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Determination of the thermodynamic properties of solid solutions of CoO and MgO by a solid-electrolyte galvanic cell in the temperature range 1273 to 1473 K
J. Chem. Thermodynamics 1974, 6, 993-998
Determination of the thermodynamic properties of solid solutions of Co0 and MgO by a solid-electrolyte galvanic cell in the temperature range 1273 to 1473 K M. RIGAUD,
G. GIOVANNETTI,
and M. HONE
Department of Metallurgical Emgineering, Ecole Polytechnique, University of Montreal, 2500 Avenue Marie Guyard, Montrkal250, P.Q., Canada (Received 26 October 1973; in revised form 28 January 1974) The activity of Co0 in solid solutions of Co0 and MgO has been determined, in the temperature range 1273 to 1473 K, by an electrochemical method. The chemical potentials, activities, and activity coefficients of Co0 and of MgO have been calculated. The mixtures exhibit slight positive deviations from ideal behavior.
1. Introduction paper deals with activity measurements of Co0 in solid solutions of Co0 and MgO in the temperature range 1273 and 1473 K. Au&rust and Muan determined the activity of Co0 in these mixtures at 1473 K by equilibrating with CO, and CO or CO, and H, gas mixtures and found ideal behavior within limits of experimental errors. Seetharaman and Abrahamc2’ measured the activity of Co0 in solid solutions of Co0 and MgO in the temperature range 1073 to 1273 K, by use of a solid-state galvanic cell, the solid electrolyte being yttria-stabilized thoria. Their results indicated slight positive deviations from ideality and conformity to a regular-solution model. Due to the erratic behaviour of their cell, they observed no regular trend in the variation of e.m.f. with temperature, except for solid solutions with a high mole fraction of COO. Hence a third study on solid solutions of Co0 and MgO was justified.
The present
2. Experimental CELL
The cell used in this investigation
is of the type:
PtlCo, xCo0-1-(1-x)Mg0~Zr0,,
CaOlCoO,
Co,Pt.
The electrolyte, zirconia stabilized with 15 moles per cent of calcia, was purchased from Zirconium Corp. of America, in cylindrical rod form. The rod was then sliced to form disks of a given thickness. The cell is schematically shown in figure 1. The
994
M. RIGAUD,
G. GIOVANNETTI,
AND M. HONE
6
FIGURE 1. Schematic representation of the galvanic cell used: 1, the platinum wire; 2, O-ring; 3, internal tube; 4, external tube; 5, the electrolyte ZrO&aO; 6, Co(s) and Coo(s); 7, Co(s) and {xCoO+(l -x)MgO}(ss).
electrolyte disk was bonded at the end of the inner tube, of Vycor, effectively forming two isolated compartments, one for each electrode, thus minimizing the possibility of oxygen transport from one electrode to the other via the gas phase. The external tube contained the reference electrode, a mixture of pure Co and Co0 powders (equal masses). The powders were carefully mixed and then pressed in the tube. The internal compartment contained the Co and (xc00 + (1 -x)MgO} mixture (equal masses), also pressed tightly in the tube. The two tubes were then sealed with cement. The platinum wire leads were taken through seals to the exterior of the cells where the e.m.f. was measured to an accuracy of kO.2 mV by means of a Tacussel potentiometer. This instrument has an impedance of 1Or2 !GI, and therefore draws negligible current through the cell. PREPARATION
AND ANALYSIS
OF THE SAMPLES
Co0 was prepared by the thermal decomposition of cobalt carbonate (Fisher reagent grade) at 673 K, for 2 h, in a flow of dry nitrogen in a thermobalance. The purity of the Co0 was confirmed by thermogravimetric analysis, X-ray diffraction analysis, and chemical analysis. To prepare the solid solutions, for each composition, Co0 powder was mixed with “Baker analysed” reagent grade MgO. The mixture was then pressed at 275 MPa to form pellets. The superficial crust of each pellet was removed to eliminate contamination from the die. The pellets were then sintered, first under a nitrogen atmosphere at 1673 K for 16 h, in a large MgO crucible. The pellets were stacked to prevent contact with the cylindrical wall of the crucible. After removal from the furnace, the
ACTIVITY
OF
Co0
IN
SOLID
SOLUTIONS
OF
Co0
AND
MgO
995
pellets on the top and the bottom of the stack were discarded. Each pellet was then broken and reformed, and the sintering repeated. The following five compositions calculated from masses taken: 11.91, 40.28, 60.32, 78.05, and 98.69 mass per cent of Co0 correspond to mole fractions x of COO: 0.063,0.258, 0.453, 0.593, and 0.889. X-ray analysis conlirmed the formation of homogeneous solid solutions. Since both MgO and Co0 are cubic and have similar lattice parameters, chemical analysis was used to check the exact composition of the solid solutions. CELL OPERATION
The cell was introduced in an alumina tube, closed at one end in a vertical furnace. In order to prevent current leakage and radio frequency interference, all wires were shielded and a Faraday cage was placed around the furnace. The temperature of the cell was measured with a Pt-to-(Pt+ 10 mass per cent of Rh) thermocouple located at the level of the electrolyte. The temperature of the furnace was controlled by use of another thermocouple. The temperature was first raised to 1473 K and the cell was left at this temperature for 24 h to ensure equilibration of the electrodes. Equilibration was assumed when the measured e.m.f. remained within kO.2 mV for a period of several hours. The ceil temperature was then lowered by 40 K increments to 1273 K and the e.m.f. was measured at each temperature after an equilibration period of 2 to 3 h. The same procedure was repeated as the temperature was raised from 1273 to 1473 K. The e.m.f.‘s observed on approaching the same temperature from above and from below were reproducible to t-O.5 mV. One series of measurements at x = 0.063 was replicated and the same uncertainty observed. The reversibility of the cell was checked at the end of each series of measurements by passing a current of 300 uA for 1 min (18 mC) and measuring the e.m.f. of the cell afterwards. The e.m.f. decreased very rapidly at first and reached within 10 min the initial value. The cell was then short-circuited for a few seconds; the e.m.f. went from zero to its initial value in less than 5 min. In addition, it was found by chemical analysis that the composition of the solid solutions used in the experiments did not change even after several days in the cell (generally 5 d).
3. Resuits It was assumed that the deviations from stoichiometry in the oxide species were negligible. Also, since the difference between the standard Gibbs energies of formation of Co0 and of MgO is sufficiently large, MgO was presumably not reduced by Co at the solution electrode. The overall cell reaction may therefore be represented by COO(S) = CoO(ss), where ss denotes a solid solution, giving -2EF
= p(Co0, ss, T, x)-p(Co0, s, T) = RT ln(a(Co0, ss, T, x)} = RT ln(xf(Co0,
ss, T, x)>, (1) The experimental values of the e.m.f. Emeasured for the five compositions investigated are listed in table 1 at different temperatures. The e.m.f. was a linear function of
h%.kZTGAUD, 0.
496 TABLE
1. Experimental
x = 0.063 EJmV TIK 1457.7 1402.2 1359.0 1321.0 1261.0 1269.9 1313.6 1411.4 1460.0
GfOVANNBl”ri,
values of the e.m.f. solid solutions (xc00
x = 0.258 EjmV
1462.2 1406.2 1373.8 1324.1 1279.1 1268.2 1329.9 1378.9 1422.7 1474.1
E measured + (1 -
M.
58.3 54.5 51.1 47.1 46.9 44.3 49.7 53.1 55.3 58.6
1463.6 1418.3 1388.3 1325.6 1261.6 1276.8 1304.4 1377.5 1417.5 1480.5
HONE
at different x)MgO}
x = 0.453 E/mV riK
T/K
117.0 110.2 102.9 94.2 89.8 90.0 94.6 109.0 119.6
AND
temperatures
T for
x = 0.593 E/mV TIK
42.7 38.6 39.5 34.3 29.7 32.0 32.8 36.4 40.6 44.5
1463.3 1422.4 1377.7 1313.7 1222.3 1273.3 1304.6 1365.9 1409.4 1457.7
x = 0.889 E/mV
T/K
33.3 28.9 25.8 25.3 18.5 22.8 23.3 27.5 28.9 30.16
1456.0 1422.8 1417.8 1371.8 1334.6 1251.0 1278.2 1320.8 1376.8 1461.5
11.9 11.0 10.2 6.84 7.38 5.48 5.58 6.70 7.50 9.50
temperature for all compositions. The equations of the least-squares regression lines are given in table 2. Values of the chemical potential difference for Co0 were calculated from equation (1) at 1473, 1373, 1273, and 1173 K (the last being an extrapolated temperature from the values given in table 2), and are reported in table 3. The activity coefhcientsf(Mg0) of MgO in the solid solutions (xc00 + (1 - x)MgO} were obtained by use of the Gibbs-Duhem equation in its integrated form: In(f(Mg0,
TABLE for the five mole
fractions
x of Co0
x 0.063 0.258 0.453 0.593 0.889
TABLE
3. Chemical
T/K
potential (xc00
x= 1 {x/(1 -x)}d
A
B
0.150 0.070 0.063 0.051 0.028
101.8 44.9 48.9 42.7 30.7
& f * -+ I-t
203 89 107 126 123
ss, T, $1,
-4136 -2065 -1426 -1013 -252
1273 ss, T) - ACoO, j, f f f &
167 71 103 109 101
(2)
is the average
/mV 103 51.9 37.1 26.4 8.2
differences {,u(COO, ss, T) - p(CoO, + (1 - x)MgO} at four temperatures (c&b = 4.184 J)
(p(Co0, -3442 -1740 -1137 -778 -121
ln{f(CoO,
2. The coefficients of the equation E]mV = AT/K - B and the temperature range 1273 to 1473 K; value in this range
1173
x 0.063 0.258 0.453 0.593 0.889
X=X s
ss, T, x)} = -
1 0.4 0.5 0.7 0.6
s, 2”)) in the solid
solutions
T
1373 s, TMxil,h -4829 -2390 -1716 -1247 -383
& f rt f f.
1473 molwf
zt 155 f 66 rt 82 It 103 f 93
-5523 -2715 -2005 -1482 -5k4
+ f i z’c 5
173 72 89 113 102
ACTIVITY
OF Co0 IN SOLID SOLUTIONS
OF Co0 AND MgO
997
and integrating graphically by the trapezoidal method. To obtain the value of ln(f(MgO, ss, T, x --+ 1)) we used the Redlich method, which consists in equating the areas represented by the two sides of the thermodynamic relation: 1
In{f(CoO, ss, T, x))dx = ‘ln{f(MgO, ss, T, x))dx. (3) s0 s0 The results obtained for a(Ng0) and forf(Mg0) are given in table 4 with the corresponding quantities of COO. TABLE
U(CO&
fO0)
4. Values of the activities a and of the activity coefficients fof Co0 and of MgO in the solid solutions {Xc00 + (1 - x)MgO) at 1273 K 0.1930.063 f 0.007 3.01 1.00 0.94
0.44oi
0.2580.007 1.70 1.13 0.84
0.570.453 f 0.01 1.26 1.33 0.73
0.670.593 f 0.014 1.13 1.49 0.61
0.900.889 rt 0.016 1.Ol 2.16 0.24
4. conclusions The activity-composition relations for Co0 in solid solutions of Co0 and MgO which have been measured are in disagreement with previously reported results.(1*2) The difference is small but experimentally significant. The solutions of Co0 and MgO behave neither as ideal nor as regular solutions. The solutions show positive deviations from ideal behavior, as shown in figure 2.
0.6
e 0.4
'0
0.2
0.4.
0.6
0.8
1
x FIGURE 2. Activities u of Co0 and of MgO in the solid solutions (xCoO+(l -x)MgO} at 1273 K. 0 with uncertainty bounds, measured values for a(Co0); 0, calculated values for a(Mg0); 0, values for a(Co0) from Seetharamen and Abraham. (a, The limiting values implied by the tangents drawn on the figure are f(CoO,ss,l273 K, x+0) = 4.01 and f(MgO,ss,1273 K, x+1) = 3.16.
998
M. RIGAUD.
G. GIOVANNETTI,
AND M. HONE
The financial aid of the Ministry of Education of the Province of Quebec to one of the authors (G. Giovannetti), and of the National Research Council of Canada in providing equipment funds is gratefully acknowledged. REFERENCES 1. Auckrust, E.; Muan, A. Tram Met. Sot. AZh4E 1963,227, 1378. 2. Seetharaman, S.; Abraham, K. P. J. Electrochem. Sot. India. 1971, 20 54.
Determination of the thermodynamic properties of solid solutions of Co0 and MgO by a solid-electrolyte galvanic cell in the temperature range 1273 to 1473 K M. RIGAUD,
G. GIOVANNETTI,
and M. HONE
Department of Metallurgical Emgineering, Ecole Polytechnique, University of Montreal, 2500 Avenue Marie Guyard, Montrkal250, P.Q., Canada (Received 26 October 1973; in revised form 28 January 1974) The activity of Co0 in solid solutions of Co0 and MgO has been determined, in the temperature range 1273 to 1473 K, by an electrochemical method. The chemical potentials, activities, and activity coefficients of Co0 and of MgO have been calculated. The mixtures exhibit slight positive deviations from ideal behavior.
1. Introduction paper deals with activity measurements of Co0 in solid solutions of Co0 and MgO in the temperature range 1273 and 1473 K. Au&rust and Muan determined the activity of Co0 in these mixtures at 1473 K by equilibrating with CO, and CO or CO, and H, gas mixtures and found ideal behavior within limits of experimental errors. Seetharaman and Abrahamc2’ measured the activity of Co0 in solid solutions of Co0 and MgO in the temperature range 1073 to 1273 K, by use of a solid-state galvanic cell, the solid electrolyte being yttria-stabilized thoria. Their results indicated slight positive deviations from ideality and conformity to a regular-solution model. Due to the erratic behaviour of their cell, they observed no regular trend in the variation of e.m.f. with temperature, except for solid solutions with a high mole fraction of COO. Hence a third study on solid solutions of Co0 and MgO was justified.
The present
2. Experimental CELL
The cell used in this investigation
is of the type:
PtlCo, xCo0-1-(1-x)Mg0~Zr0,,
CaOlCoO,
Co,Pt.
The electrolyte, zirconia stabilized with 15 moles per cent of calcia, was purchased from Zirconium Corp. of America, in cylindrical rod form. The rod was then sliced to form disks of a given thickness. The cell is schematically shown in figure 1. The
994
M. RIGAUD,
G. GIOVANNETTI,
AND M. HONE
6
FIGURE 1. Schematic representation of the galvanic cell used: 1, the platinum wire; 2, O-ring; 3, internal tube; 4, external tube; 5, the electrolyte ZrO&aO; 6, Co(s) and Coo(s); 7, Co(s) and {xCoO+(l -x)MgO}(ss).
electrolyte disk was bonded at the end of the inner tube, of Vycor, effectively forming two isolated compartments, one for each electrode, thus minimizing the possibility of oxygen transport from one electrode to the other via the gas phase. The external tube contained the reference electrode, a mixture of pure Co and Co0 powders (equal masses). The powders were carefully mixed and then pressed in the tube. The internal compartment contained the Co and (xc00 + (1 -x)MgO} mixture (equal masses), also pressed tightly in the tube. The two tubes were then sealed with cement. The platinum wire leads were taken through seals to the exterior of the cells where the e.m.f. was measured to an accuracy of kO.2 mV by means of a Tacussel potentiometer. This instrument has an impedance of 1Or2 !GI, and therefore draws negligible current through the cell. PREPARATION
AND ANALYSIS
OF THE SAMPLES
Co0 was prepared by the thermal decomposition of cobalt carbonate (Fisher reagent grade) at 673 K, for 2 h, in a flow of dry nitrogen in a thermobalance. The purity of the Co0 was confirmed by thermogravimetric analysis, X-ray diffraction analysis, and chemical analysis. To prepare the solid solutions, for each composition, Co0 powder was mixed with “Baker analysed” reagent grade MgO. The mixture was then pressed at 275 MPa to form pellets. The superficial crust of each pellet was removed to eliminate contamination from the die. The pellets were then sintered, first under a nitrogen atmosphere at 1673 K for 16 h, in a large MgO crucible. The pellets were stacked to prevent contact with the cylindrical wall of the crucible. After removal from the furnace, the
ACTIVITY
OF
Co0
IN
SOLID
SOLUTIONS
OF
Co0
AND
MgO
995
pellets on the top and the bottom of the stack were discarded. Each pellet was then broken and reformed, and the sintering repeated. The following five compositions calculated from masses taken: 11.91, 40.28, 60.32, 78.05, and 98.69 mass per cent of Co0 correspond to mole fractions x of COO: 0.063,0.258, 0.453, 0.593, and 0.889. X-ray analysis conlirmed the formation of homogeneous solid solutions. Since both MgO and Co0 are cubic and have similar lattice parameters, chemical analysis was used to check the exact composition of the solid solutions. CELL OPERATION
The cell was introduced in an alumina tube, closed at one end in a vertical furnace. In order to prevent current leakage and radio frequency interference, all wires were shielded and a Faraday cage was placed around the furnace. The temperature of the cell was measured with a Pt-to-(Pt+ 10 mass per cent of Rh) thermocouple located at the level of the electrolyte. The temperature of the furnace was controlled by use of another thermocouple. The temperature was first raised to 1473 K and the cell was left at this temperature for 24 h to ensure equilibration of the electrodes. Equilibration was assumed when the measured e.m.f. remained within kO.2 mV for a period of several hours. The ceil temperature was then lowered by 40 K increments to 1273 K and the e.m.f. was measured at each temperature after an equilibration period of 2 to 3 h. The same procedure was repeated as the temperature was raised from 1273 to 1473 K. The e.m.f.‘s observed on approaching the same temperature from above and from below were reproducible to t-O.5 mV. One series of measurements at x = 0.063 was replicated and the same uncertainty observed. The reversibility of the cell was checked at the end of each series of measurements by passing a current of 300 uA for 1 min (18 mC) and measuring the e.m.f. of the cell afterwards. The e.m.f. decreased very rapidly at first and reached within 10 min the initial value. The cell was then short-circuited for a few seconds; the e.m.f. went from zero to its initial value in less than 5 min. In addition, it was found by chemical analysis that the composition of the solid solutions used in the experiments did not change even after several days in the cell (generally 5 d).
3. Resuits It was assumed that the deviations from stoichiometry in the oxide species were negligible. Also, since the difference between the standard Gibbs energies of formation of Co0 and of MgO is sufficiently large, MgO was presumably not reduced by Co at the solution electrode. The overall cell reaction may therefore be represented by COO(S) = CoO(ss), where ss denotes a solid solution, giving -2EF
= p(Co0, ss, T, x)-p(Co0, s, T) = RT ln(a(Co0, ss, T, x)} = RT ln(xf(Co0,
ss, T, x)>, (1) The experimental values of the e.m.f. Emeasured for the five compositions investigated are listed in table 1 at different temperatures. The e.m.f. was a linear function of
h%.kZTGAUD, 0.
496 TABLE
1. Experimental
x = 0.063 EJmV TIK 1457.7 1402.2 1359.0 1321.0 1261.0 1269.9 1313.6 1411.4 1460.0
GfOVANNBl”ri,
values of the e.m.f. solid solutions (xc00
x = 0.258 EjmV
1462.2 1406.2 1373.8 1324.1 1279.1 1268.2 1329.9 1378.9 1422.7 1474.1
E measured + (1 -
M.
58.3 54.5 51.1 47.1 46.9 44.3 49.7 53.1 55.3 58.6
1463.6 1418.3 1388.3 1325.6 1261.6 1276.8 1304.4 1377.5 1417.5 1480.5
HONE
at different x)MgO}
x = 0.453 E/mV riK
T/K
117.0 110.2 102.9 94.2 89.8 90.0 94.6 109.0 119.6
AND
temperatures
T for
x = 0.593 E/mV TIK
42.7 38.6 39.5 34.3 29.7 32.0 32.8 36.4 40.6 44.5
1463.3 1422.4 1377.7 1313.7 1222.3 1273.3 1304.6 1365.9 1409.4 1457.7
x = 0.889 E/mV
T/K
33.3 28.9 25.8 25.3 18.5 22.8 23.3 27.5 28.9 30.16
1456.0 1422.8 1417.8 1371.8 1334.6 1251.0 1278.2 1320.8 1376.8 1461.5
11.9 11.0 10.2 6.84 7.38 5.48 5.58 6.70 7.50 9.50
temperature for all compositions. The equations of the least-squares regression lines are given in table 2. Values of the chemical potential difference for Co0 were calculated from equation (1) at 1473, 1373, 1273, and 1173 K (the last being an extrapolated temperature from the values given in table 2), and are reported in table 3. The activity coefhcientsf(Mg0) of MgO in the solid solutions (xc00 + (1 - x)MgO} were obtained by use of the Gibbs-Duhem equation in its integrated form: In(f(Mg0,
TABLE for the five mole
fractions
x of Co0
x 0.063 0.258 0.453 0.593 0.889
TABLE
3. Chemical
T/K
potential (xc00
x= 1 {x/(1 -x)}d
A
B
0.150 0.070 0.063 0.051 0.028
101.8 44.9 48.9 42.7 30.7
& f * -+ I-t
203 89 107 126 123
ss, T, $1,
-4136 -2065 -1426 -1013 -252
1273 ss, T) - ACoO, j, f f f &
167 71 103 109 101
(2)
differences {,u(COO, ss, T) - p(CoO, + (1 - x)MgO} at four temperatures (c&b = 4.184 J)
(p(Co0, -3442 -1740 -1137 -778 -121
ln{f(CoO,
2. The coefficients of the equation E]mV = AT/K - B and the temperature range 1273 to 1473 K; value in this range
1173
x 0.063 0.258 0.453 0.593 0.889
X=X s
ss, T, x)} = -
1 0.4 0.5 0.7 0.6
s, 2”)) in the solid
solutions
T
1373 s, TMxil,h -4829 -2390 -1716 -1247 -383
& f rt f f.
1473 molwf
zt 155 f 66 rt 82 It 103 f 93
-5523 -2715 -2005 -1482 -5k4
+ f i z’c 5
173 72 89 113 102
ACTIVITY
OF Co0 IN SOLID SOLUTIONS
OF Co0 AND MgO
997
and integrating graphically by the trapezoidal method. To obtain the value of ln(f(MgO, ss, T, x --+ 1)) we used the Redlich method, which consists in equating the areas represented by the two sides of the thermodynamic relation: 1
In{f(CoO, ss, T, x))dx = ‘ln{f(MgO, ss, T, x))dx. (3) s0 s0 The results obtained for a(Ng0) and forf(Mg0) are given in table 4 with the corresponding quantities of COO. TABLE
U(CO&
fO0)
4. Values of the activities a and of the activity coefficients fof Co0 and of MgO in the solid solutions {Xc00 + (1 - x)MgO) at 1273 K 0.1930.063 f 0.007 3.01 1.00 0.94
0.44oi
0.2580.007 1.70 1.13 0.84
0.570.453 f 0.01 1.26 1.33 0.73
0.670.593 f 0.014 1.13 1.49 0.61
0.900.889 rt 0.016 1.Ol 2.16 0.24
4. conclusions The activity-composition relations for Co0 in solid solutions of Co0 and MgO which have been measured are in disagreement with previously reported results.(1*2) The difference is small but experimentally significant. The solutions of Co0 and MgO behave neither as ideal nor as regular solutions. The solutions show positive deviations from ideal behavior, as shown in figure 2.
0.6
e 0.4
'0
0.2
0.4.
0.6
0.8
1
x FIGURE 2. Activities u of Co0 and of MgO in the solid solutions (xCoO+(l -x)MgO} at 1273 K. 0 with uncertainty bounds, measured values for a(Co0); 0, calculated values for a(Mg0); 0, values for a(Co0) from Seetharamen and Abraham. (a, The limiting values implied by the tangents drawn on the figure are f(CoO,ss,l273 K, x+0) = 4.01 and f(MgO,ss,1273 K, x+1) = 3.16.
998
M. RIGAUD.
G. GIOVANNETTI,
AND M. HONE
The financial aid of the Ministry of Education of the Province of Quebec to one of the authors (G. Giovannetti), and of the National Research Council of Canada in providing equipment funds is gratefully acknowledged. REFERENCES 1. Auckrust, E.; Muan, A. Tram Met. Sot. AZh4E 1963,227, 1378. 2. Seetharaman, S.; Abraham, K. P. J. Electrochem. Sot. India. 1971, 20 54.