometallurgical partitioning process of trans-uranic elements from high-level liquid waste. Journal of Nuclear Science and Technology. 2000;37:75-83. DOI: 10.1080/18811248.2000.9714869

[5] Lebedev VA. Selectivity of Liquid Metal Electrodes in Molten Halide. Chelyabinsk:

[6] Smolenski V, Novoselova A, Osipenko A, Maershin A. Thermodynamics and separation factor of uranium from lanthanum in liquid eutectic gallium-indium alloy/molten salt

system. Electrochimica Acta. 2014;145:81-85. DOI: 10.1016/j.electacta.2014.08.081

Nuclear Systems GLOBAL'99; 29 August-2 September; Wyoming; 1999

Yana Luk'yanova5 and Alexander Osipenko<sup>5</sup>

Federal University, Ekaterinburg, Russia

, Vladimir Volkovich<sup>4</sup>

http://dx.doi.org/10.5772/intechopen.72451

,

121

where C is the concentration of In in Ga-In alloy (wt.%).

Figure 8. Three-dimensional logΘU/La � C(Ga–In) � 1/T graph for U/La couple.
