**2. Principals of the method**

We perform measurements of the EMF or chemical potential across the electrochemical cells with liquid electrolyte, such as:

(-) A | A (n+) in the electrolyte |AxB(1-x) (+) (I)

x represents a molar fraction of component A in liquid or solid alloy AxB(1-x). The component A (usually a pure metal) is the negative electrode, the alloy AxB(1-x) where the component B is more noble than A, is the positive electrode.

The chemical potential of pure metal A (A) *<sup>A</sup>* , is always higher than its chemical potential in the alloy AxB(1-x) or ( (A) *<sup>A</sup>* )> (AxB(1-x)) *<sup>A</sup>* )

$$\Delta\mu\_A = RT \ln(\left(a\_A^{(\text{AxB(1-x)})} / a\_A^{(\text{A})}\right) = RT \ln a \text{ } \text{\textquotedblleft} \text{\textquotedblright} \tag{1}$$

If (A) *Aa = 1*, we can simplify the equation (1) and we have the equation (2).

$$
\Delta\mu\_A = RT \ln(a\_A^{\text{(AxB(1-x))}}) \tag{2}
$$

(A) *A* is the change of the chemical potential of component A in its transition from a pure metal A into an alloy AxB(1-x) in reference conditions. The measurement of EMF as a function of temperature leads to partial thermodynamic functions.

$$
\Delta\mu\_A = \Delta\overline{H}\_A - T \cdot \Delta\overline{S}\_A \tag{3}
$$

$$
\Delta\mu\_A = -\mathbf{n} \cdot \mathbf{F} \cdot \mathbf{E} \tag{4}
$$

$$
\Delta \overline{H}\_A = -\mathbf{n} \cdot \mathbf{F} \cdot \mathbf{a} \tag{5}
$$

$$
\Delta \overline{S}\_A = \mathfrak{n} \cdot F \cdot b \tag{6}
$$

$$
\Delta \overline{S}\_A = - \left( \partial \Delta \mu\_A \;/ \, \partial T \right)\_P = nF \left( \partial \mathbb{E} \;/ \, \partial T \right)\_P \tag{7}
$$

where *b* is *tg*( ) (see Fig.1)

72 Electrochemical Cells – New Advances in Fundamental Researches and Applications

Experimental studies are the primary information sources for thermodynamic properties and phase diagrams of all systems. The method of electromotive force (EMF) is one of the most important methods of the physicochemical analysis. One peculiarity of the EMF is its

Improving the accuracy and reproducibility of measurements leads to the increase of the

temperature *(T)* and atomic fraction *(xi)* obtained with uncertainties of 500 J/mol (especially in a narrow temperature range) give only rough estimates of partial entropy and

temperature *(T)* and atomic fraction *(xi)* from 10 to 50 J/mol not only leads to the various thermodynamic properties of the system (partial entropies ( *<sup>f</sup> Si* ) and enthalpies ( f i H ) of components, phase enthalpies of transformation ( *<sup>f</sup> Hitr*, ), partial enthalpies at infinite

diagram in detail (liquidus and solidus, miscibility gaps, invariant points, stoichiometry

We perform measurements of the EMF or chemical potential across the electrochemical cells

x represents a molar fraction of component A in liquid or solid alloy AxB(1-x). The component A (usually a pure metal) is the negative electrode, the alloy AxB(1-x) where the component B

The chemical potential of pure metal A (A) *<sup>A</sup>* , is always higher than its chemical potential in

*Aa /* (A)

*<sup>A</sup>* <sup>=</sup>*RT ln(* (AxB(1-x))

(A) *A* is the change of the chemical potential of component A in its transition from a pure metal A into an alloy AxB(1-x) in reference conditions. The measurement of EMF as a function

*<sup>A</sup>* <sup>=</sup>*RT ln(* (AxB(1-x))

*Aa = 1*, we can simplify the equation (1) and we have the equation (2).

of temperature leads to partial thermodynamic functions.

), thermal capacities (Сp), but also gives a possibility to study the phase

(-) A | A (n+) in the electrolyte |AxB(1-x) (+) (I)

*Aa ) = RT ln a*

*/a*

*Aa )* (2)

(1)

*i (T, xi)* versus

*i(T, xi)* versus

proportionality to the chemical potential:

*F*=96485.34 C/mol is the constant of Faraday,

*E* is electromotive force.

enthalpy of the components.

deviations, ordering, etc...)

**2. Principals of the method** 

with liquid electrolyte, such as:

is more noble than A, is the positive electrode.

the alloy AxB(1-x) or ( (A) *<sup>A</sup>* )> (AxB(1-x)) *<sup>A</sup>* )

dilution ( *<sup>f</sup> Hi*

If (A)

*E* of one of the system components,

where *n* is a charge of the ion responsible for the potential,

quality and quantity of information about the system. Values of

An accuracy improvement in determining of the chemical potential *(*

*i = nF*

$$
\Delta \overline{H}\_A = \Delta \mu\_A + T \Delta \overline{S}\_A = nF \left[ T \left( \hat{\varepsilon} \mathbb{E} \left/ \hat{\varepsilon} T \right\rangle\_\mathbb{P} - E \right] \tag{8}
$$

Fig. 1. Graphical relation of measured values E(T) with partials thermodynamic functions a = - *HA* and b = *SA* .

The integral thermodynamic functions can be calculated with help of Gibbs-Duhem or Gibbs-Duhem- Margules equations:

Gibbs-Duhem equation for the two-component system AB is:

$$
\Delta\Phi = \mathbf{x}\_1 \Delta\overline{\Phi}\_1 + (1 - \mathbf{x}\_1) \Delta\overline{\Phi}\_2 \tag{9}
$$

The Margules equation is generalized by Gibbs-Duhem equation:

$$
\Delta\Phi = \left(1 - \chi\_i\right) \int\_0^{\chi\_1/1 - \chi\_1} \Delta\overline{\Phi}\_A d\left(\frac{\chi\_1}{1 - \chi\_1}\right) \tag{10}
$$

The partial and integral thermodynamic values are presented by the terms *Фi* and *Ф* , respectively.

Electrochemical Cells with the Liquid Electrolyte

the solidus line.

in the Study of Semiconductor, Metallic and Oxide Systems 75

If the alloy is sufficiently plastic, its can be drilled with a hole a little larger than the diameter the conductor wire and compress with the vise. Sometimes, the reference electrodes or measuring one are extremely fragile, and it is impossible to ensure good contact between the wire and the sample. In this case, we prepare the mechanic mixture of powder studied alloys with powder or filling of a more plastic inert metal and then we press the pellets. This added inert plastic metal serves as a matrix of the studied material. For this reason tantalum fillings are mixed in proportion 1:1. We used this procedure in forming the reference manganese electrodes (Vassiliev et al., 1993). It is better to work with the pellets (Vassiliev et al., 1968). Sometimes using the samples in the form of ingot leads to distortion of the measurement results of the EMF, especially if these measurements are made lower of solidus temperature (Terpilowski et al., 1965). If the study of alloys is carried out over a wide temperature range, from liquid homogeneous state to mixed solid-liquid and then to solid states, the EMF measurements are reliable if they are carried out at the complete solide state (of the studied phases) but the temperature should not be more than 100-150 K below

Fig. 2.The four-part dismountable mold is shown in this picture: 1-punch, 2-four-section dismountable block cylinder from high strength tempered steel, 3 - constricting clamp with

twotightening bolts, 4 – support with groove for tungsten wire.

If we can ignore the homogeneity regions of the intermediate phases of certain binary phase diagram, we can calculate the integral properties of these phases by combining equations.

For example, the system lutetium-indium in the region 0-50 at % Lu has two intermediate phases of 1:2.5 and 1:1. Calculation of the thermodynamic integral properties is easily carried out, if we have in our possession, the partial thermodynamic properties of these phases:

Lu+ 2.5In LuIn2.5 ' *<sup>f</sup>ФLu* is partial thermodynamic value of formation LuIn2.5 for one mole of lutetium

Lu +0.667 LuIn 2.5 '' *<sup>f</sup>ФLu* is partial thermodynamic value of formation LuIn for one mole of lutetium.

Combining these equations permits to determine the integral properties of LuIn phase.

0.667Lu + 2.5 In LiIn2.5 ' *<sup>f</sup>ФLu* 2.5 *Ф*( ) *LuIn* Lu+0.667In1.667 LuIn '' *<sup>f</sup>ФLu* 1.667Lu+ 1.667In1.667 LuIn ' '' *<sup>f</sup> Lu <sup>f</sup> Lu*

The integral functions of Lu2In5 and LuIn phases are equal for one mole-atom:

$$
\Delta\_f \Phi^\cdot(L\mu\_2 I \nu\_5) = 2\Delta \overline{\Phi}^\cdot\_{L\mu} / \,\, ^\prime \Gamma
$$

''' '' ( ) (0.667 ) /1.667 2 *f f LuIn Lu <sup>f</sup> Lu*

### **3. Main experimental steps**

Here are the main experimental steps of the EMF method:


#### **3.1 Synthesis of alloys and preparation of the electrodes**

The alloy preparation techniques are different and depend on the work objectives. A study of the systems in the liquid state does not require such special treatment as annealing, while a study of alloys in solid state requires annealing for several days. And then it is necessary to avoid working with alloy ingots. As a rule we use the pellets fabricated from powedered alloys. For this reason the dismountable mold is best suited. For this reason it is necessary to use the dismountable mold (Fig.2). The internal party of this mold consists of dismountable block cylinder from high strength tempered steel of four sections (Fig.3). To fabricate a pellet we introduce the tungsten wire (diameter 0.5 mm) throughout special groove of support. Then we untroduce the powedered alloys and press the pellet by punch, using the hydrolic press. The contact between the pellet and the tungsten wire must be well secured.

If we can ignore the homogeneity regions of the intermediate phases of certain binary phase diagram, we can calculate the integral properties of these phases by combining equations. For example, the system lutetium-indium in the region 0-50 at % Lu has two intermediate phases of 1:2.5 and 1:1. Calculation of the thermodynamic integral properties is easily carried out, if we have in our possession, the partial thermodynamic properties of these

Lu+ 2.5In LuIn2.5 ' *<sup>f</sup>ФLu* is partial thermodynamic value of formation LuIn2.5 for one mole

Lu +0.667 LuIn 2.5 '' *<sup>f</sup>ФLu* is partial thermodynamic value of formation LuIn for one mole

0.667Lu + 2.5 In LiIn2.5 ' *<sup>f</sup>ФLu* 2.5 *Ф*( ) *LuIn*

Lu+0.667In1.667 LuIn '' *<sup>f</sup>ФLu*

1.667Lu+ 1.667In1.667 LuIn ' '' *<sup>f</sup> Lu <sup>f</sup> Lu*

' ' 2 5 ( ) 2 /7 *f L Lu In <sup>u</sup>*

' '' ( ) (0.667 ) /1.667 2 *f f LuIn Lu <sup>f</sup> Lu*

The alloy preparation techniques are different and depend on the work objectives. A study of the systems in the liquid state does not require such special treatment as annealing, while a study of alloys in solid state requires annealing for several days. And then it is necessary to avoid working with alloy ingots. As a rule we use the pellets fabricated from powedered alloys. For this reason the dismountable mold is best suited. For this reason it is necessary to use the dismountable mold (Fig.2). The internal party of this mold consists of dismountable block cylinder from high strength tempered steel of four sections (Fig.3). To fabricate a pellet we introduce the tungsten wire (diameter 0.5 mm) throughout special groove of support. Then we untroduce the powedered alloys and press the pellet by punch, using the hydrolic press.

The integral functions of Lu2In5 and LuIn phases are equal for one mole-atom:

''

Here are the main experimental steps of the EMF method: synthesis of alloys and preparation of the electrodes,

 dehydration of salt mixture and preparation of the electrolyte, different types of electrochemical cell and its assembly.

The contact between the pellet and the tungsten wire must be well secured.

**3.1 Synthesis of alloys and preparation of the electrodes** 

**3. Main experimental steps** 

Combining these equations permits to determine the integral properties of LuIn phase.

phases:

of lutetium

of lutetium.

If the alloy is sufficiently plastic, its can be drilled with a hole a little larger than the diameter the conductor wire and compress with the vise. Sometimes, the reference electrodes or measuring one are extremely fragile, and it is impossible to ensure good contact between the wire and the sample. In this case, we prepare the mechanic mixture of powder studied alloys with powder or filling of a more plastic inert metal and then we press the pellets. This added inert plastic metal serves as a matrix of the studied material. For this reason tantalum fillings are mixed in proportion 1:1. We used this procedure in forming the reference manganese electrodes (Vassiliev et al., 1993). It is better to work with the pellets (Vassiliev et al., 1968). Sometimes using the samples in the form of ingot leads to distortion of the measurement results of the EMF, especially if these measurements are made lower of solidus temperature (Terpilowski et al., 1965). If the study of alloys is carried out over a wide temperature range, from liquid homogeneous state to mixed solid-liquid and then to solid states, the EMF measurements are reliable if they are carried out at the complete solide state (of the studied phases) but the temperature should not be more than 100-150 K below the solidus line.

Fig. 2.The four-part dismountable mold is shown in this picture: 1-punch, 2-four-section dismountable block cylinder from high strength tempered steel, 3 - constricting clamp with twotightening bolts, 4 – support with groove for tungsten wire.

Electrochemical Cells with the Liquid Electrolyte

(Vassiliev et al., 1968).

(Morachevski et al. 2003).

in the Study of Semiconductor, Metallic and Oxide Systems 77

Fig. 4. Device for obteing of gazeous hydrogen cloride: 1- Container of concentrated sulfuric acide, 2- Tap, 3- Glass grandings, 4- Vial for potassium cloride, 5- U-shaped tube for zeolites,

chloride (dried under vacuum at temperature of 200°C) is used as a water absorbent for glycerol and also for creating an ionic conductivity of the electrolyte with chloride (AClx)

There are many examples of construction of electrochemical cells, proposed in the literature

**3.3 Different types of electrochemical cells and their assembly** 

6- Quartz tube, 7- Quartz beaker with a spout, 8- Molten electrolyte, 9- Furnace.

**Mixtures of salts Tm°C**  55.5 NaI - 44.5 KI 585 38.0 NaCl - 62.0 CaCl2 500 32.9 LiCl - 34.8 NaCl - 32.3 KCl 357 46.0 LiCl - 54.0 KCl 352 48.LiBr – 52.0 KBr 348 29.75 LiCl – 64.77 KCl - 5.48 CaCl2 320 30.3 LiCl – 69.7 RbCl 312 28.97 LiCl – 4.42 NaCl – 66.61 CsCl 299 45.0 LiBr – 55.0 RbBr 270 52.7 LiI – 47.3 KI 260 54.0 CH3COOH – 46.0 CH3COONa 233 70.0 ZnCl2 – 18 KCl – 12 NaCl 206 69.5 AlCl3 – 30.5 NaCl 152 *Solution of CaCl2 in the glycerole 40 - 180*  Table 1. Eutectic mixtures of halides (weight percent) used for preparation of electrolyte.

Fig. 3. Internal four-section dismountable block cylinder of molder (2) and support with groove (4).

#### **3.2 Salt mixture dehydratation and preparation of the electrolyte**

It is necessary to pay special attention to the preparation of salts of the electrolyte. They must be dried very carefully. It applies especially to Li, Ca, Zn and Al halides. These salts are extremely hygroscopic, and their melting without special dehydration leads to the formation oxyhalogenides which presence must be avoided. The used electrolyte in the liquid state must be completely transparent and shows no disorder or heterogeneity. The ingots of electrolyte can be stored in sealed Pyrex ampoules. Upon introduction of the electrolyte in a cell, contact with air should be minimal (no more than 10 seconds). Dehydration salts (eg LiCl + RbCl) must pass under pumping with a slowly increasing heating for 5 days to prevent formation of hydroxides. Then the dehydrated salt mixture is transferred to a silica beaker preheated to 500°C in an electrical furnace. To remove oxychlorides, the molten salts are treated with dry hydrochloride gas (HCl). Hydrogen chloride can easily be synthesized by reacting potassium chloride (KCl) or sodium chloride (NaCl) by reaction of concentrated sulfuric acid (H2SO4) (Fig.4):

$$\text{KCl} + \text{H}\_2\text{SO}\_4 \rightarrow \text{KHSO}\_4 + \text{HCl} \\ \uparrow$$

KHSO4 + H2SO4→ K2SO4 + HCl (with gentle heating).

Hydrogen chloride must be dried using zeolites loaded into a U-tube. The gas is bubbled through the melt until there are no suspended particles (about 1h).The melt prepared in this way is poured into Pyrex ampoules with a neck, which are sealed then. The electrolyte can be stored indefinitely in sealed Pyrex ampoules and may be used as required. In practice, it is possible to use the different eutectic mixtures of halides (See Table 1).

The study of some systems such as chalcogenides of zinc, cadmium, mercury, thallium, bismuth, etc. (binary or multicomponent) can be achieved in "low temperature" cell. In this case the calcium chloride (CaCl2) is dissolved in glycerol between 40 and 180°C. Calcium

Fig. 3. Internal four-section dismountable block cylinder of molder (2) and support with

It is necessary to pay special attention to the preparation of salts of the electrolyte. They must be dried very carefully. It applies especially to Li, Ca, Zn and Al halides. These salts are extremely hygroscopic, and their melting without special dehydration leads to the formation oxyhalogenides which presence must be avoided. The used electrolyte in the liquid state must be completely transparent and shows no disorder or heterogeneity. The ingots of electrolyte can be stored in sealed Pyrex ampoules. Upon introduction of the electrolyte in a cell, contact with air should be minimal (no more than 10 seconds). Dehydration salts (eg LiCl + RbCl) must pass under pumping with a slowly increasing heating for 5 days to prevent formation of hydroxides. Then the dehydrated salt mixture is transferred to a silica beaker preheated to 500°C in an electrical furnace. To remove oxychlorides, the molten salts are treated with dry hydrochloride gas (HCl). Hydrogen chloride can easily be synthesized by reacting potassium chloride (KCl) or sodium chloride

KCl + H2SO4 → KHSO4 + HCl

KHSO4 + H2SO4→ K2SO4 + HCl (with gentle heating). Hydrogen chloride must be dried using zeolites loaded into a U-tube. The gas is bubbled through the melt until there are no suspended particles (about 1h).The melt prepared in this way is poured into Pyrex ampoules with a neck, which are sealed then. The electrolyte can be stored indefinitely in sealed Pyrex ampoules and may be used as required. In practice, it

The study of some systems such as chalcogenides of zinc, cadmium, mercury, thallium, bismuth, etc. (binary or multicomponent) can be achieved in "low temperature" cell. In this case the calcium chloride (CaCl2) is dissolved in glycerol between 40 and 180°C. Calcium

**3.2 Salt mixture dehydratation and preparation of the electrolyte** 

(NaCl) by reaction of concentrated sulfuric acid (H2SO4) (Fig.4):

is possible to use the different eutectic mixtures of halides (See Table 1).

groove (4).

Fig. 4. Device for obteing of gazeous hydrogen cloride: 1- Container of concentrated sulfuric acide, 2- Tap, 3- Glass grandings, 4- Vial for potassium cloride, 5- U-shaped tube for zeolites, 6- Quartz tube, 7- Quartz beaker with a spout, 8- Molten electrolyte, 9- Furnace.


Table 1. Eutectic mixtures of halides (weight percent) used for preparation of electrolyte.

chloride (dried under vacuum at temperature of 200°C) is used as a water absorbent for glycerol and also for creating an ionic conductivity of the electrolyte with chloride (AClx) (Vassiliev et al., 1968).
