**5.6 Issues are related to the valence of An+ ion**

To obtain good experimental results, it is necessary to know rigorously the ion charge that is responsible for the EMF in cell of type (I). However, the difference in activities of pure metal A and alloy AxB(1-x) can lead to different charges of the An+ ion in the vicinity of the electrodes A and AxB(1-x). In this case, even in open circuit, a spontaneous transfer of component A to alloys AxB(1-x) is possible and a constant drift of the EMF occurs over time.

Electrochemical Cells with the Liquid Electrolyte

in the Study of Semiconductor, Metallic and Oxide Systems 93

Fig. 17. Kinetics of the exchange reaction of the alloy number 2 at the T=755K.

Fig. 18. Kinetics of the exchange reaction of the alloy number 5 at T=755K.

different parts of cell in electrolyte:

On the cathode: (m-n) A + nAm+ mAn+ On the anode: mAn+ (m-n) A + nAm+

This relates to the ions of metal that may have the different charges of ions (m> n) in

So, in the case of open circuit, there is a transfer of component A from pure metal to its alloy AxB(1-x). Near the cathode, the fraction of charged ions (n +) will be greater and near anode around of the alloy AxB(l-x) will be smaller. In another words, there is dissolution of pure metal and deposit on the surface of alloy AxB(1-x). The transfer is even faster than the temperature T and the concentration of Am+ ions is higher and the distance between electrodes is smaller. A metal is transferred through an electrolyte by ions of lower charge.

Fig. 15. EMF of alloy number 2 versus temperature and time.

Fig. 16. EMF of alloy number 5 versus temperature and time.

Fig. 15. EMF of alloy number 2 versus temperature and time.

Fig. 16. EMF of alloy number 5 versus temperature and time.

Fig. 17. Kinetics of the exchange reaction of the alloy number 2 at the T=755K.

Fig. 18. Kinetics of the exchange reaction of the alloy number 5 at T=755K.

This relates to the ions of metal that may have the different charges of ions (m> n) in different parts of cell in electrolyte:

On the cathode: (m-n) A + nAm+ mAn+

On the anode: mAn+ (m-n) A + nAm+

So, in the case of open circuit, there is a transfer of component A from pure metal to its alloy AxB(1-x). Near the cathode, the fraction of charged ions (n +) will be greater and near anode around of the alloy AxB(l-x) will be smaller. In another words, there is dissolution of pure metal and deposit on the surface of alloy AxB(1-x). The transfer is even faster than the temperature T and the concentration of Am+ ions is higher and the distance between electrodes is smaller. A metal is transferred through an electrolyte by ions of lower charge.

If an activity of component A in the cell of type (I) is reduced, it is possible to determine the thermodynamic properties even in cases of spontaneous transfer of the component A. In this case, it is necessary to take as reference electrode some electrode binary alloy AxC(1-x) , which the thermodynamic properties are well known, and it can substitute the pure metal A.

Then we have

$$
\Delta\mu\_{\rm A} = \text{RT} \cdot \ln\left(\text{a}^{\text{\tiny}}/\text{a}^{\text{\tiny}}\right) \tag{15}
$$

Electrochemical Cells with the Liquid Electrolyte

in the Study of Semiconductor, Metallic and Oxide Systems 95

correspond of thermodynamic equilibrium, because the surface of alloy is depleted by the elements of the smaller density. Especially it should be taken into account that the metallic systems with a miscibility gap. Table 6 shows the specific density of some metals. The liquation problem was noted by us in the investigation of systems based on ternary zinclead alloys (Zn-Pb-Sn, Zn-Pb-In) (David at al., 2004) and In-Sn-Ag and In-Bi-Ag (Vassiliev et al., 1998c). We observed hysteresis loops during heating and cooling of the cells in a wide temperature range for a number of alloys. In the case of the hysteresis loop, it is necessary to choose measurement results only when the temperature is lowered, starting from the homogeneous liquid region. The isothermal cell is also well serves for the thermodynamic study of metals with high vapor pressure (mercury, zinc, etc.) (Vassiliev et al., 1990; David at al., 2004). We did not observe any evaporation of zinc, even though long-term

measurements (more than two months and the temperature to 780 K) were taken.

type of electrochemical cell for EMF measuring has been used:

**measurements of ternary Pb-Sn-Sb system** 

In the systems based on zinc, the latter serves as the reference electrode and the part of both the internal calibration of the thermocouple in the cell, because the measured values E (T) give a clear kink at the melting point of zinc. The kinetic curve of solidification or melting of the metal also exhibits a characteristic jump EMF at the melting point. Such curve is easily obtained by continuous measurement of the EMF of the cell at the phase transition sol ⇆ liq. The zinc chloride must not be added to electrolyte previously. We found that the ions, forming the potential, appeared in a few hours inside the cell after the experiment began. We used the metals of 99.999% and chlorides of lithium and potassium 99.99% purity. The

Temperature range of research is limited one hand by the crystallization of the electrolyte, and on the other hand by the softening Pyrex glass. Control of the state reference electrodes of pure zinc in the course of the experiment was carried out by measuring the difference of EMF between such electrodes. If the cell functions normally, this difference is about 5 V.

Temperature correction is performed by the melting point of zinc, located in the cell.

**5.8 How to study the systems with closely spaced electrode potentials. The EMF** 

EMF measurements of the ternary system Pb-Sn-Sb (Vassiliev et al., 1995) were carried out for five alloys along the isopleth (Pb-Sn0.5Sb0.5) with xPb = 0.15, 0.20, 0.25, 0.30, 0.333 at temperatures 690 - 820K. Alloy Sn0.5Sb0.5. has been used as a reference electrode. Scheme for EMF measuring and the definition of excess functions of mixing in the ternary system Pb-Sn-Sb are shown in Fig. 19 and 20*.* To measure the EMF we can not use the alloys of the ternary Pb-Sn-Sb system as reference electrodes from pure metals. The using of tin or lead in a cell with undivided space is impossible, because their electrode potentials are almost equal and the exchange reactions take place. Cell with a diaphragm (Shourov, 1974, 1984) allows solving this problem, but the experiment is very laborious. In order to avoid the exchange reaction, we choose an alloy of tin and antimony with a component ratio 1:1 (Sn0.5Sb0.5) as the reference electrode, which chemical potential we studied in this paper using an isothermal cell without diaphragm. Activity of tin *aSn* in the Sn0.5Sb0.5 alloy at 900K is equal 0.41, that is much less than its activity in pure tin (aSn=1). So, the activity of lead becomes comparable with the activity of tin when we study the ternary alloys (Sn0.5Sb0.5)1-xPbx. Thus,

(-) Zn Zn2+ in (LiCl + KCl) liquid eutectic PbxSnyZnZ (+) (IV)

In this case the activity (*a'*) is less than 1. The difference of the chemical potential of component A between electrodes, and hence, the electromotive force will be smaller.

This problem is encountered when the system Ln -Te (Ln = lanthanide) was studied with the cell:

$$\text{(-)}\,\text{Ln} \mid \text{Ln}^{\text{(3\*)}}\text{in }\text{electrolyte} \mid \text{Ln}\_{\text{x}}\text{Te}\_{\text{(1-x)}}\text{(+)}$$

$$
\Delta\mu\_A = RT \cdot Ln \left( a\_A^{A\_x B\_{(1-x)}} \; / \; a\_A^{A\_x C\_{(1-x)}} \right),
$$

Alloys, rich in metal B (in this case by tellurium) generate an electromotive force E near 1.5 V. The substitution of the lanthanide by one of its alloys of Ln-In system (Vassiliev et al., 2009), allows to make the measurements with the following electrochemical cell:

$$a\_A^{A\_\pi \mathbb{C}\_{(1-x)}} < a\_A^{(A)} = 1$$

$$\text{(-)}\,\text{LnIn}\_{2,5}\text{+}\text{ln} \mid \text{La}^{\text{(3+)}}\text{ in electrolyte} \mid \text{Ln}\_{\text{x}}\text{Te}\_{\text{(l-x)}}\text{(+)}\tag{\text{III}}$$

The electromotive force of the cell is as twice as smaller and spontaneous transfer becomes negligible.

#### **5.7 Problem of liquation (or phase separation) of liquid alloys**

If the metal liquid system does not contain any components that provoke the exchange reactions in an electrochemical cell, the EMF method is well suited for such a system. The problem of liquation (or phase separation) is less serious, but the big difference of the specific density of alloying effects on the rate of establishment of thermodynamic equilibrium and distorts the potentiometric measurements.


Table 6. Specific density (g/cm3) of some metals.

The more the difference of the specific density of elements and their chemical interaction are weaker, the liquation influence is greater. As a consequence, the EMF measurements do not

If an activity of component A in the cell of type (I) is reduced, it is possible to determine the thermodynamic properties even in cases of spontaneous transfer of the component A. In this case, it is necessary to take as reference electrode some electrode binary alloy AxC(1-x) , which the thermodynamic properties are well known, and it can substitute the pure metal A.

In this case the activity (*a'*) is less than 1. The difference of the chemical potential of

This problem is encountered when the system Ln -Te (Ln = lanthanide) was studied with

(-) Ln Ln(3+)in electrolyte LnxTe(1-x) (+)

*<sup>A</sup> RT Ln a a A A* 

Alloys, rich in metal B (in this case by tellurium) generate an electromotive force E near 1.5 V. The substitution of the lanthanide by one of its alloys of Ln-In system (Vassiliev et al.,

> (1 ) ( ) 1 *A Cx x <sup>A</sup> A A a a*

The electromotive force of the cell is as twice as smaller and spontaneous transfer becomes

If the metal liquid system does not contain any components that provoke the exchange reactions in an electrochemical cell, the EMF method is well suited for such a system. The problem of liquation (or phase separation) is less serious, but the big difference of the specific density of alloying effects on the rate of establishment of thermodynamic

The more the difference of the specific density of elements and their chemical interaction are weaker, the liquation influence is greater. As a consequence, the EMF measurements do not

Element Specific density (g/cm3) Element Specific density (g/cm3)

2009), allows to make the measurements with the following electrochemical cell:

**5.7 Problem of liquation (or phase separation) of liquid alloys** 

equilibrium and distorts the potentiometric measurements.

Table 6. Specific density (g/cm3) of some metals.

Al 2.7 Cu 8.94 Sn 5.85 Bi 9.80 Zn 7.13 Ag 10.50 In 7.31 Pb 11.34

(1 ) (1 ) / *AB AC xx xx*

(-) LnIn2,5+In La(3+) in electrolyte LnxTe(1-x) (+) (III)

component A between electrodes, and hence, the electromotive force will be smaller.

A = RT ln ( a"/a') (15)

Then we have

the cell:

negligible.

correspond of thermodynamic equilibrium, because the surface of alloy is depleted by the elements of the smaller density. Especially it should be taken into account that the metallic systems with a miscibility gap. Table 6 shows the specific density of some metals. The liquation problem was noted by us in the investigation of systems based on ternary zinclead alloys (Zn-Pb-Sn, Zn-Pb-In) (David at al., 2004) and In-Sn-Ag and In-Bi-Ag (Vassiliev et al., 1998c). We observed hysteresis loops during heating and cooling of the cells in a wide temperature range for a number of alloys. In the case of the hysteresis loop, it is necessary to choose measurement results only when the temperature is lowered, starting from the homogeneous liquid region. The isothermal cell is also well serves for the thermodynamic study of metals with high vapor pressure (mercury, zinc, etc.) (Vassiliev et al., 1990; David at al., 2004). We did not observe any evaporation of zinc, even though long-term measurements (more than two months and the temperature to 780 K) were taken.

In the systems based on zinc, the latter serves as the reference electrode and the part of both the internal calibration of the thermocouple in the cell, because the measured values E (T) give a clear kink at the melting point of zinc. The kinetic curve of solidification or melting of the metal also exhibits a characteristic jump EMF at the melting point. Such curve is easily obtained by continuous measurement of the EMF of the cell at the phase transition sol ⇆ liq. The zinc chloride must not be added to electrolyte previously. We found that the ions, forming the potential, appeared in a few hours inside the cell after the experiment began. We used the metals of 99.999% and chlorides of lithium and potassium 99.99% purity. The type of electrochemical cell for EMF measuring has been used:

$$\text{(-)}\,\text{Zn} \mid \text{Zn}^{2+} \text{ in (LiCl} + \text{KCl)} \text{ liquid} \,\text{uteectic} \mid \text{Pb}\_x\text{Sn}\_y\text{Zn}\_Z\text{(+)} \tag{\text{IV}}$$

Temperature range of research is limited one hand by the crystallization of the electrolyte, and on the other hand by the softening Pyrex glass. Control of the state reference electrodes of pure zinc in the course of the experiment was carried out by measuring the difference of EMF between such electrodes. If the cell functions normally, this difference is about 5 V. Temperature correction is performed by the melting point of zinc, located in the cell.

### **5.8 How to study the systems with closely spaced electrode potentials. The EMF measurements of ternary Pb-Sn-Sb system**

EMF measurements of the ternary system Pb-Sn-Sb (Vassiliev et al., 1995) were carried out for five alloys along the isopleth (Pb-Sn0.5Sb0.5) with xPb = 0.15, 0.20, 0.25, 0.30, 0.333 at temperatures 690 - 820K. Alloy Sn0.5Sb0.5. has been used as a reference electrode. Scheme for EMF measuring and the definition of excess functions of mixing in the ternary system Pb-Sn-Sb are shown in Fig. 19 and 20*.* To measure the EMF we can not use the alloys of the ternary Pb-Sn-Sb system as reference electrodes from pure metals. The using of tin or lead in a cell with undivided space is impossible, because their electrode potentials are almost equal and the exchange reactions take place. Cell with a diaphragm (Shourov, 1974, 1984) allows solving this problem, but the experiment is very laborious. In order to avoid the exchange reaction, we choose an alloy of tin and antimony with a component ratio 1:1 (Sn0.5Sb0.5) as the reference electrode, which chemical potential we studied in this paper using an isothermal cell without diaphragm. Activity of tin *aSn* in the Sn0.5Sb0.5 alloy at 900K is equal 0.41, that is much less than its activity in pure tin (aSn=1). So, the activity of lead becomes comparable with the activity of tin when we study the ternary alloys (Sn0.5Sb0.5)1-xPbx. Thus,

Electrochemical Cells with the Liquid Electrolyte

(Sn0.5Sb0.5)0.80Pb0.20 , 5- (Sn0.5Sb0.5)0.85Pb0.15

**5.9 Pb-Pd system** 

in the Study of Semiconductor, Metallic and Oxide Systems 97

Fig. 21. Dependence E (T) cell and compositions of alloys (-)Sn0.5Sb0.5KCl+LiCl+Sn2+ (Sn0.5Sb0.5)1-xPbx(+) 1-(Sn0.5Sb0.5)0.666Pb0.333 , 2- (Sn0.5Sb0.5)0.70Pb0.30 , 3- (Sn0.5Sb0.5)0.75Pb0.25 , 4-

ratio (16) to find the chemical potential of ternary alloys relatively to pure tin:

alloy Sn0.5Sb0.5 and the reference electrode from pure tin.

Pb2Pd phase and the coordinates of the eutectic point.

There were obtained 39 experimental points E(T) for each ternary alloy with a maximum error ± 0.1 mV. The coefficients of linear equations Е1(Т) of ternary alloys (1-5) was obtained with respect to the reference electrode Sn0.5Sb0.5. The correction was performed using the

Where the dependence Е2(Т) (Е2/mV= 10.52+26.510-3Т) was obtained between the liquid

Finally, let us consider an example of the Pb-Pd phase diagram that has several intermediate phases Fig.22 (Vassiliev et al., 1998a). We have established a narrow region of homogeneity of the phases Pb2Pd and Pb9Pd13, and the deviation from stoichiometry of PbPd phase. We have determined also the coordinates of the gamma phase, and refined the melting point of

General trend of experimental EMF results versus temperature and composition for the Pb-Pd system is shown in the Fig.23. The points at the right of curves L2-L6 correspond to the homogeneous liquid alloys with xPd from 0.10 to 0.60). The curves L2-L6 correspond to the heterogeneous alloys (liquid and solid states). The lines at the left of the curves L2-L6 correspond to the heterogeneous solid alloys from S2 to S8 (see, please, Fig.23). Monophasic supercooled liquid alloys are on the left of lines L2-L4 with xPd from 0.25 to 0.40. Points of intersections of the lines S5 and S8, S2 and S7 , S4 and S6 correspond to the phase

*Sn* = Е1(Т)+Е2(Т) (16)

we have practically eliminated the exchange reaction between the electrodes with different contents of tin and lead. The choice of electrode Sn0.5Sb0.5 allowed us to obtain stable and reproducible results E (T) (Fig.21).

Fig. 19. Measurements of EMF ( *<sup>E</sup> Sn* )in the ternary Pb-Sn-Sb system*.* 

Fig. 20. Scheme for determining the excess functions of mixing of the ternary Pb-Sn-Sb system.

we have practically eliminated the exchange reaction between the electrodes with different contents of tin and lead. The choice of electrode Sn0.5Sb0.5 allowed us to obtain stable and

Fig. 19. Measurements of EMF ( *<sup>E</sup> Sn* )in the ternary Pb-Sn-Sb system*.* 

Fig. 20. Scheme for determining the excess functions of mixing of the ternary Pb-Sn-Sb

reproducible results E (T) (Fig.21).

system.

Fig. 21. Dependence E (T) cell and compositions of alloys (-)Sn0.5Sb0.5KCl+LiCl+Sn2+ (Sn0.5Sb0.5)1-xPbx(+) 1-(Sn0.5Sb0.5)0.666Pb0.333 , 2- (Sn0.5Sb0.5)0.70Pb0.30 , 3- (Sn0.5Sb0.5)0.75Pb0.25 , 4- (Sn0.5Sb0.5)0.80Pb0.20 , 5- (Sn0.5Sb0.5)0.85Pb0.15

There were obtained 39 experimental points E(T) for each ternary alloy with a maximum error ± 0.1 mV. The coefficients of linear equations Е1(Т) of ternary alloys (1-5) was obtained with respect to the reference electrode Sn0.5Sb0.5. The correction was performed using the ratio (16) to find the chemical potential of ternary alloys relatively to pure tin:

$$
\mu\_{\rm Sn} = \text{E}\_1(\text{T}) + \text{E}\_2(\text{T}) \tag{16}
$$

Where the dependence Е2(Т) (Е2/mV= 10.52+26.510-3Т) was obtained between the liquid alloy Sn0.5Sb0.5 and the reference electrode from pure tin.

#### **5.9 Pb-Pd system**

Finally, let us consider an example of the Pb-Pd phase diagram that has several intermediate phases Fig.22 (Vassiliev et al., 1998a). We have established a narrow region of homogeneity of the phases Pb2Pd and Pb9Pd13, and the deviation from stoichiometry of PbPd phase. We have determined also the coordinates of the gamma phase, and refined the melting point of Pb2Pd phase and the coordinates of the eutectic point.

General trend of experimental EMF results versus temperature and composition for the Pb-Pd system is shown in the Fig.23. The points at the right of curves L2-L6 correspond to the homogeneous liquid alloys with xPd from 0.10 to 0.60). The curves L2-L6 correspond to the heterogeneous alloys (liquid and solid states). The lines at the left of the curves L2-L6 correspond to the heterogeneous solid alloys from S2 to S8 (see, please, Fig.23). Monophasic supercooled liquid alloys are on the left of lines L2-L4 with xPd from 0.25 to 0.40. Points of intersections of the lines S5 and S8, S2 and S7 , S4 and S6 correspond to the phase

Electrochemical Cells with the Liquid Electrolyte

quaternary systems:

for the oxide systems also.

**7. Acknowledgements** 

**8. References** 

**6. Conclusion** 

in the Study of Semiconductor, Metallic and Oxide Systems 99

We applied successfully the described technique for different binary, ternary and

Tl-S (Vassiliev et al., 1971,1973a, 1973b, 2008), Tl-Se (Vassiliev et al., 1967,1969,1971), Tl-Te (Vassiliev et al., 1968); Cd-Te (Vassiliev et al., 1990); **Pb-Pd** (Vassiliev et al., 1998a); In-P (Vassiliev & Gachon, 2006); In-As (Abbasov et al., 1964); In-Sb (Vassiliev, 2004); In-Sn (Vassiliev et al., 1998b); Ga-As (Abbasov et al., 1964); Ga-Sb (Abbasov et al., 1964); Sn-Sb (Vassiliev 1997, 2005); Bi-Se (Vassiliev et al., 1968); Ga-Te (Abbasov et al., 1964); Mn-Te (Vassiliev et al., 1993); Rare Earth Metals (REM) with In (Vassiliev et al., 2009), Sb (Gorjacheva et al.,1981), Pb (Vassiliev et al., 1993), Te (Vassiliev et al., 1980); Cd-Hg-Te (Vassiliev et al., 1990,2004); In-Sn-Sb (Vassiliev et al., 2001); **Pb-Sn-Sb** (Vassiliev et al., 1995); Pb-Sn-Zn (David at al., 2004) In-Bi-Ag (Vassiliev et al., 1998c); In-Ni-Sb Vassiliev et al., 2003); Pb-Cu-Zn; Pb-In-Zn; Pb-In-Zn-Sn (Hertz at al., 1998). As well as, this technic can be applied

The accuracy of the proposed experimental technique does not yield the best calorimetric measurements and completeness of the information obtained by the EMF exceeds the calorimetric methods in some case. So, the proposed variant of the EMF can be called as universal and self-sufficient, and the cost of equipment used in the EMF method is much lower than the calorimetric one. EMF remains one of the most important methods in metallurgical thermodynamics.The method of electromotive force (EMF) with proposed electrocemical cells is a powerful tool to study the thermodynamic properties of metallic, semiconductor and oxyde systems. It permits to identify a set of values of the chemical potentials of one of the component of the different phases. The final result of this work

This work was financially supported by the Russian Foundation for Basic Research, project **11-08-01154** as well as the Talents Project of Guangdong Province, Guangdong, P.R. China.

Abbasov A.S. ,Nikoliskaja A.V., Gerassimov Ja.I., Vassiliev V.P. (1964) The thermodynamic

Abbasov A.S., Nikoliskaja A.V., Gerassimov Ja.I, Vassiliev V.P. (1964) The thermodynamic

Abbasov A.S., Nikoliskaja A.V., Gerassimov Ja.I., Vassiliev V.P. (1964) The thermodynamic

Dokl. AN SSSR, Vol.156, No.6, pp.1399-1402. (in Russian)

Dokl. AN SSSR, Vol.156, No.5, pp.1140-1143. (in Russian)

Dokl.AN SSSR, Vol.156, No.1, p.118-121. (in Russian)

properties of gallium antimonide investigated by the electromotive force method.

properties of indium arsenide investigated by the electromotive force method.

properties of gallium tellurides investigated by the electromotive force method.

consist of the thermodynamic optimization of the studied system.

We would like to thank Dr. S. Kulinich for helpful discussion.

transformations in solid state. Line S'1 corresponds to solid solution on the base of Pb2Pd phase. Points of intersections of the lines Si with curves Li correspond to the eutectic or peritectic transformations. Points of intersections of the E(T) for liquid homogeneous region with curves L2-L6 correspond to the points of liquidus. Invariants points (Te = 721K and Tm (Pb2Pd) = 725K) were shown in the Fig.22 and 23.

Fig. 22. Equilibrium phase diagram of the palladium-lead with our corrections.

Fig. 23. General trend of experimental EMF results versus temperature and composition for the Pb-Pd system.

We applied successfully the described technique for different binary, ternary and quaternary systems:

Tl-S (Vassiliev et al., 1971,1973a, 1973b, 2008), Tl-Se (Vassiliev et al., 1967,1969,1971), Tl-Te (Vassiliev et al., 1968); Cd-Te (Vassiliev et al., 1990); **Pb-Pd** (Vassiliev et al., 1998a); In-P (Vassiliev & Gachon, 2006); In-As (Abbasov et al., 1964); In-Sb (Vassiliev, 2004); In-Sn (Vassiliev et al., 1998b); Ga-As (Abbasov et al., 1964); Ga-Sb (Abbasov et al., 1964); Sn-Sb (Vassiliev 1997, 2005); Bi-Se (Vassiliev et al., 1968); Ga-Te (Abbasov et al., 1964); Mn-Te (Vassiliev et al., 1993); Rare Earth Metals (REM) with In (Vassiliev et al., 2009), Sb (Gorjacheva et al.,1981), Pb (Vassiliev et al., 1993), Te (Vassiliev et al., 1980); Cd-Hg-Te (Vassiliev et al., 1990,2004); In-Sn-Sb (Vassiliev et al., 2001); **Pb-Sn-Sb** (Vassiliev et al., 1995); Pb-Sn-Zn (David at al., 2004) In-Bi-Ag (Vassiliev et al., 1998c); In-Ni-Sb Vassiliev et al., 2003); Pb-Cu-Zn; Pb-In-Zn; Pb-In-Zn-Sn (Hertz at al., 1998). As well as, this technic can be applied for the oxide systems also.
