**3. Results and discussion**

### **3.1 Transient electrochemical technique**

#### **3.1.1 Voltammetric studies on inert electrodes**

Cyclic voltammetry was carried out on inert tungsten electrodes for all melts tested: eutectic LiCl-KCl, equimolar NaCl-KCl, eutectic NaCl-KCl-CsCl and individual CsCl, at several temperatures (723-1073 K). Fig. 2 (red solid line) shows the electrochemical window obtained in LiCl-KCl at 723 K. The cathodic and anodic limits of the electrochemical window correspond to the reduction of the solvent alkali metal ions and to the oxidation of chloride ions into chlorine gas, respectively.

Fig. 2 also plots the cyclic voltammogram of a LiCl-KCl-YbCl3 solution on W at 723K (blue solid line). It shows a single cathodic peak at a potential of -1.762V vs. Cl- /Cl2 and its corresponding anodic peak at -1.566V vs. the Cl-/Cl2. Similar behaviour for the reduction of Yb(III) ions has been observed in the fused equimolar NaCl-KCl mixture (Fig. 3), NaCl-KCl-CsCl eutectic (Fig. 4) and CsCl (Fig. 5). These figures show the linear sweep and the cyclic voltammograms obtained in the above systems with YbCl3 at several scan rates, respectively.

The square wave voltammetry technique was used to determine the number of electrons exchanged in the reduction of Yb(III) ions in different molten compositions. Fig. 6 shows the bell-shaped symmetric cathodic wave obtained in the LiCl-KCl-YbCl3 melt at 723 K. The number of electrons exchanged is determined by measuring the width at half height of the reduction peak, *W1/2* (V), registered at different frequencies (6– 80 Hz). W1/2 is given by the following equation, valid for reversible systems:

$$\mathcal{W}\_{1/2} = 3.52 \frac{\mathcal{R}T}{nF} \tag{1}$$

Fig. 2. Cyclic voltammograms of pure LiCl-KCl eutectic melt (red solid line). Cyclic voltammograms of LiCl-KCl-YbCl3 (9.41·10-2 mol/kg) melt (blue solid line) corresponding to the reduction reaction *Yb III e Yb II* ( ) () <sup>−</sup> + ⇔ at 723 K. Working electrode: W (surface area = 0.25 cm2). Scan rate = 0.1 V s-1

Cyclic voltammetry was carried out on inert tungsten electrodes for all melts tested: eutectic LiCl-KCl, equimolar NaCl-KCl, eutectic NaCl-KCl-CsCl and individual CsCl, at several temperatures (723-1073 K). Fig. 2 (red solid line) shows the electrochemical window obtained in LiCl-KCl at 723 K. The cathodic and anodic limits of the electrochemical window correspond to the reduction of the solvent alkali metal ions and to the oxidation of

Fig. 2 also plots the cyclic voltammogram of a LiCl-KCl-YbCl3 solution on W at 723K (blue solid line). It shows a single cathodic peak at a potential of -1.762V vs. Cl-/Cl2 and its corresponding anodic peak at -1.566V vs. the Cl-/Cl2. Similar behaviour for the reduction of Yb(III) ions has been observed in the fused equimolar NaCl-KCl mixture (Fig. 3), NaCl-KCl-CsCl eutectic (Fig. 4) and CsCl (Fig. 5). These figures show the linear sweep and the cyclic voltammograms obtained in the above systems with YbCl3 at several scan rates,

The square wave voltammetry technique was used to determine the number of electrons exchanged in the reduction of Yb(III) ions in different molten compositions. Fig. 6 shows the bell-shaped symmetric cathodic wave obtained in the LiCl-KCl-YbCl3 melt at 723 K. The number of electrons exchanged is determined by measuring the width at half height of the reduction peak, *W1/2* (V), registered at different frequencies (6– 80 Hz). W1/2 is given by the

1/2 3.52 *RT <sup>W</sup>*

Fig. 2. Cyclic voltammograms of pure LiCl-KCl eutectic melt (red solid line). Cyclic

voltammograms of LiCl-KCl-YbCl3 (9.41·10-2 mol/kg) melt (blue solid line) corresponding to the reduction reaction *Yb III e Yb II* ( ) () <sup>−</sup> + ⇔ at 723 K. Working electrode: W (surface area =

*nF* <sup>=</sup> (1)

**3. Results and discussion** 

respectively.

**3.1 Transient electrochemical technique 3.1.1 Voltammetric studies on inert electrodes** 

chloride ions into chlorine gas, respectively.

following equation, valid for reversible systems:

0.25 cm2). Scan rate = 0.1 V s-1

Fig. 3. Linear sweep voltammograms of fused NaCl-KCl-YbCl3 (3.79·10-2 mol/kg) for the reduction of Yb(III) to Yb(II) ions at different sweep potential rates at 973 K. Working electrode: W (surface area = 0.27 cm2)

Fig. 4. Linear sweep voltammograms of fused NaCl-KCl-CsCl-YbCl3 salt at different sweep rates at 873 K. [Yb(III)] = 7.45·10-2 mol kg-1. Working electrode: W (S = 0.36 cm2)

At low frequencies a linear relationship between the cathodic peak current and the square root of the frequency was found. Under these conditions the system can be considered as reversible and equation 1 can be applied [Bard & Faulkner, 1980]. The number of electrons exchanged was close to 1. The same results were obtained in NaCl-KCl, NaCl-KCl-CsCl and CsCl media.

Potentiostatic electrolysis at potentials of the cathodic peaks for all systems studied did not show the formation of the solid phase of tungsten surface after polarization. There is no plateau on the dependences potential – time. Also the working electrode did not undergo any visual change. X-ray analysis of the surface of the working electrodes after experiments also show an absence of formation of solid phase.

Electrochemistry of Tm(III) and Yb(III) in Molten Salts 269

cathodic and anodic peak potential (*Ep*) is constant and independent of the potential sweep rate (Fig. 7). On the other hand the cathodic and anodic peak current (Ip) is directly proportional to the square root of the polarization rate (υ) (Fig. 8). A linear relationship between the cathodic peak current density and the concentration of YbCl3 ions in the melt was observed (Fig. 9). From these results and according to the theory of linear sweep voltammetry technique [Bard & Faulkner, 1980] it is concluded that the redox system

> -2.5 -2 -1.5 -1 -0.5 0 **ln(v)/ln(V s-1)**

> 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

**v1/2/V1/2s-1/2**

Fig. 8. Variation of the cathodic and anodic peak current as a function of the square root of the potential scan rate in fused LiCl-KCl-YbCl3 (9.41·10-2 mol/kg) at 723K. Working

Fig. 7. Variation of the cathodic and anodic peak potential as a function of the sweep rate in fused LiCl-KCl-YbCl3 (9.41·10-2 mol/kg) at 723K. Working electrode: W (surface area = 0.25

▲ Anodic

● Cathodic

Yb(III)/Yb(II) is a reversible and controlled by the rate of the mass transfer.

**Ep/V**

cm2)



electrode: W (surface area = 0.25 cm2)




**Ip/A**

0.005

0.01

0.015

▲ Anodic

● Cathodic

0.02

0






Fig. 5. Cyclic voltammograms of a CsCl-YbCl3 (3.70·10-2 mol/kg) solution for the reaction *Yb III e Yb II* ( ) () <sup>−</sup> + ⇔ at different potential sweep rates at 973 K. Working electrode: W (surface area = 0.31 cm2)

Fig. 6. Square wave voltammogram of LiCl-KCl-YbCl3 (9.41·10-2 mol/kg) at 12 Hz at 723 K. Working electrode: W (surface area = 0.25 cm2)

The results obtained allow concluding that the reduction of Yb(III) ions takes place in a single step with the exchange of one electron and the formation of a soluble product, according to the following reaction:

$$\text{Yb}(\text{III}) \nrightarrow \text{\color{red}{e}} \iff \text{Yb}(\text{II}) \tag{2}$$

The reaction mechanism of the soluble-soluble Yb(III)/Yb(II) redox system was investigated by analyzing the voltammetric curves obtained at several scan rates. It shows that the


Fig. 5. Cyclic voltammograms of a CsCl-YbCl3 (3.70·10-2 mol/kg) solution for the reaction *Yb III e Yb II* ( ) () <sup>−</sup> + ⇔ at different potential sweep rates at 973 K. Working electrode: W

**W1/2**


Fig. 6. Square wave voltammogram of LiCl-KCl-YbCl3 (9.41·10-2 mol/kg) at 12 Hz at 723 K.

The results obtained allow concluding that the reduction of Yb(III) ions takes place in a single step with the exchange of one electron and the formation of a soluble product,

 Yb(III) + ē ⇔ Yb(II) (2) The reaction mechanism of the soluble-soluble Yb(III)/Yb(II) redox system was investigated by analyzing the voltammetric curves obtained at several scan rates. It shows that the

0.06 V/s 0.1 V/s 0.2 V/s 0.3 V/s 0.4 V/s 0.5 V/s


(surface area = 0.31 cm2)


Working electrode: W (surface area = 0.25 cm2)

according to the following reaction:




**Ip/**

**A**




0



**I/A**

0

0.01

0.02

0.03

cathodic and anodic peak potential (*Ep*) is constant and independent of the potential sweep rate (Fig. 7). On the other hand the cathodic and anodic peak current (Ip) is directly proportional to the square root of the polarization rate (υ) (Fig. 8). A linear relationship between the cathodic peak current density and the concentration of YbCl3 ions in the melt was observed (Fig. 9). From these results and according to the theory of linear sweep voltammetry technique [Bard & Faulkner, 1980] it is concluded that the redox system Yb(III)/Yb(II) is a reversible and controlled by the rate of the mass transfer.

Fig. 7. Variation of the cathodic and anodic peak potential as a function of the sweep rate in fused LiCl-KCl-YbCl3 (9.41·10-2 mol/kg) at 723K. Working electrode: W (surface area = 0.25 cm2)

Fig. 8. Variation of the cathodic and anodic peak current as a function of the square root of the potential scan rate in fused LiCl-KCl-YbCl3 (9.41·10-2 mol/kg) at 723K. Working electrode: W (surface area = 0.25 cm2)

Electrochemistry of Tm(III) and Yb(III) in Molten Salts 271

From this expression, the value of the activation energy for the Yb(III) ions diffusion process

The diffusion coefficient of ytterbium (III) ions becomes smaller with the increase of the radius of the cation of alkali metal in the line from Li to Cs (Table 1). Such behaviour takes place due to an increasing on the strength of complex ions and the decrease in contribution of D to the "hopping" mechanism. The increase of temperature leads to the increase of the

Solvent T/K D105/cm2s-1 -EA/kJmol-1

1.0 ± 0.1 2.7 ± 0.1 5.4 ± 0.1

2.8 ± 0.2 3.2 ± 0.2 4.1 ± 0.2

0.66± 0.1 1.38± 0.1 2.45± 0.1

0.9 ± 0.1 1.2 ± 0.1 1.7 ± 0.1

⎛ ⎞ ⎜ ⎟ <sup>+</sup> ⎝ ⎠ =− − + <sup>±</sup> (5)

38.3

45.4

51.3

54.4

*r* <sup>+</sup> was calculated by using the

<sup>=</sup> ∑ (6)

was calculated in the different melts tested (Table 1).

848 973

1023 1073

973 1073

1023 1073

( )

The average value of the radius of molten mixtures ( ) *<sup>R</sup>*

temperatures. Activation energy for the ytterbium ions diffusion process

**3.1.3 Apparent standard potentials of the redox couple Yb(III)/Yb(II)** 

case of a soluble-soluble reversible system [Bard & Faulkner, 1980]:

Table 1. Diffusion coefficient of Yb(III) ions in molten alkali metal chlorides at several

The variation of the logarithm of the diffusion coefficient as a function of the reverse radius of the solvent cation (r) and reverse temperatures is given by the following expression:

> <sup>158</sup> 0.0071 <sup>3596</sup> log 2.38 0.02 *Yb III <sup>T</sup> <sup>D</sup>*

*T r*

1

where *<sup>i</sup> c* is the mole fraction of *i* cations; *ir* is the radius of *i* cations in molten mixture,

The apparent standard potential of the Yb(III)/Yb(II) system was determined from the cyclic voltammograms registered in YbCl*3* solutions in the different alkali metal chlorides tested at

According to the theory of linear sweep voltammetry the following expressions, including the anodic and cathodic peak potentials and the half-wave potential, can be applied in the

*N R i i i r cr* <sup>+</sup> =

diffusion coefficients in all the solvents.

LiCl-KCl 723

NaCl-KCl 973

NaCl-KCl-CsCl 873

following equation [Lebedev, 1993]:

consist of *N* different alkali chlorides, nm.

several temperatures.

CsCl 973

Fig. 9. Variation of the cathodic peak current as a function of the concentration of YbCl3 in LiCl-KCl-YbCl3 at 723 K. Working electrode: W (S = 0.25 cm2). Scan rate = 0.1 V s-1

From the transient electrochemical techniques applied we concluded that the potential of the system [Yb(II)/Yb(0)] can not be observed in the molten alkali chlorides media because it is more negative than the potential of the solvent Me(I)/Me(0), being Me: Li, Na, K and Cs, (Fig. 1).

#### **3.1.2 Diffusion coefficient of Yb (III) ions**

The diffusion coefficient of Yb(III) ions in molten chloride media was determined using the cyclic voltammetry technique and applying the Randles-Sevčik equation, valid for reversible soluble-soluble system [Bard & Faulkner, 1980]:

$$I\_p = 0.446 \text{(nF)}^{3f2} \text{C}\_0 \text{S} \left(\frac{D\nu}{RT}\right)^{1/2} \tag{3}$$

where *S* is the electrode surface area (in cm2), *C0* is the solute concentration (in mol cm-3), *D* is the diffusion coefficient (in cm2 s-1), *F* is the Faraday constant (in 96500 C mol-1), *R* is the ideal gas constant (in J K-1 mol-1), *n* is the number of exchanged electrons, *v* is the potential sweep rate (in V s-1) and *T* is the absolute temperature (in K).

The values obtained for the different molten chlorides tested at several temperatures are quoted in Table 1.

The diffusion coefficient values have been used to calculate the activation energy for the diffusion process. The influence of the temperature on the diffusion coefficient obeys the Arrhenius's law through the following equation:

$$D = D\_o \exp\left(-\frac{E\_A}{RT}\right) \pm \Delta\tag{4}$$

where *EA* is the activation energy for the diffusion process (in kJ mol-1), *Do* is the preexponential term (in cm2 s-1) and Δ is the experimental error.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 **C/mol kg-1**

Fig. 9. Variation of the cathodic peak current as a function of the concentration of YbCl3 in

From the transient electrochemical techniques applied we concluded that the potential of the system [Yb(II)/Yb(0)] can not be observed in the molten alkali chlorides media because it is more negative than the potential of the solvent Me(I)/Me(0), being Me: Li, Na, K and Cs,

The diffusion coefficient of Yb(III) ions in molten chloride media was determined using the cyclic voltammetry technique and applying the Randles-Sevčik equation, valid for reversible

3 2

= ⎜ ⎟

where *S* is the electrode surface area (in cm2), *C0* is the solute concentration (in mol cm-3), *D* is the diffusion coefficient (in cm2 s-1), *F* is the Faraday constant (in 96500 C mol-1), *R* is the ideal gas constant (in J K-1 mol-1), *n* is the number of exchanged electrons, *v* is the potential

The values obtained for the different molten chlorides tested at several temperatures are

The diffusion coefficient values have been used to calculate the activation energy for the diffusion process. The influence of the temperature on the diffusion coefficient obeys the

> exp *<sup>A</sup> <sup>o</sup> <sup>E</sup> D D*

where *EA* is the activation energy for the diffusion process (in kJ mol-1), *Do* is the pre-

*RT* ⎛ ⎞ <sup>=</sup> ⎜ ⎟ − ±Δ

<sup>0</sup> 0.446( ) *<sup>p</sup> <sup>D</sup> I nF C S* 1 2

⎝ ⎠ (3)

⎝ ⎠ (4)

*RT* ⎛ ⎞ ν

LiCl-KCl-YbCl3 at 723 K. Working electrode: W (S = 0.25 cm2). Scan rate = 0.1 V s-1


**3.1.2 Diffusion coefficient of Yb (III) ions** 

soluble-soluble system [Bard & Faulkner, 1980]:

Arrhenius's law through the following equation:

sweep rate (in V s-1) and *T* is the absolute temperature (in K).

exponential term (in cm2 s-1) and Δ is the experimental error.



**Ip/A**

(Fig. 1).

quoted in Table 1.


0

From this expression, the value of the activation energy for the Yb(III) ions diffusion process was calculated in the different melts tested (Table 1).

The diffusion coefficient of ytterbium (III) ions becomes smaller with the increase of the radius of the cation of alkali metal in the line from Li to Cs (Table 1). Such behaviour takes place due to an increasing on the strength of complex ions and the decrease in contribution of D to the "hopping" mechanism. The increase of temperature leads to the increase of the diffusion coefficients in all the solvents.


Table 1. Diffusion coefficient of Yb(III) ions in molten alkali metal chlorides at several temperatures. Activation energy for the ytterbium ions diffusion process

The variation of the logarithm of the diffusion coefficient as a function of the reverse radius of the solvent cation (r) and reverse temperatures is given by the following expression:

$$\log D\_{\text{Yb(III)}} = -2.38 - \frac{3596}{T} + \frac{\left(0.0071 + \frac{158}{T}\right)}{r} \pm 0.02\tag{5}$$

The average value of the radius of molten mixtures ( ) *<sup>R</sup> r* <sup>+</sup> was calculated by using the following equation [Lebedev, 1993]:

$$r\_{R^{+}} = \sum\_{i=1}^{N} c\_{i}r\_{i} \tag{6}$$

where *<sup>i</sup> c* is the mole fraction of *i* cations; *ir* is the radius of *i* cations in molten mixture, consist of *N* different alkali chlorides, nm.

#### **3.1.3 Apparent standard potentials of the redox couple Yb(III)/Yb(II)**

The apparent standard potential of the Yb(III)/Yb(II) system was determined from the cyclic voltammograms registered in YbCl*3* solutions in the different alkali metal chlorides tested at several temperatures.

According to the theory of linear sweep voltammetry the following expressions, including the anodic and cathodic peak potentials and the half-wave potential, can be applied in the case of a soluble-soluble reversible system [Bard & Faulkner, 1980]:

Electrochemistry of Tm(III) and Yb(III) in Molten Salts 273

The variation of the apparent standard potential of the redox couple Yb(III)/Yb(II) as a function of the reverse radius of the solvent cation (r) and the temperature was calculated.

> (0.104 4 10 ) 3.031 8 10 *Yb III Yb II <sup>T</sup> E T*

Normally, lanthanide chlorides dissolved in alkali chloride melts are solvated by the

Papatheodorou & Kleppa, 1974; Yamana et al., 2003]. In the case of ytterbium, [ ]<sup>3</sup> *YbCl*<sup>6</sup>

complex ions are present in the melts [Novoselova et al., 2004]. Their relative stability increases with the increase of the solvent cation radius, and the apparent standard redox potential shifts to more negative values. Our results are in a good agreement with the

Using the values of the apparent standard redox potentials the formal free Gibbs energy

YbCl2(l) + ½ Cl2(g) ⇔ YbCl3(l) (19)

\* *G nFEYb III Yb II* ( ) ()

Its temperature dependence allows calculating the enthalpy and entropy of the YbCl3

The apparent standard Gibbs energy of formation of *YbCl3* in the different solvents tested

The changes of the thermodynamic parameters of the redox reaction (19) versus the radius of the solvent cation show the increasing in strength of the Yb-Cl bond in the complex ions

Linear sweep voltammograms for the reduction of Yb(III) solution at inert tungsten (1) and active aluminum (2) electrodes at 873 K are presented in Fig. 10. The voltammogram on

\* 184.80 0.033 2.46 Δ =− + ⋅ ± *G T YbCl* kJ/mol [723-973 K] LiCl-KCl (22)

\* 195.96 0.036 2.46 Δ =− + ⋅ ± *G T YbCl* kJ/mol [973-1075 K] NaCl-KCl (23)

\* 218.25 0.041 2.46 Δ =− + ⋅ ± *G T YbCl* kJ/mol [973-1079 K] CsCl (25)

\* 211.52 0.041 2.43 Δ =− + ⋅ ± *G T YbCl* kJ/mol [723-1073 K] NaCl-KCl-CsCl (24)

\* 4

( )/ ( )

chloride ions forming different complex ions like [ ]<sup>3</sup> *LnCl*<sup>6</sup>

5

<sup>−</sup> and [ ]<sup>2</sup> *LnCl*<sup>4</sup>

<sup>∗</sup> Δ =− (20)

\* *G H TS* ∗ ∗ Δ =Δ − Δ (21)

<sup>−</sup> [Barbanel, 1985;

−

*r* <sup>−</sup> <sup>−</sup> − ⋅ =− + ⋅ + (18)

The relation obtained is:

literature ones [Smirnov, 1973].

changes of the redox reaction

can be expressed as:

[ ] <sup>3</sup> *YbCl*<sup>6</sup>

3

3

3

<sup>−</sup> in the line from LiCl to CsCl.

**3.1.5 Voltammetric studies on active electrodes** 

3

**3.1.4 Thermodynamics properties** 

was calculated according to following expression:

formation by means of the relation [Bard & Faulkner, 1980]:

$$E\_P^C = E\_{1f2} - 1.11\frac{RT}{F} \tag{6}$$

$$E\_P^A = E\_{1/2} + 1.11\frac{RT}{F} \tag{7}$$

$$\frac{\left(E\_p^{\triangle} + E\_p^A\right)}{2} = E\_{1/2} \tag{8}$$

where the half-wave potential is given by:

$$E\_{\rm If2} = E\_{\rm Yb(III)f\rm Pb(II)}^0 + \frac{RT}{F} \ln\left(\frac{D\_{\rm Yb(II)}}{D\_{\rm Yb(III)}}\right)^{\rm If2} + \frac{RT}{F} \ln\left(\frac{\mathcal{Y}\_{\rm Yb(III)}}{\mathcal{Y}\_{\rm Pb(II)}}\right) \tag{9}$$

It is known that for concentrations of electroactive species lower than 3 to 5·10-2 in mole fraction scale, their activity coefficient is almost constant. In these conditions, it is more convenient using the apparent standard redox potential concept ( \* *EYb III Yb II* ( ) () ) expressed as follows [Smirnov, 1973]:

$$E^\*\_{\mathcal{Y}\mathfrak{b}(\mathrm{III})\mathfrak{f}^\*\mathfrak{b}(\mathrm{II})} = E^0\_{\mathcal{Y}\mathfrak{b}(\mathrm{III})\mathfrak{f}^\*\mathfrak{b}(\mathrm{II})} + \frac{RT}{F} \ln\left(\frac{\mathcal{Y}\mathfrak{b}(\mathrm{III})}{\mathcal{Y}\mathfrak{b}(\mathrm{II})}\right) \tag{10}$$

The formal standard redox potentials of \* *EYb III Yb II* ( ) () were calculated from the following equations:

$$E\_{\text{Yb(III)/Yb(II)}}^{\*} = E\_p^C + 1.11 \frac{RT}{F} + \frac{RT}{F} \ln\left(\frac{D\_{\text{ox}}}{D\_{rel}}\right)^{1/2} \tag{11}$$

$$E\_{Yb(III)/Yb(II)}^{\*} = E\_P^A - 1.11\frac{RT}{F} + \frac{RT}{F} \ln\left(\frac{D\_{ox}}{D\_{red}}\right)^{1/2} \tag{12}$$

$$E\_{Yb(III)/Yb(II)}^{\*} = \frac{\left(E\_P^{\mathbb{C}} + E\_P^A\right)}{2} + \frac{RT}{F} \ln\left(\frac{D\_{ox}}{D\_{red}}\right)^{1/2} \tag{13}$$

From the peak potential values measured in the cyclic voltammograms and the diffusion coefficients of Yb(III) and Yb(II) the following empirical equation for the apparent standard redox potentials versus the Cl–/Cl2 reference electrode in different solvents were obtained.

$$E\_{Yb(III)f^{t}(II)}^{\*} = -(1.915 \pm 0.005) + (3.5 \pm 0.2) \times 10^{-4} T, \quad V \quad \text{[723-973 K]} \quad \text{LiCl-KCl} \tag{14}$$

$$E\_{\mathcal{H}(\text{III})\backslash\mathcal{H}(\text{II})}^{\*} = -\text{(2.031} \pm 0.005) + \text{(3.7} \pm 0.2) \times 10^{-4} T, \quad V \quad \text{[973-1075 K]} \quad \text{NaCl-KCl} \quad \text{(15)}$$

$$E\_{\text{Y6(III)}f16(II)}^{\*} = -(2.192 \pm 0.016) + (4.3 \pm 0.2) \times 10^{-4} T\_{\prime} \quad V \quad \text{[723-1073 K]} \quad \text{NaCl-KCl-CsCl} \tag{16}$$

$$E\_{\mathcal{I}\mathcal{H}(\mathcal{III})\mathcal{J}\mathcal{H}(\mathcal{II})}^{\*} = -(2.262 \pm 0.004) + (4.2 \pm 0.2) \times 10^{-4} T\_{\prime} \quad V \quad \text{[973-1079 K]} \quad \text{CsCl} \tag{17}$$

1 2 1.11 *<sup>C</sup>*

1/2 1.11 *<sup>A</sup>*

*RT E E*

1 2 2 *C A E E P P <sup>E</sup>*

0 ( ) ( )

=+ + ⎜ ⎟ ⎜⎟

It is known that for concentrations of electroactive species lower than 3 to 5·10-2 in mole fraction scale, their activity coefficient is almost constant. In these conditions, it is more convenient using the apparent standard redox potential concept ( \* *EYb III Yb II* ( ) () ) expressed as

\* 0 ( )

The formal standard redox potentials of \* *EYb III Yb II* ( ) () were calculated from the following

( )/ ( ) 1.11 ln *<sup>C</sup> ox Yb III Yb II P*

( )/ ( ) 1.11 ln *<sup>A</sup> ox Yb III Yb II P*

*C A P P ox Yb III Yb II*

From the peak potential values measured in the cyclic voltammograms and the diffusion coefficients of Yb(III) and Yb(II) the following empirical equation for the apparent standard redox potentials versus the Cl–/Cl2 reference electrode in different solvents were obtained.

*RT RT <sup>D</sup> E E*

( )/ ( ) ln 2

*E E RT <sup>D</sup> <sup>E</sup>*

*RT RT <sup>D</sup> E E*

*FD F*

*F*

1 2

*F*

*FF D*

*FF D*

*F D* + ⎛ ⎞ = + ⎜ ⎟

( ) 1/2

=+ + ⎜ ⎟

=− + ⎜ ⎟

( ) () (1.915 0.005) (3.5 0.2) 10 , *E T Yb III Yb II <sup>V</sup>* <sup>−</sup> =− ± + ± × [723-973 K] LiCl-KCl (14)

( ) () (2.031 0.005) (3.7 0.2) 10 , *E T Yb III Yb II <sup>V</sup>* <sup>−</sup> =− ± + ± × [973-1075 K] NaCl-KCl (15)

( ) () (2.262 0.004) (4.2 0.2) 10 , *E T Yb III Yb II <sup>V</sup>* <sup>−</sup> =− ± + ± × [973-1079 K] CsCl (17)

( ) () (2.192 0.016) (4.3 0.2) 10 , *E T Yb III Yb II <sup>V</sup>* <sup>−</sup> =− ± + ± × [723-1073 K] NaCl-KCl-CsCl (16)

⎛ ⎞ <sup>=</sup> <sup>+</sup> ⎜ ⎟

ln ln *Yb II Yb III*

( ) ( )

*Yb III Yb II*

⎝ ⎠ ⎝⎠

⎛ ⎞ ⎛⎞

*RT E E*

*<sup>F</sup>* = − (6)

= + (7)

<sup>+</sup> <sup>=</sup> (8)

γ

γ

( ) ln *Vb III*

1/2

1/2

*Yb II*

*red*

*red*

⎝ ⎠

*red*

⎝ ⎠

⎝ ⎠

⎛ ⎞

⎛ ⎞

⎜ ⎟ ⎝ ⎠

γ

γ

(9)

(10)

(11)

(12)

(13)

*P*

*P*

*RT <sup>D</sup> RT E E*

( ) () ( ) ()

*RT E E*

*Yb III Yb II Yb III Yb II*

( )

12 ( ) ( )

\*

\*

\*

\* 4

\* 4

\* 4

\* 4

*Yb III Yb II*

where the half-wave potential is given by:

follows [Smirnov, 1973]:

equations:

The variation of the apparent standard potential of the redox couple Yb(III)/Yb(II) as a function of the reverse radius of the solvent cation (r) and the temperature was calculated. The relation obtained is:

$$E\_{\text{Yb(III)}/\text{Yb(II)}}^{\*} = -3.031 + 8 \cdot 10^{-4} T + \frac{(0.104 - 4 \cdot 10^{-5} T)}{r} \tag{18}$$

Normally, lanthanide chlorides dissolved in alkali chloride melts are solvated by the chloride ions forming different complex ions like [ ]<sup>3</sup> *LnCl*<sup>6</sup> <sup>−</sup> and [ ]<sup>2</sup> *LnCl*<sup>4</sup> <sup>−</sup> [Barbanel, 1985; Papatheodorou & Kleppa, 1974; Yamana et al., 2003]. In the case of ytterbium, [ ]<sup>3</sup> *YbCl*<sup>6</sup> − complex ions are present in the melts [Novoselova et al., 2004]. Their relative stability increases with the increase of the solvent cation radius, and the apparent standard redox potential shifts to more negative values. Our results are in a good agreement with the literature ones [Smirnov, 1973].

#### **3.1.4 Thermodynamics properties**

Using the values of the apparent standard redox potentials the formal free Gibbs energy changes of the redox reaction

$$\text{YbCL}\_{2(\emptyset)} + \text{!} \nmid \text{Cl}\_{2(\emptyset)} \Leftrightarrow \text{YbCl}\_{3(\emptyset)} \tag{19}$$

was calculated according to following expression:

$$
\Delta \mathbf{G}^\* = -n \text{FE}\_{\text{Yb(III)} \uparrow \text{fb} \text{(II)}}^\* \tag{20}
$$

Its temperature dependence allows calculating the enthalpy and entropy of the YbCl3 formation by means of the relation [Bard & Faulkner, 1980]:

$$
\Delta G^\ast = \Delta H^\ast - T\Delta S^\ast \tag{21}
$$

The apparent standard Gibbs energy of formation of *YbCl3* in the different solvents tested can be expressed as:

$$
\Delta G\_{\text{YbCl}\_3}^{\circ} = -184.80 + 0.033 \cdot T \pm 2.46 \text{ kJ/mol} \quad \text{[723-973 K]} \quad \text{LiCl-KCl} \tag{22}
$$

$$
\Delta G\_{\text{YbCl}\_3}^{\*} = -195.96 + 0.036 \cdot T \pm 2.46 \text{ kJ/mol} \quad \text{[973-1075 K]} \quad \text{NaCl-KCl} \tag{23}
$$

$$
\Delta G\_{\text{M}\text{Cl}\_3}^{\circ} = -211.52 + 0.041 \cdot T \pm 2.43 \text{ kJ/mol} \quad \text{[723-1073 K]} \quad \text{NaCl-KCl-CsCl} \tag{24}
$$

$$
\Delta G\_{\text{Y6Cl}\_3}^{\*} = -218.25 + 0.041 \cdot T \pm 2.46 \text{ kJ/mol} \quad \text{[973-1079 K]} \quad \text{CsCl} \tag{25}
$$

The changes of the thermodynamic parameters of the redox reaction (19) versus the radius of the solvent cation show the increasing in strength of the Yb-Cl bond in the complex ions [ ] <sup>3</sup> *YbCl*<sup>6</sup> <sup>−</sup> in the line from LiCl to CsCl.

#### **3.1.5 Voltammetric studies on active electrodes**

Linear sweep voltammograms for the reduction of Yb(III) solution at inert tungsten (1) and active aluminum (2) electrodes at 873 K are presented in Fig. 10. The voltammogram on

Electrochemistry of Tm(III) and Yb(III) in Molten Salts 275

0 50 100 150 200 250 300 350 400 450 500 **t/s**

Fig. 12. The dependence of potential – time, obtained after short polarization of Al electrode in NaCl-KCl-CsCl-YbCl3 melt at 873 K. [Yb(III)] = 3.1710-2 mol kg-1. Edep. = –3.4 V; tdep. = 9 s Potentiostatic electrolysis at the potential –2.92 V shows the formation of solid cathodic product on a surface of Al electrode. Phase diagram of the system Al-Yb, Fig. 11, show the

The dependence potential – time, obtained after shot polarization of aluminum working electrode, show the existence of two waves at potentials average –2.88 V and –3.04 V vs. Cl– /Cl2, Fig. 12. It can be combined with the formation of two intermetallic compounds Al3Yb and Al2Yb. The X-ray analysis of the deposits, obtained after potentiostatic electrolysis at the potential –2.88 V show the existence of Al3Yb alloy on the surface of aluminum electrode

Analyzing the results of investigations it can be concluded that the mechanism of the reduction of Yb(III) ions in fused NaCl-KCl-CsCl eutectic on active electrode occurs in two

Yb(III) + ē = Yb(II) (26)

Potentiostatic electrolysis allow to deposit Al3Yb or the mixture of Al2Tm and Al3Tm alloys

The typical dependences of the redox potential of the couple Yb3+/Yb2+ with different ratio Yb(III)/Yb(II) versus the duration at the temperature 818 K in NaCl-KCl-CsCl-YbCl3 melt

The same type of the pictures was obtained for Tm3+/Tm2+ and Yb3+/Yb2+ systems in all investigations solvents. The equilibrium potential were fixed after 30-90 minutes after finishing of the electrolysis and depends from the conditions of the experiment. If the value

**3.2.1 Apparent standard potentials of the redox couple Ln(III)/Ln(II)** 

Yb(II) + nAl + 2 ē = AlnYb, (27)

and at potential –3.04 V show the existence of the mixture of Al3Yb and Al2Yb alloys.


where *n* is equal 2, 3.

are presented in Fig. 13.

Al3Yb + Al2Yb

Al3Yb + Al

formation of two intermetallic compounds Al3Yb and Al2Yb.

steps with the formation of Al3Yb and Al2Yb alloys:

as a thin films on the aluminum surface.

**3.2 Electromotive force method** 

Al

**Å/V**

aluminum working electrode show the existence of two cathodic peaks at the potentials approximately –1.92 V and –2.92 V vs. Cl–/Cl2 instead of one on tungsten electrode. Potentiostatic electrolysis at potential –1.92 V did not show the formation of solid phase on tungsten and aluminum surfaces after polarization. So we can suppose passing the reaction (2) at this potential on inert and active electrodes.

Fig.10. Linear sweep voltammograms of fused NaCl-KCl-CsCl-YbCl3 salt on inert W electrode (1) and active Al electrode (2) at 873 K. [Yb(III)] = 8.26·10-2 mol kg-1. Working electrode: W (S = 0.23 cm2); Al (S = 0.47 cm2)

Fig. 11. Phase diagram of Yb-Al system

aluminum working electrode show the existence of two cathodic peaks at the potentials approximately –1.92 V and –2.92 V vs. Cl–/Cl2 instead of one on tungsten electrode. Potentiostatic electrolysis at potential –1.92 V did not show the formation of solid phase on tungsten and aluminum surfaces after polarization. So we can suppose passing the reaction

Fig.10. Linear sweep voltammograms of fused NaCl-KCl-CsCl-YbCl3 salt on inert W electrode (1) and active Al electrode (2) at 873 K. [Yb(III)] = 8.26·10-2 mol kg-1. Working

(2) at this potential on inert and active electrodes.

electrode: W (S = 0.23 cm2); Al (S = 0.47 cm2)

Fig. 11. Phase diagram of Yb-Al system

Fig. 12. The dependence of potential – time, obtained after short polarization of Al electrode in NaCl-KCl-CsCl-YbCl3 melt at 873 K. [Yb(III)] = 3.1710-2 mol kg-1. Edep. = –3.4 V; tdep. = 9 s

Potentiostatic electrolysis at the potential –2.92 V shows the formation of solid cathodic product on a surface of Al electrode. Phase diagram of the system Al-Yb, Fig. 11, show the formation of two intermetallic compounds Al3Yb and Al2Yb.

The dependence potential – time, obtained after shot polarization of aluminum working electrode, show the existence of two waves at potentials average –2.88 V and –3.04 V vs. Cl– /Cl2, Fig. 12. It can be combined with the formation of two intermetallic compounds Al3Yb and Al2Yb. The X-ray analysis of the deposits, obtained after potentiostatic electrolysis at the potential –2.88 V show the existence of Al3Yb alloy on the surface of aluminum electrode and at potential –3.04 V show the existence of the mixture of Al3Yb and Al2Yb alloys.

Analyzing the results of investigations it can be concluded that the mechanism of the reduction of Yb(III) ions in fused NaCl-KCl-CsCl eutectic on active electrode occurs in two steps with the formation of Al3Yb and Al2Yb alloys:

$$\text{Yb(III)} + \text{\color{red}{e}} = \text{Yb(II)}\tag{26}$$

$$\text{Yb(II)} + \text{nAl} + 2 \text{ è} = \text{Al}\_{\text{n}} \text{Yb}\_{\text{}} \tag{27}$$

where *n* is equal 2, 3.

Potentiostatic electrolysis allow to deposit Al3Yb or the mixture of Al2Tm and Al3Tm alloys as a thin films on the aluminum surface.

#### **3.2 Electromotive force method**

#### **3.2.1 Apparent standard potentials of the redox couple Ln(III)/Ln(II)**

The typical dependences of the redox potential of the couple Yb3+/Yb2+ with different ratio Yb(III)/Yb(II) versus the duration at the temperature 818 K in NaCl-KCl-CsCl-YbCl3 melt are presented in Fig. 13.

The same type of the pictures was obtained for Tm3+/Tm2+ and Yb3+/Yb2+ systems in all investigations solvents. The equilibrium potential were fixed after 30-90 minutes after finishing of the electrolysis and depends from the conditions of the experiment. If the value

Electrochemistry of Tm(III) and Yb(III) in Molten Salts 277

**1**

**2**

carbon indicated electrode. [Yb3+] = 3.96 mol%. [Tm3+] = 4.28 mol%

equations (29-32) the number of exchange electrons for the reaction (33):

0 0.5 1 1.5 2 2.5 **ln[Ln(III)]/[Ln(II)]**

Fig. 14. Variation of the equilibrium potential of the couple Ln3+/Ln2+ as a function of the napierian logarithm ratio of concentrations [Ln3+] and [Ln2+] in fused NaCl-KCl-CsCl eutectic (1 - Yb; 2 – Tm) at 818 K and in fused CsCl (3 – Yb; 4 – Tm) at 973 K on vitreous

The number of exchange electrons (*n*) taking part in the process of electrochemical reduction of rare-earth trichlorides was determined from the slopes of the straight lines. From

The chemical analysis of the solidified thulium or ytterbium chloride melts performed after experiments confirmed the results of the electrochemical measurements. The difference in concentrations of LnCl2 determined by coulometry (i.e., calculated from the amount of electric charge passed through the melt for the reduction of Ln3*+* ions) and analytically did

The temperature dependences of apparent standard redox potentials of Ln3+/Ln2+ systems on vitreous carbon indicated electrode were linear in the whole temperature range studied, Fig. 15. The experiment data were fitted to the following equations using Software Origin

\* 5 (3.742 0.006) (105.0 0.6) 10 0.001 / *Tm Tm E T* + + *<sup>V</sup>* <sup>−</sup> =− ± + ± ⋅ ± [823-973 K] (Na-K-Cs)Cl (34)

\* 5 (2.580 0.013) (80.6 1.5) 10 0.003 / *Yb Yb E T* + + *<sup>V</sup>* <sup>−</sup> =− ± + ± ⋅ ± [823-973 K] (Na-K-Cs)Cl (35)

\* 5 (4.029 0.03) (124.0 2.7) 10 0.005 / *Tm Tm E T* + + *<sup>V</sup>* <sup>−</sup> =− ± + ± ⋅ ± [973-1123 K] CsCl (36)

\* 5 (2.464 0.008) (65.0 0.7) 10 0.001 / *Yb Yb E T* + + *<sup>V</sup>* <sup>−</sup> =− ± + ± ⋅ ± [973-1123 K] CsCl (37)

3 2 Ln Ln *e* <sup>+</sup> <sup>+</sup> + = (33)

**3**

**4**


was 0.99 ± 0.01 for Tm and 0.99 ± 0.02 for Yb.

not exceed 2.5 %.

Pro version 7.5:

3 2

3 2

3 2

3 2

**E/V**

of potential is constant during 30-40 minutes within the limits of ± 0.001 V then it is possible to say that the investigation system is in equilibrium conditions. The value of the apparent redox potential is determined by:

$$E\_{\rm Ln^{3+}}{}\_{\rm Ln^{2+}} = E\_{\rm Ln^{3+}}^{\*}{}\_{\rm Ln^{2+}} + \frac{RT}{nF} \ln\left(\frac{[Ln^{3+}]}{[Ln^{2+}]}\right) \tag{28}$$

where 3 2 *Ln Ln E* + + is the equilibrium potential of the system, V; 3 2 \* *Ln Ln E* <sup>+</sup> <sup>+</sup> is the apparent standard redox potential of the system, V; *n* is the number of exchange electrons; *[Ln3+]* and *[Ln2+]* are the concentrations of lanthanide ions in mole fraction.

Variation of the equilibrium potential of the couple Ln3+/Ln2+ as a function of the napierian logarithm ratio of concentrations [Ln3+] and [Ln2+] in fused LnCl3 solutions on vitreous carbon indicated electrode at 818 K (NaCl-KCl-CsCl eutectic) and at 973 K (CsCl) is shown

Fig. 13. The typical dependences of the redox potential of the couple Yb3+/Yb2+ versus the duration in NaCl-KCl-CsCl-YbCl3 melt. Temperature – 818 K. Initial concentration of [Yb3+] = 3.96 mol%. Working electrode – GC. **1** – ln[Yb3+]/[Yb2+] = 1.96; **2** – ln[Yb3+]/[Yb2+] = 1.58; **3** – ln[Yb3+]/[Yb2+] = 0.54; **4** – ln[Yb3+]/[Yb2+] = 0

In Fig. 14. Linear dependences of 3 2 *Ln Ln* / *<sup>E</sup>* <sup>+</sup> <sup>+</sup> *vs.* 3 2 ln([ ] [ ]) *Ln Ln* <sup>+</sup> <sup>+</sup> obeys the Nernst's law by the following equations using Software Origin Pro version 7.5:

$$E\_{Tm^{3+}/Tm^{2+}} = -(2.827 \pm 0.005) + (0.083 \pm 0.005) \ln([Tm^{3+}]/[Tm^{2+}]) \pm 0.007 \,/\, V \quad \text{CsC1} \tag{29}$$

$$E\_{\text{Tm}^{3+}/\text{Tm}^{2+}} = -\{2.906 \pm 0.001\} + \{0.070 \pm 0.001\} \text{In} \{ \text{Tm}^{3+} \} \{ \text{Tm}^{2+} \} \pm 0.002 \text{ / V} \quad \text{(Na-K-Cs)} \text{Cl} \text{(30)}$$

$$E\_{"\gamma b^{3+}/\gamma b^{2+}} = -(1.809 \pm 0.001) + (0.086 \pm 0.001) \ln([Yb^{3+}] \left[ [Yb^{2+}] \right] \pm 0.002 \text{ / V} \quad \text{CsCl} \tag{31}$$

$$E\_{"\text{Yb}"} / \text{ft}^{2\*} = -(1.805 \pm 0.005) + (0.071 \pm 0.004) \ln(\text{Yb}^{3+}] \text{[} \text{Yb}^{2+}\text{]} \text{]} \pm 0.006 \text{ / V} \quad \text{(Na-K-Cs)} \text{Cl} \quad \text{(32)}$$

of potential is constant during 30-40 minutes within the limits of ± 0.001 V then it is possible

[ ] *Ln Ln Ln Ln RT Ln E E nF Ln* ++ ++

standard redox potential of the system, V; *n* is the number of exchange electrons; *[Ln3+]* and

Variation of the equilibrium potential of the couple Ln3+/Ln2+ as a function of the napierian logarithm ratio of concentrations [Ln3+] and [Ln2+] in fused LnCl3 solutions on vitreous carbon indicated electrode at 818 K (NaCl-KCl-CsCl eutectic) and at 973 K (CsCl) is shown

> 0 500 1000 1500 2000 2500 3000 3500 4000 4500 **Duration/s**

Fig. 13. The typical dependences of the redox potential of the couple Yb3+/Yb2+ versus the duration in NaCl-KCl-CsCl-YbCl3 melt. Temperature – 818 K. Initial concentration of [Yb3+] = 3.96 mol%. Working electrode – GC. **1** – ln[Yb3+]/[Yb2+] = 1.96; **2** – ln[Yb3+]/[Yb2+] =

In Fig. 14. Linear dependences of 3 2 *Ln Ln* / *<sup>E</sup>* <sup>+</sup> <sup>+</sup> *vs.* 3 2 ln([ ] [ ]) *Ln Ln* <sup>+</sup> <sup>+</sup> obeys the Nernst's law by

/ (2.827 0.005) (0.083 0.005)ln([ ] [ ]) 0.007 / *Tm Tm E T* + + *<sup>m</sup> Tm <sup>V</sup>* + + =− ± + ± <sup>±</sup> CsCl (29)

/ (1.809 0.001) (0.086 0.001)ln([ ] [ ]) 0.002 / *Yb Yb E Y* + + *<sup>b</sup> Yb <sup>V</sup>* + + =− ± + ± <sup>±</sup> CsCl (31)

3 2

3 2

3 2

3 2

+ + =− ± + ± ± (Na-K-Cs)Cl (32)

+ + =− ± + ± ± (Na-K-Cs)Cl(30)

<sup>3</sup> \*

= + ⎜ ⎟

2 [ ] ln

⎝ ⎠

+ + ⎛ ⎞

\*

(28)

*Ln Ln E* <sup>+</sup> <sup>+</sup> is the apparent

to say that the investigation system is in equilibrium conditions. The value of the apparent redox potential is determined by:

*[Ln2+]* are the concentrations of lanthanide ions in mole fraction.


3 2

3 2

3 2

3 2

1.58; **3** – ln[Yb3+]/[Yb2+] = 0.54; **4** – ln[Yb3+]/[Yb2+] = 0

the following equations using Software Origin Pro version 7.5:

/ (2.906 0.001) (0.070 0.001)ln([Tm ] [Tm ]) 0.002 / V *Tm Tm E* + +

/ (1.805 0.005) (0.071 0.004)ln([Yb ] [Yb ]) 0.006 / V *Yb Yb E* + +



**E/V**



32 32

where 3 2 *Ln Ln E* + + is the equilibrium potential of the system, V; 3 2

Fig. 14. Variation of the equilibrium potential of the couple Ln3+/Ln2+ as a function of the napierian logarithm ratio of concentrations [Ln3+] and [Ln2+] in fused NaCl-KCl-CsCl eutectic (1 - Yb; 2 – Tm) at 818 K and in fused CsCl (3 – Yb; 4 – Tm) at 973 K on vitreous carbon indicated electrode. [Yb3+] = 3.96 mol%. [Tm3+] = 4.28 mol%

The number of exchange electrons (*n*) taking part in the process of electrochemical reduction of rare-earth trichlorides was determined from the slopes of the straight lines. From equations (29-32) the number of exchange electrons for the reaction (33):

$$\mathbf{L}\mathbf{n}^{3+} + \mathbf{e} = \mathbf{L}\mathbf{n}^{2+} \tag{33}$$

was 0.99 ± 0.01 for Tm and 0.99 ± 0.02 for Yb.

The chemical analysis of the solidified thulium or ytterbium chloride melts performed after experiments confirmed the results of the electrochemical measurements. The difference in concentrations of LnCl2 determined by coulometry (i.e., calculated from the amount of electric charge passed through the melt for the reduction of Ln3*+* ions) and analytically did not exceed 2.5 %.

The temperature dependences of apparent standard redox potentials of Ln3+/Ln2+ systems on vitreous carbon indicated electrode were linear in the whole temperature range studied, Fig. 15. The experiment data were fitted to the following equations using Software Origin Pro version 7.5:

$$E\_{\text{Tm}^{3+}/\text{Tm}^{2+}}^{\*} = -\left\{3.742 \pm 0.006\right\} + \left\{105.0 \pm 0.6\right\} \cdot 10^{-5} T \pm 0.001 \,/\, V \,\, \left[823 \text{-} 973 \text{ K}\right] \,\left(\text{Na-K-Cs}\right) \text{Cl} \,\, \left(34\right) \,\text{K}$$

$$E\_{\gamma b^{\ominus} f \gamma b^{\ominus}}^{\*} = -\text{(2.580} \pm 0.013) + \text{(80.6} \pm 1.5) \cdot 10^{-5} T \pm 0.003 \text{ / V} \quad \text{[823-973 K]} \text{ (Na-K-Cs)Cl} \tag{35}$$

$$E\_{Tm^{3+}f\text{Tm}^{2+}}^{\*} = -(4.029 \pm 0.03) + (124.0 \pm 2.7) \cdot 10^{-5} T \pm 0.005 \text{ / V} \tag{973-1123 K} \text{ ScCl} \tag{36}$$

$$E\_{"\eta^3"}^\* \mu\_{"\delta^2"} = -\text{(2.464} \pm 0.008) + \text{(65.0} \pm 0.7) \cdot 10^{-5} T \pm 0.001 \,/\, V \quad \text{[973-1123 K] CsCl} \tag{37}$$

Electrochemistry of Tm(III) and Yb(III) in Molten Salts 279

\* \*

The temperature dependence of the Gibbs energy change can be described by the following

The experiment data were fitted to the following equations using Software Origin Pro

By the expression (40) one can calculate the apparent equilibrium constants for the redox

reaction (38) in fused salts. The temperature dependences are the following:

<sup>46787</sup> ln 14.40 0.02 *Keq <sup>T</sup>*

<sup>28602</sup> ln 7.54 0.01 *Keq <sup>T</sup>*

<sup>3761</sup> log 2.09 0.02 *YbCl <sup>T</sup>*

The activity coefficients of YbCl3 in fused salts was determined from the difference between the apparent Gibbs free energy derived from the experimental measurements and the standard Gibbs free energy for pure compounds obtained in the literature [Barin, 1994]:

The dependence of the activity coefficient of YbCl3 versus the reverse temperature is given by the expressions (50, 51). Database for thulium compounds is absent in the literature

It is also possible to estimate the equilibrium chlorine gas pressure above an alkali metal chloride melts containing hulium or ytterbium tri- and dichlorides for the reaction (52) by

<sup>44997</sup> ln 13.78 0.01 *Keq <sup>T</sup>*

<sup>31114</sup> ln 10.56 0.01 *Keq <sup>T</sup>*

\* .

> \* .

3

γ

γ

[Barin, 1994].

<sup>4436</sup> log 1.23 0.02 *YbCl <sup>T</sup>*

3

\* .

> \* .

\* 3 *G T* (354.1 0.6) (94.5 0.6) 10 0.1 / *kJ mol* <sup>−</sup> Δ =− ± + ± ⋅ ± TmCl3-NaCl-KCl-CsCl (42)

\* 3 *G T* (249.0 1.3) (77.8 0.1) 10 0.3 / *kJ mol* <sup>−</sup> Δ =− ± + ± ⋅ ± YbCl3-NaCl-KCl-CsCl (43)

\* 3 *G T* (388.8 0.9) (119.7 0.9) 10 0.2 / *kJ mol* <sup>−</sup> Δ =− ± + ± ⋅ ± TmCl3-CsCl (44)

\* 3 *G T* (237.8 0.8) (62.7 0.7) 10 0.1 / *kJ mol* <sup>−</sup> Δ =− ± + ± ⋅ ± YbCl3-CsCl (45)

−+ ± TmCl3-NaCl-KCl-CsCl (46)

−+ ± YbCl3-NaCl-KCl-CsCl (47)

−+ ± TmCl3-CsCl (48)

=− + ± YbCl3-CsCl (49)

=− − ± YbCl3-NaCl-KCl-CsCl (50)

=− − ± YbCl3-CsCl (51)

equation:

version 7.5:

. Δ =− *G RT K* ln *eq* (40)

\*\* \* Δ*G H TS* =Δ − Δ (41)

The results of our investigations show that at equal temperatures the apparent redox potentials of thulium ( 3 2 ) \* *Tm Tm <sup>E</sup>* + + are more negative than ytterbium ( 3 2 ) \* *Yt Yb E* + + . The comparison of data for apparent standard redox potentials of thulium (-2.822 V) and ytterbium (-1.831 V) in molten *CsCl* ( 0.165 *Cs r nm* <sup>+</sup> = ) with data in fused NaCl-KCl-CsCl eutectic ( . 0.137 *eut r n* <sup>+</sup> = *m* ) [Lebedev, 1993] for thulium (-2.720 V) and ytterbium (-1.796 V) at 973 K show the natural shift of the potential values to more negative region in line LiCl-CsCl.

Fig. 15. Apparent standard redox potentials of the Ln3+/Ln2+ system as a function of the temperature on vitreous carbon indicated electrode. 1 – System YbCl3-YbCl2-NaCl-KCl-CsCl. 2 – System TmCl3-TmCl2-NaCl-KCl-CsCl. 3 – System YbCl3-YbCl2-CsCl. 4 – System TmCl3-TmCl2-CsCl

Typical complexes of dilute solution of lanthanide chlorides in alkali chloride melts are <sup>3</sup> *LnCl*<sup>6</sup> <sup>−</sup> and <sup>2</sup> *LnCl*<sup>4</sup> <sup>−</sup> [Papatheodorou & Kleppa, 1974; Yamana et al., 2003]. Their relative stability increases with increasing of solvent cation radius from Li+ to Cs+ and the apparent standard redox potentials are shifted to more negative values. These results are in good agreement with literature data concerning the second coordination sphere influence on apparent standard redox potentials.

#### **3.2.2 Thermodynamics properties**

Using the values of the apparent standard redox potentials the formal free Gibbs energy changes and the apparent equilibrium constants of the redox reaction (38):

$$\text{LnCl}\_{2(l)} + \text{l/}s\text{Cl}\_{2(l)} \Leftrightarrow \text{LnCl}\_{3(l)}\tag{38}$$

can be calculated using the well-known expressions:

$$
\Delta \mathbf{G}^\* = \mathbf{n} F E\_{\mathrm{Lr}^{3+}}^\* {}\_{\mathrm{Lr}^{2+}} \tag{39}
$$

and

The results of our investigations show that at equal temperatures the apparent redox

comparison of data for apparent standard redox potentials of thulium (-2.822 V) and

973 K show the natural shift of the potential values to more negative region in line LiCl-

**1**

**2**

800 850 900 950 1000 1050 1100 1150 **T/K**

Fig. 15. Apparent standard redox potentials of the Ln3+/Ln2+ system as a function of the temperature on vitreous carbon indicated electrode. 1 – System YbCl3-YbCl2-NaCl-KCl-CsCl. 2 – System TmCl3-TmCl2-NaCl-KCl-CsCl. 3 – System YbCl3-YbCl2-CsCl. 4 – System

Typical complexes of dilute solution of lanthanide chlorides in alkali chloride melts are

stability increases with increasing of solvent cation radius from Li+ to Cs+ and the apparent standard redox potentials are shifted to more negative values. These results are in good agreement with literature data concerning the second coordination sphere influence on

Using the values of the apparent standard redox potentials the formal free Gibbs energy

LnCl2(l) + ½ Cl2(g) ⇔ LnCl3(l) (38)

\* \*

3 2

*Ln Ln* Δ = *G nFE* + + (39)

changes and the apparent equilibrium constants of the redox reaction (38):

<sup>−</sup> [Papatheodorou & Kleppa, 1974; Yamana et al., 2003]. Their relative

*r n* <sup>+</sup> = *m* ) [Lebedev, 1993] for thulium (-2.720 V) and ytterbium (-1.796 V) at

*Tm Tm <sup>E</sup>* + + are more negative than ytterbium ( 3 2 ) \*

**3**

**4**

*r nm* <sup>+</sup> = ) with data in fused NaCl-KCl-CsCl

*Yt Yb E* + + . The

potentials of thulium ( 3 2 ) \*

eutectic ( . 0.137 *eut*

TmCl3-TmCl2-CsCl

<sup>−</sup> and <sup>2</sup> *LnCl*<sup>4</sup>

apparent standard redox potentials.

**3.2.2 Thermodynamics properties** 

can be calculated using the well-known expressions:

<sup>3</sup> *LnCl*<sup>6</sup>

and

CsCl.

ytterbium (-1.831 V) in molten *CsCl* ( 0.165 *Cs*


**E\*/V**

$$
\Delta G^{\circ} = -RT\ln K\_{eq.}^{\circ} \tag{40}
$$

The temperature dependence of the Gibbs energy change can be described by the following equation:

$$
\Delta \mathbf{G}^\* = \Delta H^\* - T\Delta \mathbf{S}^\* \tag{41}
$$

The experiment data were fitted to the following equations using Software Origin Pro version 7.5:

$$
\Delta G^\circ = -\text{(354.1} \pm 0.6) + \text{(94.5} \pm 0.6) \cdot 10^{-3} T \pm 0.1 \quad \text{kJ/mol} \quad \text{TmCl-NaCl-KCl-CsCl} \tag{42}
$$

$$
\boldsymbol{\Lambda G}^\* = -(249.0 \pm 1.3) + (77.8 \pm 0.1) \cdot 10^{-3} T \pm 0.3 \quad \text{kJ/mol} \quad \text{YbCl-NaCl-KCl-CsCl} \tag{43}
$$

$$
\Delta G^\circ = -(388.8 \pm 0.9) + (119.7 \pm 0.9) \cdot 10^{-3} T \pm 0.2 \quad \text{kJ/mol} \quad \text{TmCl}\_3\text{-CsCl} \tag{44}
$$

$$
\Delta G^\circ = -(237.8 \pm 0.8) + (62.7 \pm 0.7) \cdot 10^{-3} T \pm 0.1 \quad kJ/mol \quad \text{YbCl-} \text{-CsCl} \tag{45}
$$

By the expression (40) one can calculate the apparent equilibrium constants for the redox reaction (38) in fused salts. The temperature dependences are the following:

$$\ln K\_{eq.}^{\*} - 13.78 + \frac{44997}{T} \pm 0.01 \quad \text{TmCl} \text{-NaCl-KCl-CsCl} \tag{46}$$

$$\ln K\_{eq.}^{\*}-10.56 + \frac{31114}{T} \pm 0.01 \quad \text{YbCl3-NaCl-KCl-CsCl} \tag{47}$$

$$\ln K\_{eq.}^{\*} - 14.40 + \frac{46787}{T} \pm 0.02 \quad \text{TmCl3-CsCl} \tag{48}$$

$$\ln K\_{eq.}^{\*} = -7.54 + \frac{28602}{T} \pm 0.01 \quad \text{YbCl}\_{3}\text{-CsCl} \tag{49}$$

The activity coefficients of YbCl3 in fused salts was determined from the difference between the apparent Gibbs free energy derived from the experimental measurements and the standard Gibbs free energy for pure compounds obtained in the literature [Barin, 1994]:

$$\text{Y}\log\gamma\_{\text{Yb}\_3} = -1.23 - \frac{4436}{T} \pm 0.02 \quad \text{YbCl}\_3\text{-NaCl-KCl-CsCl} \tag{50}$$

$$\text{V}\,\log\gamma\_{\text{Yb}\,\text{Cl}\_3} = -2.09 - \frac{3761}{T} \pm 0.02 \quad \text{YbCl}\,\text{-CscCl} \tag{51}$$

The dependence of the activity coefficient of YbCl3 versus the reverse temperature is given by the expressions (50, 51). Database for thulium compounds is absent in the literature [Barin, 1994].

It is also possible to estimate the equilibrium chlorine gas pressure above an alkali metal chloride melts containing hulium or ytterbium tri- and dichlorides for the reaction (52) by

Electrochemistry of Tm(III) and Yb(III) in Molten Salts 281

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Barin, I. (1994). *Thermochemical Data of Pure Substances*, Third Edition, Wiley-VCH, ISBN 3-

Bermejo, M.R., Gomez, J., Medina, J., Martinez, A.M. & Castrillejo, Y. (2006). The

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Bermejo, M.R., Barrado, E., Martinez, A.M. & Castrillejo, Y. (2008). Electrodeposition of Lu

Castrillejo, Y., Bermejo, M.R., Diaz Arocas, P., Martinez, A.M. & Barrado, E. (2005). The

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John Wiley & Sons Inc., ISBN 0-471-05542-5, USA.

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pp. 280-288, ISSN 0013-4686.

527-30993-4, USA.

0022-0728.

0728.

ISSN 0013-4686.

$$\text{LnCl}\_{3(l)} \Leftrightarrow \text{LnCl}\_{2(l)} + \text{l/} \text{Cl}\_{2(g)}\tag{52}$$

well-known equation (53) [Smirnov, 1973]. Such kind of calculations were done for the concentration ratio of [Ln3+]/Ln2+] equals one in fused NaCl-KCl-CsCl eutectic and individual CsCl.

$$\frac{RT}{2F}\ln{P\_{Cl\_2}} = E\_{Ln^{3+}}\prime\_{Ln^{2+}} + \frac{RT}{F}\ln{\frac{Ln^{3+}}{[Ln^{2+}]}}\tag{53}$$

The calculated values are summarized in Table 2. The average value of the radius of these molten mixtures in this line, *pro tanto*, is 0.137; 0.165 nm [Lebedev, 1993]. From the data given in Table 2 one can see that the relative stability of lanthanides(III) complexes ions is naturally increased in the line (NaCl-KCl-CsCl)eut. – CsCl.


Table 2. The comparison of the base thermodynamic properties of Tm and Yb in molten alkali metal chlorides at 973 K. Apparent standard redox potentials are given in the molar fraction scale

#### **4. Conclusion**

The electrochemical behaviour of [ ] <sup>3</sup> *YbCl*<sup>6</sup> <sup>−</sup> ions in fused alkali metal chlorides was investigated. It was found that the reduction of Yb(III) to Yb(II) ions is a reversible process being controlled by the rate of the mass transfer. The diffusion coefficient of [ ] <sup>3</sup> *YbCl*<sup>6</sup> <sup>−</sup> ions was determined at different temperatures in all investigation systems. The apparent standard electrode potential of the redox couple 3 2 *Yb Yb* /<sup>+</sup> <sup>+</sup> was calculated from the analysis of the cyclic voltammograms registered at different temperatures. The apparent standard redox potentials of 3 2 \* *Tm Tm E* <sup>+</sup> <sup>+</sup> and 3 2 \* *Yb Yb E* <sup>+</sup> <sup>+</sup> in molten alkali metal chlorides were also determined by *emf* method. The basic thermodynamic properties of the reactions *TmCl2(l) + ½ Cl2(g)* ⇔ *TmCl3(l*) and *YbCl2(l) + ½ Cl2(g)* ⇔ *YbCl3(l)* were calculated.

The influence of the nature of the solvent (ionic radius) on the thermodynamic properties of thulium and ytterbium compounds was assessed. It was found that the strength of the Ln– Cl bonds increases in the line from Li to Cs cation.

## **5. References**

Barbanel, Ya.A. (1985). *Coordination Chemistry of f-elements in Melts*, Energoatomizdat, Moscow, Russia.

 LnCl3(l) ⇔ LnCl2(l) + ½ Cl2(g) (52) well-known equation (53) [Smirnov, 1973]. Such kind of calculations were done for the concentration ratio of [Ln3+]/Ln2+] equals one in fused NaCl-KCl-CsCl eutectic and

> [ ] ln ln 2 [ ] *Cl Ln Ln RT RT Ln P E F F Ln* + +

The calculated values are summarized in Table 2. The average value of the radius of these molten mixtures in this line, *pro tanto*, is 0.137; 0.165 nm [Lebedev, 1993]. From the data given in Table 2 one can see that the relative stability of lanthanides(III) complexes ions is

properties NaCl-KCl-CsCl CsCl NaCl-KCl-CsCl CsCl E\*/V –2.721 –2.822 –1.796 –1.846 ∆G\*/(kJmol-1) –262.6 –272.3 –173.3 –178.2 ∆H\*/(kJmol-1) –354.1 –388.8 –249.0 –258.7 ∆S\*/(JK-1mol-1) 94.5 119.7 77.8 82.8

γ – – 1.610-6 9.010-7

eq. 1.311014 4.401014 2.08109 3.80109 <sup>2</sup> *pCl* /*Pa* 5.8610-29 1.0510-24 2.3110-19 6.9210-20

Table 2. The comparison of the base thermodynamic properties of Tm and Yb in molten alkali metal chlorides at 973 K. Apparent standard redox potentials are given in the molar

investigated. It was found that the reduction of Yb(III) to Yb(II) ions is a reversible process being controlled by the rate of the mass transfer. The diffusion coefficient of [ ] <sup>3</sup> *YbCl*<sup>6</sup>

was determined at different temperatures in all investigation systems. The apparent standard electrode potential of the redox couple 3 2 *Yb Yb* /<sup>+</sup> <sup>+</sup> was calculated from the analysis of the cyclic voltammograms registered at different temperatures. The apparent

\*

also determined by *emf* method. The basic thermodynamic properties of the reactions

The influence of the nature of the solvent (ionic radius) on the thermodynamic properties of thulium and ytterbium compounds was assessed. It was found that the strength of the Ln–

Barbanel, Ya.A. (1985). *Coordination Chemistry of f-elements in Melts*, Energoatomizdat,

⇔

*Tm Tm E* <sup>+</sup> <sup>+</sup> and 3 2

3 2

+ <sup>+</sup> = + (53)

<sup>−</sup> ions in fused alkali metal chlorides was

*Yb Yb E* <sup>+</sup> <sup>+</sup> in molten alkali metal chlorides were

 *YbCl3(l)* were calculated.

<sup>−</sup> ions

3 2 <sup>2</sup>

Thermodynamic Tm Yb

naturally increased in the line (NaCl-KCl-CsCl)eut. – CsCl.

individual CsCl.

K\*

fraction scale

**4. Conclusion** 

*TmCl2(l) + ½ Cl2(g)*

**5. References** 

The electrochemical behaviour of [ ] <sup>3</sup> *YbCl*<sup>6</sup>

\*

 *TmCl3(l*) and *YbCl2(l) + ½ Cl2(g)*

standard redox potentials of 3 2

⇔

Moscow, Russia.

Cl bonds increases in the line from Li to Cs cation.


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**0**

**12**

*Japan*

Hironori Nakajima *Kyushu University*

**Electrochemical Impedance Spectroscopy Study**

Solid oxide fuel cell (SOFC) has advantages including high efficiency power generation by operation at 500-1000 ◦C, which results in a low environmental load. Moreover, SOFCs provide high quality waste heat, and the use of hydrocarbon fuels such as city gas, liquefied petroleum gas, and alcohol is relatively easy. However, for practical use, optimization of the electrode and electrolyte materials and the structure of the cell are required to improve the performance. In addition, optimization of the operation conditions and improvement of cell

Mass transfers of the fuel and oxygen at the anode and cathode, respectively, greatly affect the cell performance by giving rise to the concentration overpotentials which result in the voltage loss of the cell. The concentration overpotentials including the Nernst loss by the fuel and oxygen depletions in the cell (Li, 2007; Morita et al., 2002) also affect the cell durability since they cause current distribution which leads to temperature distribution in the cell and anode oxidation. The current distribution also prevents effective use of whole electrode areas in a

This chapter describes the concentration overpotentials and current distribution in an intermediate temperature anode-supported microtubular SOFC which can be operated in the temperature range of 500-800 ◦C (IT-SOFC) with an analysis by electrochemical impedance

EIS has been widely employed for the analysis of fuel cells. In particular, the author's group has developed diagnosis methods of operating status of the polymer electrolyte fuel cell (PEFC) by analyzing the variation of resistances and capacitances of equivalent circuit models

For the SOFC, a number of EIS analyses have been reported (Barsoukov & Macdonald, 2005; Esquirol et al., 2004; Horita et al., 2001; Huang et al., 2007; Ishihara et al., 2000; Jiang, 2002; Leonide et al., 2010; McIntosh et al., 2003). Although many of those reports focused on the characterization of developed materials, there were very few reports (Barfod et al., 2007) that analyze each impedance of the anode and cathode in the full cell impedance of a practical cell

spectroscopy (EIS) and cell surface temperature measurements.

simultaneously and separately by applying EIS under operation.

of the PEFC (Konomi & Saho, 2006; Nakajima et al., 2008).

**1. Introduction**

cell geometry.

durability need to be addressed.

**of the Mass Transfer in an Anode-Supported**

**Microtubular Solid Oxide Fuel Cell**

