Measurements on Galvanic Cells Involving Solid Electrolytes, Kalevi Kiukkola and Carl Wagner

Materials Research Activities

Measurements on Galvanic Cells Involving Solid Electrolytes

Kalevi Kiukkola¹ and Carl Wagner

Department of Metallurgy, Massachusetts Institute of Technology, Cambridge, Massachusetts

ABSTRACT

Electromotive force measurements on galvanic cells involving solid electrolytes have been made in order to obtain the standard molar free energy of formation of CoO, NiO, CuO, Ag₂S, AgSe, PbS, and several phases of the system Ag-Te at elevated temperatures.

Haber and Tolloczko (1), Katayama (2), Reinhold (3, 4), Treadwell, Ammann, and Zurrer (5), Croatto and Bruno (6), Rose, Davis, and Ellingham (7), Sator (8), and others have shown that emf measurements on galvanic cells involving solid electrolytes may yield valuable thermodynamic data. The following investigations have been made in order to show new potentialities of emf measurements on galvanic cells involving solid electrolytes for the determination of the standard molar free energy of formation of oxides, sulfides, selenides, and tellurides at elevated temperatures.

Oxide Cells

General

In order to obtain the standard molar free energy of formation of CoO, NiO, and Cu₂O, cells of type

A, A(O) | electrolyte | B, B(O) (I)

involving oxides A(O) and B(O) of metals A and B have been investigated. The electrolyte was a solid solution of ZrO₂ and CaO involving oxygen ion vacancies according to Hund (9). Electrical conduction due to migration of oxygen ions via vacancies has been ascertained by tests described below. Analogous solid oxide solutions were tested but found to be less satisfactory.
For predominant ionic conduction due to migration of oxygen ions in the electrolyte, the virtual cell reaction may be expressed in terms of oxygen transfer from the right-hand to the left-hand electrode. Hence the emf E of cell (I) is

where

and

, respectively, are the partial molar free energies of oxygen on the left-hand and the right-hand side of cell (I), F_o2° is the standard molar free energy of oxygen, and F is the Faraday constant.

In most experiments reported below, a mixture of iron and wüstite was used on the left-hand side of cell (I). Upon combining values of the CO₂/CO ratio over iron and wüstite according to Darken and Gurry (10) and standard molar free energies of formation for CO and CO2 according to Coughlin (11), values for the relative partial molar free energy

over iron and wüstite have been calculated and are listed in Table I. Upon substituting these values and experimental values of E in Eq. [1], values of

over metal B and oxide B(O) and the standard molar free energy of formation of oxide B(O) have been calculated for B = Co, Ni, Cu.

Table I. Free energy values for the system iron-oxygen from gas equilibrium measurements

In some runs, a mixture of wüstite and magnetite was used on the left-hand side of the cell in order to define the oxygen potential. For the evaluation of these experiments, values of

over wüstite and magnetite have been calculated and are also listed in Table I.

Preparation of the Electrolytes

The following solid solutions were prepared according to Hund (9, 12),

A: 0.85 ThO₂ + 0.15 LaO_1.5

B: 0.75 ThO₂ + 0.25 LaO_1.5

C: 0.85 ThO₂ + 0.15 CaO

D: 0.85 ZrO₂ + 0.15 CaO

E: 0.60 ZrO₂ + 0.40 CaO

To prepare electrolytes A and B, a solution of Th(NO₃)₄ and La₂O₃ in dilute nitric acid was precipitated with ammonia. The coprecipitated hydroxides were converted into oxides as is described below for ZrO₂-CaO. Electrolyte C was prepared by evaporating a solution of Th(NO₂)₄ and CaCO, in dilute nitric acid. Similarly, to prepare electrolytes D and E, zirconyl nitrate was dissolved in boiling concentrated nitric acid and calcium carbonate was dissolved in dilute nitric acid. A mixture of these solutions was evaporated in a porcelain dish to dryness on a water bath. The remaining solid material was dried overnight at 120°C, ground in an agate mortar, decomposed at about 500°C, and fired 12 hr at 1000°C and 12 hr at 1250°C in a Pt boat with grinding after each firing. The powder was pressed into tablets 0.5 cm in diameter and about 0.2 cm thick at a pressure of about 10 tons/cm². The tablets were finally sintered overnight in a Pt boat under air at 1400°-1450°C.

Fig. 1. Cell for measurements with solid oxide electrolyte

When the powder was fired at a temperature below 1250°C, it was too voluminous and not suitable for pressing tablets. On the other hand, when the powder was fired at higher temperatures, it was not sufficiently reactive to yield dense tablets during the final sintering.

Arrangement of the Cell

A cell of type (I) consists of a tablet of a mixture of metal A and its oxide, a tablet of the electrolyte, and a tablet of a mixture of metal B and its oxide between Pt disks connected with Pt leads. The cell assembly is shown in Fig. 1. Since one lead goes to the top and the other lead to the bottom of the furnace, the external resistance between the leads in parallel to the cell is determined by the resistivity of the structural components of the cell assembly which are at room temperature with a negligible leakage current. The small distance between the electrodes minimizes local temperature differences within the cell and therefrom eventually resulting thermoelectric forces. The temperature of the cell can be measured with the help of a thermocouple next to the top electrode of the cell.

To assemble the cell, the bottom brass head with the vycor rod was lowered until the top of the vycor rod was outside the furnace. After assembling the cell on top of the vycor rod, the outer vycor tube was brought in position and the remaining parts of the cell assembly were installed so that the cell was under light pressure. Finally the whole cell assembly was raised so that the cell was in the middle of the resistance-heated furnace.

Use of an outer transparent vycor tube facilitated assembling of the cell but limited the maximum operating temperature to about 1150°C.

All measurements were made in purified nitrogen or argon. The gas was purified by passing over ascarite, anhydrous magnesium perchlorate, active copper at 200°C (13), and finally once more over ascarite and anhydrous magnesium perchlorate. The upper part of the copper tower was oxidized in order to remove hydrogen or hydrocarbons possibly present in the tank gas.

Conductivity Measurements

At elevated temperatures, concentrations of excess electrons and electron holes in the solid oxide electrolytes are presumably determined by the oxygen partial pressure of the surrounding atmosphere by virtue of the reactions

0₂(g) + 4 excess electrons + 2 anion vacancies = 2 0^2- [2]

0₂(g) + 4 valence electrons + 2 anion vacancies = 2 0^2- + 4 electron holes [3]

In view of the low total conductivity, concentrations of excess electrons and electron holes are much smaller than the concentration of anion vacancies. Thus, concentrations of anion vacancies and valence electrons are virtually independent of the external oxygen partial pressure. Hence, on applying the ideal law of mass action to Eqs. [2] and [3], it follows that

c_- = K₁(p_o₂)^-1/4 [4]

c₊ = K₂(p_o₂)^1/4 [5]

where c_ and c+, respectively, are the concentrations of excess electrons and electron holes, and K₁ and K₂ are constants.
In view of Eqs. [4] and [5], an appreciable contribution of excess electrons or electron holes is indicated by a rise of the total conductivity with decreasing or increasing oxygen partial pressure, respectively.
In order to test the dependence of the total conductivity on oxygen partial pressure, the electrical resistance of electrolyte tablets was measured between Pt electrodes with alternating current at 870°C. In order to minimize contact resistance, the tablets were provided either with thin Au layers applied by vacuum vaporization, or with thin Pt films obtained by cathodic sputtering.

The following atmospheres were used.

1. Oxygen of atmospheric pressure, p_o₂ = 1 atm,

2. Air of atmospheric pressure, p_o₂ = 0.21 atm,

3. Nitrogen of atmospheric pressure, p_o₂ ~ 10^-5 to 10^-3 atm,

4. Argon saturated with water vapor at room temperature with an addition of electrolytic hydrogen corresponding to a H₂O/H₂ ratio of the order of unity, p_o₂ ~ 10^-17 atm,

5. Hydrogen of atmospheric pressure saturated with water vapor at 25°C, p_o₂ ~ 10^-20 atm,

6. Hydrogen of atmospheric pressure saturated with water vapor at 0°C, p_o₂ ~ 4 x 10^-22 atm.

The electrical conductivity of electrolyte D (0.85 ZrO₂ + 0.15 CaO) at 870°C was found to be virtually constant (about 1.6 x 10^-4 ohm^-1cm^-1) when the oxygen partial pressure was varied within the aforementioned wide limits. In contrast, the conductivity of ThO₂-La₂O₃ solid solutions varied up to 50% whereby an objectionable magnitude of electronic conduction is indicated. Even greater variations have been observed with electrolyte C (ThO₂ + CaO). For this reason, the following measurements have been made with solid ZrO₂-CaO solutions.

Electronic conduction in ThO₂-La₂O₃ and ThO₂-CaO samples may have been caused by the presence of impurities. Further investigations are needed in order to clarify the nature of electronic conduction in such solid oxide solutions.

In order to determine small contributions of electronic conduction in ionic conductors, polarization measurements are profitable as has been shown recently (14). Measurements on the cell

Fe, wüstite | (ZrO₂ + CaO) | Au (II)

confirmed that electronic conduction yields only a minor contribution to the total conductivity. These measurements, however, were not carried sufficiently far in order to make possible a comprehensive quantitative evaluation.

Measurements on Cells Involving Iron Oxides

To verify the presupposition of predominant ionic conduction in ZrO₂-CaO solid solutions, there was investigated the cell

Fe, Fe_xO | (ZrO₂ + CaO) | Fe_yO, Fe₃O₄ (III)

where Fe_xO and Fe_yO denote wüstite coexisting with metallic iron and with magnetite, respectively.

Two-phase mixtures Fe, Fe_xO and Fe_yO, Fe₃O₄, with Fe/O ratios of 2 and 0.875, respectively, were made by pressing well mixed hydrogen-reduced iron powder (-200 mesh, Mallinckrodt A.R.) and magnetite powder (-200 mesh, prepared from C.P. Fe₂O₃) into tablets at a pressure of 10 tons/cm².

In each run, the emf of the cell was measured at rising and falling temperature. In general, steady potentials were attained more rapidly at higher temperatures than at lower temperatures. A single run lasted one or two days, or even longer. Observed emf values were plotted vs. temperature. Runs were considered to be satisfactory when values for ascending and descending temperatures agreed within 1 or 2 mv. Values for even temperatures read from these plots are listed in Table II.

Table II. Electromotive force E of cell (III) Fe, Fe_xO | electrolyte | Fe_yO, Fe₃0₄

In some runs, potentials were found to be ill-defined. In these runs, the electrolyte was not sufficiently dense as was indicated by penetration of the constituents of the electrodes toward the interior of the electrolyte tablet, possibly because of capillary suction by virtue of plastic flow, or surface diffusion. Other runs failed probably because of harmful impurities in the oxides used for the preparation of the electrolyte.

Table III. Electromotive force E of cell (IV) Fe, wustite | (0.85 ZrO₂ + 0.15 CaO) | Co, CoO and standard free energy change DF° of the reaction Co(s) + 1/2 O₂(g) = CoO(s) from emf measurements and calculations by Coughlin (11)

The observed emf values may be compared with the results of gas equilibrium investigations. To this end, one may rewrite Eq. [1] as

where the subscripts I and II, respectively, refer to the left-hand and the right-hand electrode of cell (I). Numerical values of these ratios according to Darken and Gurry (10) are listed in Table I. Emf values calculated from Eq. [6], which are listed in the last column of Table II, agree very satisfactorily with observed emf values.

Standard Molar Free Energy of Formation of Cobalt Oxide

Results for the cell Fe, Fe_xO | (0.85 ZrO₂+0.15 CaO) | Co, CoO (IV) and the standard molar free energy of formation DF° of cobalt oxide are shown in Table III. Reliable values were obtained only above 900°C. The reproducibility of the emf values is ±0.002 v or better corresponding to an uncertainty in DF° of ±0.1 kcal.

Fig. 2. Standard free energy change DF° of the reaction CoO(s) + CO(g) = Co(s) + CO₂(g) from gas equilibrium measurements [+ Emmett and Shultz (15), X Watanabe (16), D Schenck and Wesselkock (17)] and emf measurements (o). The uncertainty in the latter value is indicated by the length of the arrow.

Upon substituting observed emf values and CO₂/CO ratios over iron and wüstite in Eq. [6], CO₂/CO ratios over cobalt and cobalt oxide and the standard free energy change of the reaction

CoO(s) + CO(g) = Co(s) + CO₂(g) [7]

have been calculated. Fig. 2 shows these values together with values deduced from gas equilibrium measurements by Emmett and Shultz (15), Watanabe (16), and Schenck and Wesselkock (17) as a function of temperature. Both sets of data supplement each other and may be represented by a smooth curve.

Upon combining DF° values for reaction [7] and the water gas equilibrium calculated from data compiled by Coughlin (11), the standard free energy change for the reaction

CoO(s) + H₂(g) = Co(s) + H₂0(g) [8]

has been calculated. Fig 3 shows that these data agree with values calculated from determinations of the H₂0/H₂ ratio over cobalt and cobalt oxide according to Emmett and Shultz (18) and Kleppa (19) but differ from those reported by Shibata and Mori (20), possibly because of their neglect of thermal diffusion.

Fig. 3. Standard free energy change DF° of the reaction CoO(s) + H₂(g) = Co(s) + H₂0(g) from gas equilibrium measurements [+ Emmett and Shultz (18), X Kleppa (19), D Shibata and Mori (20)] and emf measurements (o).

Standard Molar Free Energy of Formation of Nickel Oxide

Results of the cell Fe, Fe_xO | 0.85 ZrO₂ + 0.15 CaO) | Ni, NiO (V) are shown in Table IV. The reproducibility of the emf values is 0.002 v or better, corresponding to an uncertainty in DF° of ±0.1 kcal. Results were compared with results of gas equilibrium measurements in the same way as for cobalt, see Fig. 4 and 5. DF° values deduced from emf values for the reduction of NiO by means of CO lie between values calculated from CO₂/CO ratios according to Schenck and Wesselkock (17), Watanabe (21), and Fricke and Weitbrecht (22). Since the CO₂/CO ratios over nickel and nickel oxide are fairly large (63 to 454), errors are probably greater than for the analogous equilibria in the systems Fe-O and Co-O. DF° values for the reduction of NiO by means of H₂ according to Pease and Cook (23) are in accord with DF° values calculated from emf values at higher temperatures as is shown in Fig. 5.

Fig. 4. Standard free energy change DF° of the reaction NiO(s) + CO(g) = Ni(s) + CO₂(g) from gas equilibrium measurements [D Schenck and Wesselkock (17), X Watanabe (21), + Fricke and Weitbrecht (22)] and emf measurements (o).

Fig. 5. Standard free energy change of the reaction NiO(s) + H₂(g) = Ni(s) + H₂0(g) from gas equilibrium measurements [+ Pease and Cook (23)] and emf measurements (o).

For a comparison, Table IV lists standard molar free energies of the formation of nickel oxide recommended by Coughlin (11). These values are about 1 kcal more positive than values calculated from emf measurements. No explanation for this divergence can be given.

Table IV. Electromotive force E of the cell (V) Fe, wüstite | (0.85 ZrO₂ + 0.15 CaO) | Ni, NiO and standard free energy change DF° of the reaction Ni(s) + 1/2 0₂(g) = NiO(s) from emf measurements and calculations by Coughlin (11)

Standard Molar Free Energy of Formation of Cuprous Oxide

Emf values of the cells

Fe, Fe_xO | electrolyte | Cu, Cu₂O (VI)

Fe_yO, Fe₃O₄ | electrolyte | Cu, CuO (VII)

with the electrolytes (0.85 ZrO₂ + 0.15 CaO) and (0.6 ZrO₂ + 0.4 CaO) are shown in Table V. Values for the standard molar free energy of formation of cuprous oxide are listed in Table VI. These values agree fairly well with results deduced from emf measurements made by Treadwell (24) with a correction for thermoelectric effects (25). Treadwell investigated the cell

Cu(s) | Cu₂O(s), borate melt | porcelain | Ag(l), O₂(g) (VIII)

which involves the reaction 2Cu + 1/2 O₂ = Cu₂O on passing two faradays if oxygen ions alone carry the current in porcelain as an intermediate solid electrolyte.

Table V. Electromotive force E of the cells
Fe, Fe_xO | electrolyte | Cu, CuO₂ (VI)

Fe_yO, Fe₃O₄ | electrolyte | Cu, Cu₂0 (VI)

Table VI. Standard free energy change DF° of the reaction 2 Cu(s) + 1/2 0₂(g) = Cu₂O(s) calculated from emf values of cells (VI) and (VII), emf measurements of Treadwell (24) (Tr) corrected for thermoelectric effects (25), and calculations by Coughlin (Co) (11).

The reproducibility of the emf values is ±0.002 v or better, corresponding to an uncertainty in DF° of ±0.1 kcal. For a comparison, Table VI also lists values of DF° calculated from various sources by Coughlin (11) with an estimated uncertainty of +1.5 kcal. These values are about 1 kcal more negative than values from emf measurements.
No CO₂/CO and H₂O/H₂ equilibrium ratios over Cu and Cu₂O have been determined since these ratios are inconveniently high.

Roberts and Smyth (26) have determined oxygen partial pressures over liquid copper and solid Cu₂O between 1119° and 1184°C. Therefrom values between -14,100 and -14,250 cal for the standard molar free energy of formation of Cu₂O are calculated. These values are considerably more positive than the values listed in Table VI. In view of inherent difficulties discussed in the paper by Roberts and Smyth, it seems probable that the effect of side reactions has not been sufficiently eliminated in their measurements of oxygen partial pressures.

Standard Molar Free Energy of Formation of Silver Sulfide

Reinhold (4) has already determined the emf of the cell

Ag(s) | AgI(s) | Ag₂S(s), S(l), C (IX)

involving the virtual cell reaction

2Ag(s) + S(l) = Ag₂S(s) [9]

Additional measurements were made in order to obtain a higher accuracy. The setup of the cell is shown in Fig. 6. To assemble the cell, silver iodide was melted in the Pyrex tube, and the graphite electrode B, the glass tube A, and the thermocouple shield were immersed. Then the cell was transferred to another furnace whose temperature was below the melting point of AgI but above its transformation point at 146°C. After the AgI had solidified, sulfur was introduced into glass tube A, and the graphite electrode C was brought in contact with the AgI. To start a run, silver sulfide was formed electrolytically at graphite rod C by passing a current of 5 to 20 ma for about half an hour with graphite rod B as anode. In some runs, more silver sulfide was formed after the first emf measurements had been made. In other runs, graphite rod C was wrapped with silver wire which transformed to silver sulfide. The emf values were found to be independent of the procedure of preparation of silver sulfide and its amount.

Fig. 6. Cell Ag(s) | Agl(s) | Ag₂S(s), S(l), C

Observed emf values are shown in Table VII. They agree with Reinhold's values within 0.01 v, which is the limit of accuracy of the latter values. In addition, Table VII lists values for the free energy of formation of silver sulfide computed from emf values with the aid of the formula

DF° = -2EF [10]

The reproducibility of the emf values is ±0.001 v, corresponding to an uncertainty in DF° of ±0.05 kcal. The equilibrium of the reaction

Ag₂S(s) + H₂(g) = 2Ag(s) + H₂S(g) [11]

has been investigated by various authors, most recently by Rosenqvist (27) between 490° and 900°C. DF° values for reaction [11] extrapolated to 200°-400°C from Rosenqvist's data agree within ±0.2 kcal with values calculated from standard molar free energies of formation of AgS according to Table VII and values for H₂S recommended by Rossini, et al. (28) and Kelley (29).

Table VII. Electromotive force E of cell (IX) Ag(s) | AgI(s) | Ag₂S(s), S(I), C and standard free energy change DF° of the reaction 2 Ag(s) + S(I) = Ag₂S(s)

Standard Molar Free Energy of Formation of Silver Selenide

Similarly, the emf of the cell

Ag(s) | AgI(s) | Ag₂Se(s), Se(s, l), C (X)

has been determined. Results are shown in Table VIII.

The emf of cell (X) was found to be well reproducible below 380°C. In some runs, higher, unsteady potentials were observed above 380°C, presumably because Ag₂Se dissolved in liquid selenium (30) and its amount was insufficient for saturation. Only if excess silver selenide is present, the chemical potentials of silver and selenium are well defined. Even under these conditions, a correction for the calculation of the standard free energy of silver selenide is needed because selenium as a reactant is not present in its standard state. This correction is supposedly not significant below 400°C because the solubility of Ag₂Se in liquid selenium is small (31)

Solid-state coulometric titrations analogous to those made with Ag₂S (32) indicate variations of the Ag/Se ratio as low as 0.004 to 0.005 between 200°-300°C. Therefore, deviations from the ideal compo-sition of silver selenide in cell (X) are insignificant.

Cell (X) has previously been investigated by Reinhold (4). These values show considerable scatter and differ up to 0.1 v from values shown in Table VIII for unknown reasons.

Table VIII. Electromotive force E of the cell (X) Ag(s) | Agl(s) | Ag₂Se(s), Se(s,l), C and standard free energy change DF° of the reaction 2 Ag(s) + Se(s,l) = Ag₂Se(s)

From the temperature dependence of the standard free energy of formation of Ag₂Se it follows that

2 Ag(s) + Se(l) = Ag₂Se(s)

DF° = -13.46 - 0.0074 X (T - 500) kcal;

DF° = -9.76 kcal; AS° = 7.4 e.u. at T > 500°K [12]

Upon using enthalpy and entropy increments of Ag, Se, and Ag₂Se between 298° and 500°K as compiled by Kelley (29), the values of AH° and AS0 at 298°K are obtained. Therefrom DF° = DH °- TDS° at 298°K may be calculated. Thus,

2 Ag(s) + Se(s) = Ag₂Se(s)

DF° = -11.94 kcal; DH° = -11.38 kcal;

DF° = S° = 5.24 e.u. at 298°K [13]

The value DH° = -11.38 kcal seems to be more consistent than the value of -2.9 kcal, which was obtained by Fabre (33) on combining the values for several reactions which were investigated calorimetrically.

The standard molar entropy of Ag₂Se at 298°K is obtained as

S°_Ag₂se = DS° + 2S°_Ag + S°_Se

= 5.24 + 2 X 10.206 + 10.0 = 35.65 e.u. at 298°K [14]

with standard entropy values for Ag and Se recommended by Rossini, et al. (28).

Standard Molar Free Energy of Formation of Lead Sulfide

Solid lead chloride, pure or doped with KCl, is known to be an anionic conductor (34-36). Thus, the standard free energy of formation of lead sulfide should be obtainable from a cell analogous to cell (IX),

Pb(s) | PbCl₂(s) | PbS(s), S(1), C (XI)

The emf of cell (XI) was found to be not well reproducible, presumably for the following reason. In view of the shrinkage during the solidification of PbCl₂ and lack of plasticity, no tight seal of lead chloride between the two electrodes was obtained and, therefore, sulfur vapor could diffuse to the lead electrode so that a mixed potential rather than an equilibrium potential prevailed.

Therefore, a cell involving a Ag-Ag₂S electrode instead of a sulfur electrode was investigated,

Pb(s, l) | PbCl₂(+KCl) | I PbS(s), Ag₂S(s), Ag(s) (XII)

with the virtual cell reaction

Pb(s,l) + Ag₂S(s) = PbS(s) + 2 Ag(s) [15]

Preliminary investigations have shown that the solubility of Ag₂S in PbS is less than 1 mole % below 400°C. Similarly, a low solubility of PbS in Ag₂S is assumed. Ag₂S and PbS are, therefore, considered to be present virtually in their standard states.

The electrolyte was solid lead chloride containing 0.5 w/o KCl in order to increase the conductivity, presumably due to a higher anion vacancy concentration (37). To prepare the electrolyte, PbCl₂ and KCl were melted under a stream of argon containing a small amount of chlorine. The solidified melt was crushed to powder.

In order to extend measurements above the melting point of lead at 327°C, a crucible of lead chloride filled with liquid lead was used. Fig. 7 shows the assembled cell which was placed in the furnace shown in Fig. 1.

Fig. 7. Cell Pb(s, l) | PbCl₂(+KCI) | PbS(s), Ag₂S(s), Ag(s)

Crucibles of lead chloride were pressed in the tool shown in Fig. 8. A nearly uniform density was obtained by applying pressure from top and bottom punches and by providing nearly equal compression ratios of the powder at the bottom and in the walls of the crucible. The pressed crucibles were ejected through the upper end of the die, which was slightly tapered. The crucibles were used either as such, or after sintering under argon at about 400°C. Different procedures did not result in systematic differences in the measured emf.

Fi. 8. Tool for pressing PbCl₂ crucibles

On replacing the lower punch by a short steel rod, cylindrical tablets of a mixture of Ag, Ag₂S, and PbS for the right-hand electrode in cell (XII) could be made.

Results of emf measurements are listed in Table IX.

Upon combining DF° values for reactions [9] and [15], values for the standard free energy of formation of PbS are obtained. These values are also shown in Table IX.

The equilibrium

PbS(s) + H₂(g) = Pb(l) + H₂S(g) [16]

has been investigated by Jellinek and Zakowski (38), Jellinek and Deubel (39), and Sudo (40). DF° values for reaction [16] calculated from standard free energies of formation of PbS listed in Table IX and values for HS recommended by Rossini, et al. (28) and Kelley (29) are consistent with Sudo's measurements (40) but diverge from earlier measurements by Jellinek and his associates (38, 39).

Table IX. Electromotive force E of the cell (XII) Pb(s,l) | PbCl₂ (+KCI) | PbS(s), Ag₂S(s), Ag(s) and standard free energy change DF° of the reaction Pb(s,l) + S(l) = PbS(s)

The System Silver-Tellurium

The phase diagram of the system silver-tellurium has been investigated by Pelabon (41), Pellini and Quercigh (42), Chikashige and Saito (43), Koern (44), and Kracek and Ksanda (45). In addition to the compound Ag₂Te, which has a congruent melting point at about 958oC, there is at least one other intermediate phase involving a smaller Ag/Te ratio with an incongruent melting point, for which the formulas

AgTe (42), Ag₇Te₄ = Ag_1.75Te (43), Ag₁₂Te₇ = Ag_1.71Te( 44), and Ag_l.50Te (45)

have been suggested.

To clarify, the activity aAg of silver in Ag-Te "alloys" has been determined as a function of the Ag/Te ratio by measuring the emf of the cell

Ag(s) | AgI(s) | (Ag,Te) (XIII)

Since silver iodide is an ionic conductor, the emf E of the cell (XIII) is

E = -(RT/F) ln aAg = -F^M_Ag [17]

where FMAg is the partial molar free energy of mixing of silver for pure solid silver as reference state.

Upon passing current across cell (XIII) from right to left, a definite amount of silver can be transferred from the alloy to the left-hand electrode consisting of pure silver. Thus, cell (XIII) permits a solid-state titration analogous to that used for silver sulfide (32). The change in the Ag/Te ratio, Dg, is in view of Faraday's law

Dg = it / n_TeF [18]

where i is the current applied during time t, n_Te is the number of moles of tellurium, and F is the Faraday constant.

At the beginning of a titration, the Ag-Te alloy was equilibrated with metallic silver by short-circuiting cell (XIII). Subsequently, silver was removed. In contradistinction to measurements of the analogous cell for the system Ag-S, a steady potential was attained not immediately but only after about half an hour.

Results for 250° and 300°C are shown in Fig. 9 and 10. Points indicated by solid squares were obtained from measurements of cells with predetermined constant composition of the Ag-Te alloy. There are three regions involving a variable potential E corresponding to three different phases designated as a, g, and e. The one-phase regions are separated by two-phase regions indicated by plateaus in the E vs. Dg plots.

Fig. 9. Emf E of cell Ag | AgI | (Ag, Te) vs. Ag/Te ratio r at 250°C

Fig. 10. Emf E of cell Ag | AgI | (Ag, Te) vs. Ag/Te ratio r at 300°C

Since the homogeneity range of the alpha phase is rather narrow, it may be assumed without considerable error that the phase equilibrated with metallic silver has nearly the formula Ag₂Te whereupon the Ag/Te ratio shown on top of Fig. 9 and 10 may be calculated as

g = 2 - Dg [19]

At 300°C, the Ag/Te ratio ranges from 1.99 to 2.00 for the a phase, from 1.88 to 1.91 for the g phase, and from 1.63 to 1.66 for the e phase.

From the values shown in Fig. 9 and 10, the free energy of formation of a one-phase or two-phase alloy involving N_Ag g-atom Ag and (1-N_Ag) g-atom Te may be calculated as (46)

Upon dividing F^M by N_Te = (1 - N_Ag), the standard molar free energies of formation DF° of the silver tellurides having the formulas Ag₂Te, Ag_1.90Te, and Ag_1.64Te have been calculated. These values are listed in Table X.

Table X. Thermodynamic values for the system silver-tellurium

The emf of the cell

Ag | AgNO₃(aq) | (Ag,Te) (XIV)

has been determined at room temperature by Puschin (47). A plot of emf vs. the Ag/Te ratio does not indicate another compound in addition to Ag₂Te. It is possible, however, that the scatter in Puschin's plot of E vs. composition obscures small steps corresponding to different compounds. Moreover, complete electrochemical equilibrium may not have been reached at room temperature as has been found, e.g., for the system Cu-Zn by Sauerwald (48).

Manuscript received August 9, 1956. The paper is based on a thesis submitted by K. Kiukkola in partial fulfillment of requirements for the degree of D.Sc. in metallurgy, Massachusetts Institute of Technology, Cambridge, Mass. Work was done under Contract AT(30-1)-1002 with the U.S.A.E.C.

Any discussion of this paper will appear in a Discussion Section to be published in the December 1957 JOURNAL.

1 Present address: Ratakatu 5 B 18, Helsinki, Finland.

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