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An entropy meter based on the thermoelectric potential of a nonisothermal solid-electrolyte cell
w-533 J. Chem. Thermodynamics 1977,
9, 101 l-4020
An entropy meter based on the thermoelectric potential of a nonisothermal solid-electrolyte cell C. B. ALCOCK,
K. FITZNER,”
and
K. T. JACOB
Department of Metallurgy and Materials Toronto, Toronto, Canaaiz MSS IA4
Science, University of
(Received 6 December 1976) The theory, design, and performance of a solid electrolyte twin thermocell for the direct determination of the partial molar entropy of oxygen in a single-phase or multiphase mixture are described. The difference between the Seeheck co&icients of the concentric thermocells is directly related to the difference in the partial molar entropy of oxygen in the electrodes of each thermocell. The measured potentials are sensitive to small deviations from equilibrium at the electrodes. Small electric disturbances caused by simultaneous potential measurements or oxygen fluxes caused by large oxygen potential gradients between the electrodes also disturb the thermoelectric potential. An accuracy of 5~0.5 calth K-l mol-1 has been obtained by this method for the entropies of formation of NiO and NiAlz04. This “entropy meter” may he used for the measurement of the entropies of formation of simple or complex oxides with significant residual contributions which cannot be detected by heat-capacity measurements.
1. Jiltroduction The mixing of carions and vacancies on one or more crystallographic
sites of complex
oxide structures, or lack of magnetic ordering at temperatures accessible to heatcapacity measurements, give rise to residual contributions to the entropy. These contributions are well known in feldspars and inverse spinels and are probably present in a large family of oxides. At present the entropy of these oxides can be obtained only by combining equilibrium measurement of the Gibbs free energy and calorimetric measurementof the enthalpy of formation under similar conditions along with a “third-law” analysis of the results. Although entropies can be obtained in principle from the temperature coefficient of the Gibbs free energy of formation, the
accuracy of this method depends on the attainment of the same equilibrium internal structure after each temperature cycle. It is generally recognized that meaningful entropies can be derived in that way only if the Gibbs free energy is measured over the large temperature range (300 to 600 K), the phases are equilibrated for a long period at each temperature and detailed structure investigations are carried out on the phases in equilibrium. A simple and direct method for the measurement of entropies would facilitate data acquisition and contribute to a greater understanding of the relation between entropy and the crystallographic and electronic structure of complex oxides. a Onleavefrom the Institutefor MetalsResearch, PolishAcademy 30-059Krakow, Poland. 69
of Science,
25 Reymonta
Street.
1012
C. B. ALCOCK,
K. FITZNER,
AND
K. T. JACOB
2. Theoly The general equations derived by Howard and Lidiard’r) for the thermoelectric potential of thermocells can be simplified for solid oxide electrolytes’29 j) in which conduction is practically entirely due to oxygen ion migration. For a thermocell: Pt)O, 1 CaO+ZrO, 1 O,JPt, Tl T2 the expression for the Seebeck coefficient 9 is t,b= dE/dT = {25(0’-)-4s(e-,
Pt) - S(0,)}/4F,
(1)
(2)
where F is the Faraday constant, s(O’-) and !?(e-, Pt) are the entropies of transport of 02- ions and electrons, and S(0,) is the partial molar entropy of oxygen in the atmosphere at the electrodes. The entropy of transport is composed of both kinetic and thermodynamic terms and may be expressed as g(02-) = S(O’-)+Q*(O’-)/T, (3) or 3(02-) = S(O’-, vib) +S(O’-, cord’) +Q*(O’-)/T (4) = R(4 ln(v/v’)+3 In(Rv/kT)) +R In C, +Q*(O;)/T, where S(02-) is the partial molar entropy of oxide ions, which may be split into vibrational and configurational terms, Q*(O’-) is the enthalpy of transport of oxide ions, v is the Einstein frequency of vibration of ions in a perfect crystal, v’ is the vibrational frequency of ions near vacancies, h is the Planck constant, and C, is the mole fraction of vacancies on the oxygen sublattice : Ca = (x/2)-x for CaO -I- ZrO,, Co = (x/2)+x for Y203 +ZrO,, where x is the mole fraction of the dopant. The entropy of transport of electrons in the platinum leads has a value of 0.58 cal, K-r mol-’ at 1500 K and exhibits a small temperature dependence of 3 x low4 Cal,, Kw2 mol-‘.(4)t F or an electrolyte system such as CaO+Zr02 the variation of the Seebeck coefficient with the composition of the electrolyte is approximately given by the second term on the right-hand side of equation (4), if the oxygen vacancies do not form complexes. While the vibrational term may be approximately constant for each electrolyte system, it may be expected to depend on the nature of the dopant. Ruka et 01.‘~’ have pointed out that while the Seebeck coefficient cannot as yet be calculated with sufficient accuracy, the difference in Seebeck coefficients for two gas mixtures is directly related to the difference in partial entropy of oxygen in the two gas mixtures; d43as I)-ll/(gas 2) = {SW 2, gas 1) - S(O,, gas 2))/4~. (5) In this paper we investigate the possibility of using the above relation for the direct determination of the entropies of formation of oxides. When the mutual solubility of a metal and its oxide is small the relative partial molar entropy of oxygen in the metal + oxide mixture is simply related to the molar entropy of formation of the oxide. For the reaction: Ni(s) +$0,(g) = NiO(s), AS(O,, Ni +NiO) = 2AS”(NiO). -f Throughout
this paper calth = 4.184 J; ml 2= 101.325 kPa.
(6)
(7)
AN ENTROPY
1013
METER
For reactions involving gases the partial entropy of oxygen is a function of the gas composition and standard entropy change for the reaction. For example, the relative partial molar entropy of oxygen in a gas mixture of carbon monoxide and carbon dioxide is given by CO(g) +30,(g) = cwh (8) AS(Oz) = 2AS”(8) -2R In{p(CO,)/p(CO)), (91 where AS”(g) is the standard entropy change for reaction (8). If pure oxygen is used as the atmosphere in one thermocell, and a second cell in the same temperature gradient contains a mixture of Ni-t NiO, then by combining equations (5) and (7) one obtains the expression : AS”(Ni0)
= 2F($(O,)-
+(Ni +NiO)}.
(10)
If a mixture of carbon monoxide and carbon dioxide is used as the atmosphere in the reference thermocell instead of oxygen, the following equation can be applied, AS”(Ni0)
= 2F($(CO +CO,)-$(Ni
+NiO))
+AS”(8)-
R ln(p(CO,)/p(CO)).
(11)
Analogous expressions may be derived for the entropy of formation of NiAl,O*. For an (oxygen + inert gas) mixture the relative partial molar entropy is equal to -R In{p(O,)/p). It may therefore be possible to obtain values for the composition of such a simple gas mixture by measuring the Seebeck coefficient of a solid electrolyte in the gas mixture: ln(p(O,)/p}
= - 4F{ll/(O,) - tj(O, +inert gas))/R.
(121
Similarly the composition of a CO+COz gas mixture may also be obtained from thermoelectric potential measurements. The advantage of such an arrangement over the conventional isothermal galvanic-cell technique for oxygen-potential measurement is that a separate reference electrode is not required once the Seebeck coefficient of the electrolyte has been determined at any known oxygen pressure. Additional information from the mass balance equation is required to derive the composition of a multi-component gas mixture from measurements of the relative partial molar entropy of oxygen of this kind. The accuracy of gas analysis from the thermoelectric potential of “cells without reference electrodes” will also be evaluated in this study. 3. Design of twin thermocell A twin thermocell was designed to provide the information required for the use of equation (5). The difference in the thermoelectric potential of two concentric thermocells, each being equilibrated with a separate gas or condensed phase mixture and placed in the same temperature gradient, was measured by a “Princeton Applied Research” digital electrometer model TM 165. A schematic representation of the cell is shown in figure 1. A metal + oxide (Ni -tNiO or Ni +NiAl,O, +ct-Al,O,) pellet B was placed inside a closed-end calcia-stabilized zirconia tube A. The zirconia tube A was firmly attached to a water-cooled brass head by O-ring seals. The electrode pellet B was covered with a porous platinum foil G and pressed down by a second
1014
C. B. ALCOCK,
K. FITZNER,
a
AND K. T. JACOB
G?
FIGURE 1. Schematicdiagramof the twin thermocellfor the measurement of the entropy of formationof oxides;A and C arecalcia-stabilized zirconiatubesof the samecomposition,B andD aremetal+ oxidepelletsof the samecomposition,G and G’ arethin porousplatinumfoils, F and H are aluminasheaths for platinumleadsE and E’, I is the reactiontube andT1 andTz arePt-to(Pt + 13massper centof Rh) thermocouples. concentric calcia-stabilized
zirconia tube C of smaller diameter, open at both ends and identical in composition to the outer tube A. A second metal + oxide electrode D, with a hole drilled in its centre, was placed on top of the inner calcia-stabilized tube, with a porous platinum foil G’ inserted between the pellet and the tube. Platinum leads B to the lower electrode, insulated by an alumina sheath F, pass through the hole D in the upper electrode. The assembly inside the outer zirconia tube A is pressed down by a spring-loaded twin-bore alumina sheath H. Two thin bands of platinum were coated on the outer surface of the zirconia tube A at levels corresponding to the pellets B and D. Two Pt-to(Pt + 13 mass per cent Rh) thermocouples were attached to these platinized bands. The cell arranged in this manner was lowered into a vertical alumina reaction tube I, placed inside a molybdenum-wound furnace. Oxygen, oxygen + argon, or CO+CO, was passed through the reaction tube I, while a purified argon stream was passed through the assembly inside the zirconia tube A. The cell was placed in the furnace in such a way that the temperature gradient between the upper and lower electrodes was approximately 100 K. The arrangement allowed not only the measurement of the two thermoelectric potentials developed under separately controlled oxygen potentials but also the measurement of the e.m.f.‘s of the two isothermal galvanic cells, one at temperature T1 and the other at temperature T2, each having one metal + oxide electrode and another gas electrode. MATERIALS
Nickel and nickel oxide powders used in this study were 99.98 moles per cent pure and were supplied by Fisher Scientific Company. a-Alumina was supplied by Research Inorganic Chemical Company and was 99.995 moles per cent pure. The NiAl,O,
AN ENTROPY METER
1015
spine1 was prepared by heating (NiO + Al,O,) in air at 1600 K for 12 h. The formation of the spine1 was confirmed by X-ray diffraction analysis. The electrode pellets containing NiAI,O, were prepared by mixing Ni, NiAl,04, and cc-Al,O, in relative amounts 1.5, 1, and 1, compacting and sintering in evacuated silica capsules at 1375 K for 8 h. Pellets were contained in an alumina crucible which was placed inside the silica capsule. All gases and gas mixtures used in this study were obtained from Matheson of Canada. The argon, 99.998 moles per cent pure, was further purified by passing it over copper and titanium at 800 and 1150 K respectively. PROCEDURE
The twin thermocell was constructed as described above; oxygen, oxygen + argon, or CO + CO, was passed through the reaction tube at a flow rate of 200 cm3 min- ‘, and the zirconia tube A was flushed with purified argon at a rate of approximately 100 cm3 min- 1 for 12 h. The furnace was then heated to the required temperature. After a steady-state temperature profile had been attained, the temperature gradient was measured by the thermocouples T1 and T2. The thermoelectric potential of the calcia-stabilized zirconia tube A was then measured between the platinum leads of the two thermocouples. Attempts to measure this thermoelectric potential and thermocouple potential simultaneously on high-impedance digital voltmeters resulted in large fluctuations in the thermoelectric potential. An approximately 30 min interval after each measurement of the thermocouple voltage was required before stable (2 0.5 mV) thermoelectric potentials could be obtained using the common platinum leads. The two isothermal e.m.f.‘s at temperatures Tl and T, between the gas phase in the reaction tube and metal + oxide pellets were recorded. Finally the thermoelectric potential of calcia-stabilized zirconia tube C in contact with metal + oxide electrodes was measured between the platinum leads E and E’. This potential was very sensitive to small departures from thermodynamic equilibrium arising, for example, from polarization or lack of thermal equilibrium at the metal + oxide electrodes. For example, a f 10 mV deviation from equilibrium at these electrodes, indicated by the e.m.f. of the two isothermal galvanic cells, can cause approximately 25 per cent error in the measured thermoelectric potential. The two isothermal galvanic cells are therefore useful indicators of the existence of thermodynamic equilibrium at the metal + oxide electrodes, without which reliable thermoelectric potentials cannot be obtained. 4. Results Due to the permeability of the calcia-stabilized zirconia tube A to oxygen, the metal + oxide electrode was found to polarize by forming an outer coating of oxide, when pure oxygen was used as the reference gas for the thermoelectric potential measurements. This problem was overcome by using a CO +CO1 gas mixture, in which the mole ratio n(CO)/n(CO,) was l/33.5, as the reference gas, and reducing the oxygen potential gradient across the zirconia tube A. In figure 2 the e.m.f.‘s of the
C. B. ALCOCK,
1016 140
K. FITZNER,
I
I
I
AND
I
120-
K. T. JACOB I
I
I
I
I 1300
I
1
./@/
NO-
o/;
SO-
/-
4o:--yp--e, 20
o- 20
-
* I
I 1100
I Qk.\ 1200
I
1400
T/K - 273.15 FIGURE 2. The electromotive force of two isothermal cells at !I”1 and Ta: A, PtlNi + NiOl CaO + ZrO&O + CO@‘t, and B, PtJNi + NiA1204 i uA120&a0 + ZrO$O + COa(Pt with n(CO)/x(COz) = l/33.5 in the gas phase. 0, Reading at temperature T, ; 0, reading at temperature values reported in the literature.‘5*B) Ta; -,
0.2
I
I
----o?I(CO)/n (CO,) = l/33.5 -
*--~-~Q-~~-“~-D~a_--,-~-
O.l0 -r
- OIT; SC
o-b
;“E -O.l-* B
----
a A
I
‘Ni + NiO
-u--u---u--75n--a--O~------a=
Y
.,n
Y
I
Y Y Ni + NiAI,O, + AI,?, -
n (CO>/nCC02)= 9.53 -
----~-----n----~--------~
_____
- 0.2- 0.3- 0.4-f----L-----
*
____
+--------a--.--*=
02
- 0.5 -
0.9999 Ar + 0.ooO10, & ____ ----*-----’ 1 I
- 0.6---p------q---.-----I 1300 1400
1500
1600
/K FIGURE 3. Seebeck coefficient of calcia-stabilized zirconia containing 15 moles per cent of calcia in equilibrium with various electrodes. a, Seebeck coefficients obtained from twin thermocell with CO + CO2 mixture having n(CO)/n(CO,) equal to l/33.5 as the reference gas; b, Seebeck coefficients of pure oxygen, oxygen + argon (~(0~) = lo-* atm} and CO -I- CO2 {n(CO)/n(CO,) = 9.53) gas mixtures obtained independently in separate experiments,
1017
AN ENTROPY METER
two isothermal cells at temperatures TI and T2 are compared with those obtained in previous measurements(‘* ‘) with (Ni + NiO) and (Ni f NiA120, + a-Al,O,) electrodes. The good agreement obtained between these measurements and the earlier work indicates that the oxygen potentials over the pellets had attained their equilibrium values. The Seebeck coefficient, $ = E/AT, of the calcia-stabilized zirconia tubes A and C is plotted in figure 3 as a function of the average temperature, (T) = (Tl f T,)/2. The results indicate a small temperature dependence of the Seebeck coefficient. The mean-squares regression equations representing the variation of the Seebeck coefficient with temperature are summarized in table 1. Although the value of the Seebeck coefficient of the zirconia tube equilibrated with the metal + oxide could not be measured, as indicated earlier, directly against that of pure oxygen in this study, the Seebeck coefficients of pure oxygen, an (oxygen + argon) mixture with an oxygen partial pressure of 10e4 atm, and a (CO+CO,) mixture with n(CO)/n(CO,) equal to 9.53, were measured in independent experiments and are plotted in figure 3. Slightly different thermoelectric potentials were obtained TABLE 1. Measured Seebeckcoefficient of zirconia containing 15 moles per cent of calcia. The mean temperature (TI + T,)/Z is denoted by (atm = 101.325kPa) _ ---.
Electrode Pure oxygen (1 atm) Oxygen + argon {p(OJ = IOU4atmj co + co,{n(co)/n(co,) = l/33.5) co $- co,{n(co)/n(co,) = 9.53) Ni + NiO Ni + NiA1204 $ a-AlzOs
v/mV K-l -0.497 -0.695 $0.102 -0.105 -0.069 -0.08
+ + + + +
5.1 x 10-+(7->/K 5.4 x 10-5/K
when the zirconia tube A was held in a tilted position relative to the furnace tube. It appears that when the zirconia tube was not coaxial with the furnace tube, the thermoelectric potential did not correspond to the measured temperature gradient. While care was taken to see that the zirconia tube was coaxial with the furnace tube during the measurements reported in this paper, some uncertainty from this source is present in the reported Seebeck coefficients. The relative position of the zirconia tube was less important with the twin thermocell, when the differences in thermoelectric potentials are measured; the effect of position is probably the same on each thermocell. Part of the variation in cell potential with geometry may be caused by changes in gas velocity profiles and circulation patterns. From measurements in the limited temperature interval covered in this study, the small temperature dependence of the Seebeck coefficient cannot be accurately determined, and may be neglected in view of the experimental error (kO.5 mV) in the thermoelectric potential. The entropy of formation of NiO and NiA1204 calculated at a mean temperature of 1500 K are shown in table 2. The entropy change for reaction (8) was taken from JANAF tables.(‘)
C. B. ALCOCK,
1018 TABLE
K. FITZNER,
AND K. T. JACOB
2. Comparison of the entropies of formation of NiO and NiAlaOl obtained from Seebeck coefficient of twin thermocell with values in literature Wta = 4.184 J) ASp(1500 K)/caltr, K-l mol-l from Seebeck coefficients from literature NiO NiA1204 a
-20.46 f 0.45 -17.46 X!K0.5
-20.035 f 0.2 - 17.725 f 0.3
a For the reaction Ni + 40, + a-AlaOa=NiAlzO1.
5. Discussion SEEBECK
COEFFICIENT
Information available in the literature on the Seebeck coefficient of zirconia-based electrolytes is compared with the results obtained in this study in table 3. The values obtained in this study for zirconia containing 15 moles per cent of calcia is in good agreement with the measurements of Fischer,(‘) Ruka et al.,c3) Chebotin et a1.,(” and Pizzini et Al. The values obtained by Stein et al.,(“) and Fischer and Pieper for zirconia containing 15 moles per cent of calcia, and by Goto et a1.(r3) for zirconia containing 8 moles per cent of calcia are not compatible with our measurements. The small, almost negligible, positive temperature dependence of the Seebeck coefficient obtained in this study is supported by the results of Ruka et uL,“~’ and Fischer and Pieper, (12) but is in contrast to the positive temperature dependence suggested by Stein et al. (lr) for calcia + zirconia, and the negative temperature dependence found by Goto et uI.(‘~’ and Chebotin et aLcg’for calcia + zirconia, by Fridman et a1.(r4’ for yittria + zirconia and by Volchenkova et a1.(15) for scandia + zirconia. TABLE
3. Comparison of the Seebeck coefficients of ZrOa based solid electrolytes (atm = 101.325 kPa)
Investigators
~___-___-
Composition of electrolyte
Fischer@) Ruka et ~2.‘~’ Stein et al.“” Goto et ~1.“~’ Chebotin et al.“)
0.12CaO + O.lSCaO + 0.15CaO + O.OSCaO + 0.15CaO +
Pizzini et a[.(lO)
0.208CaO + 0.792ZrOa 0.215CaO + 0.785Zr02 0.255CaO + 0.745ZrOa 0.31CaO + 0.69ZrOa 0.19YaO1 -t 0.81ZrOz 0.1Yz03 + 0.9Zr0, 0.2Y103 -t O.SZrO2 0.3Y203 + 0.7Zr02 0.4YzO3 + 0.6Zr02 0.125Sc203 + 0.875ZrOz 0.13CaO -+ 0.87ZrGz 0.15CaO + 0.85ZrOa
Fridman et a1.“4)
Volchenkova et ~1.“~’ Fischer and Pieper”‘) This study
v/mV K-l
T/K
platm
-0.43 -0.44 -0.26 -0.57 -0.42 -0.45 -0.408 -0.397 -0.389 -0.382 -0.354 -0.47 -0.44 -0.43 -0.42 -0.4 -0.3 -0.43 to -0.41
1273 973 to 1573 1473 1473 1373 1373 1373 1373 1373 1373 1373 1448 1448 1448 1448 1273 1373 to 1923 1300 to 1625
1 1 0.21 1
_
0.88ZrGa 0.85Zr02 0.85Zr02 0.92ZrG2 0.85Zr0,
k.21 1 1 1 1 1 0.21 0.21 0.21 0.21 1 0.21 1
AN ENTROPY ENTROPY
METER
1019
MEASUREMENT
The entropy of formation of NiO and NiAI,O, obtained from the twin thermocell, with a CO-I- CO2 gas containing 2.9 volume per cent of CO as the reference, agrees well (table 2) with those obtained from thermal data on NiO(‘@ and the temperature coefficient of the oxygen potential of Ni+NiAl,O, + cl-Al,O, mixtures.@’ If one combines the information on the oxygen potential of this three-phase mixture with the calorimetric enthalpy of formation of NiAI,O,, (I’) the entropy of formation of NiA120, according to the reaction: NiO+a-Al,O, = NiA1,04 is -(17.73 + 0.3) Cal,, K-’ mol-’ at 1000 K. The Seebeck coefficient measured in this study is plotted as a function of the relative partial molar entropy of oxygen in figure 4. The experimental results, except
s (02)/cal,hK-l ndl FIGURE 4. Variation of the Seebeckcoefficientsof calcia-stabilized zirconia containing 15 moles per cent calcia with partial molar entropy of oxygenat 1500K. 0, Experimental points; -, theoretical slope predicted by equation (5). for a point representing the CO + CO, mixture containing 90.5 per cent by volume of CO, indicate a small deviation from the theoretical slope of 1/4F suggested by equation (5). Presence of impurities in commercial calcia-stabilized zirconia tubes, and larger experimental uncertainty in independently determined Seebeck coefficients under pure oxygen, oxygen + argon, and CO+C02 (90.5 per cent by volume of CO) mixtures, may account for some of this deviation. The results, however, suggest that the term representing the entropy of transport of oxygen in equation (2) varies slightly with oxygen partial pressure. At the oxygen potential corresponding to the CO + CO2 gas mixture containing 90.5 per cent by volume of CO, there may be a small contribution of electrons to the transport number. The numerically smaller Seebeck coefficient for this gas mixture may be a manifestation of this electronic contribution to the conductivity of calcia-stabilized zirconia. By choosing a reference electrode, with a partial molar entropy of oxygen close to that of the test electrode, the probable error in entropy measurement caused by the small deviation from theoretical slope in figure 4 can be minimized. Alternatively an empirical calibration of the entropy
1020
C. B. ALCOCK, K. FITZNER,
AND K. T. JACOB
meter, with a number of electrodes whose partial molar entropies of oxygen are known, may be employed. Based on our experiments the following improvements to the design of the twin thermocell are suggested. (1) The geometric construction of the cell may be altered so that the reference gas is in contact with both the inner and outer surface of the zirconia tube A. The horizontal gradient in oxygen potential across the wall of the tube can thus be eliminated, so that any potential uncertainty arising from the coupling of horizontal and vertical potential gradients in the tube can be avoided. (2) The use of liquid electrodes, saturated in one or more components, would accelerate the attainment of equilibrium by increasing the diffusion coefficients and enabling better contact with the electrolyte. (3) Separate platinum leads may be used for the measurement of the thermoelectric potential of the zirconia tube and for temperature measurement with Pt-to-Pt(Rh) thermocouples. These separate leads may be attached to isolated thin platinized bands on the electrolyte to minimize electrical interference. (4) The reference gas should have values for oxygen potential and partial molar entropy close to that of the experimental electrode. OXYGEN
SENSORS WITHOUT
A REFERENCE
ELECTRODE
From the reproducibility of the thermoelectric potentials obtained in this study, it can be estimated that if the temperature gradient is read with an accuracy of + 1 K over a 100 K interval, the oxygen pressure can be measured within about a factor of 3. Thus the accuracy of the method is poor in comparison to isothermal galvanic cells using the same solid electrolyte where an accuracy of f5 per cent in oxygen partial pressure can readily be obtained. Where the constraints of design of reactors require that no reference electrode be used, it is possible to get a rough estimate of oxygen pressure by Seebeck coefficient measurements. Financial assistance from the National acknowledged.
Research Council of Canada is gratefully
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
Howard, R. E.; Lidiard, A. B. Disc. Faraday Sot. 1957, 23, 113. Pitzer, K. S. J. Phys. Chem. l%l, 65, 147. Ruka, R. J.; Bauerle, J. E., Dykstra, L. J. Electrochem. Sot. lP68, 115, 479. Cusack, N.; Kendall, P. Proc. Phys. Sot. (London) 1958, 72, 898. Steele, B. C. H. Electromotive Force Measurements in High Temperature Systems. Alcock, C. B. ; editor. Inst. Min. Met. (London). 1968. Jacob, K. T.; Alcock, C. B. To be published. Stull, D. R.; Prophet, H. JANAF Thermodynamic Tables 2nd edition, NSRDS-NBS-37. U.S. Government Printing Office: Washington, D.C. 1971. Fischer, W. Z. Naturfirsch. A 1967, 2% 1575. Chebotin. V. N.: Fridman. S. L.: Pal’auev. S. F. Soviet Electrochem. 1970. 6. 1257. Pizzini, S.; Riccardi, C.; Wagner; V.; Sinistri, C. Z. Naturforsch. A 1970, !25; 559. Stein, G.; Lecante, A.; Guillou, M.; Millet, J. C.R. Acad. Sci. Paris 1968, 267, 1660. Fischer, W. A.; Pieper, C. Arch. Eisenhuttenw. 1973, 44, 251. Goto. K.; Ito, T.; Someno, M., Trans. Met. Sot. AIME 1969, 245, 1662. Fridman,.S. L.; Pal’guev, S. F.; Chebotin, V. N., Soveit Electiochem. 1959, 5, 325. Volchenkova .Z. S. :Pal’nuev. S. F. : Fridman.S. L. :Sizintseva.N. F. Soviet Electrochem. 1973.9.33 1. Wicks, C. E.f Block, Fy E. ‘U.S. GUY. Mink Euil. No. 605. U.S. Government Printing ‘O&e: Washington, D.C. 1963. Navrotsky, A.; Kleppa, 0. J. J. Inorg. Nucl. Chem. 1968, 30, 479.
9, 101 l-4020
An entropy meter based on the thermoelectric potential of a nonisothermal solid-electrolyte cell C. B. ALCOCK,
K. FITZNER,”
and
K. T. JACOB
Department of Metallurgy and Materials Toronto, Toronto, Canaaiz MSS IA4
Science, University of
(Received 6 December 1976) The theory, design, and performance of a solid electrolyte twin thermocell for the direct determination of the partial molar entropy of oxygen in a single-phase or multiphase mixture are described. The difference between the Seeheck co&icients of the concentric thermocells is directly related to the difference in the partial molar entropy of oxygen in the electrodes of each thermocell. The measured potentials are sensitive to small deviations from equilibrium at the electrodes. Small electric disturbances caused by simultaneous potential measurements or oxygen fluxes caused by large oxygen potential gradients between the electrodes also disturb the thermoelectric potential. An accuracy of 5~0.5 calth K-l mol-1 has been obtained by this method for the entropies of formation of NiO and NiAlz04. This “entropy meter” may he used for the measurement of the entropies of formation of simple or complex oxides with significant residual contributions which cannot be detected by heat-capacity measurements.
1. Jiltroduction The mixing of carions and vacancies on one or more crystallographic
sites of complex
oxide structures, or lack of magnetic ordering at temperatures accessible to heatcapacity measurements, give rise to residual contributions to the entropy. These contributions are well known in feldspars and inverse spinels and are probably present in a large family of oxides. At present the entropy of these oxides can be obtained only by combining equilibrium measurement of the Gibbs free energy and calorimetric measurementof the enthalpy of formation under similar conditions along with a “third-law” analysis of the results. Although entropies can be obtained in principle from the temperature coefficient of the Gibbs free energy of formation, the
accuracy of this method depends on the attainment of the same equilibrium internal structure after each temperature cycle. It is generally recognized that meaningful entropies can be derived in that way only if the Gibbs free energy is measured over the large temperature range (300 to 600 K), the phases are equilibrated for a long period at each temperature and detailed structure investigations are carried out on the phases in equilibrium. A simple and direct method for the measurement of entropies would facilitate data acquisition and contribute to a greater understanding of the relation between entropy and the crystallographic and electronic structure of complex oxides. a Onleavefrom the Institutefor MetalsResearch, PolishAcademy 30-059Krakow, Poland. 69
of Science,
25 Reymonta
Street.
1012
C. B. ALCOCK,
K. FITZNER,
AND
K. T. JACOB
2. Theoly The general equations derived by Howard and Lidiard’r) for the thermoelectric potential of thermocells can be simplified for solid oxide electrolytes’29 j) in which conduction is practically entirely due to oxygen ion migration. For a thermocell: Pt)O, 1 CaO+ZrO, 1 O,JPt, Tl T2 the expression for the Seebeck coefficient 9 is t,b= dE/dT = {25(0’-)-4s(e-,
Pt) - S(0,)}/4F,
(1)
(2)
where F is the Faraday constant, s(O’-) and !?(e-, Pt) are the entropies of transport of 02- ions and electrons, and S(0,) is the partial molar entropy of oxygen in the atmosphere at the electrodes. The entropy of transport is composed of both kinetic and thermodynamic terms and may be expressed as g(02-) = S(O’-)+Q*(O’-)/T, (3) or 3(02-) = S(O’-, vib) +S(O’-, cord’) +Q*(O’-)/T (4) = R(4 ln(v/v’)+3 In(Rv/kT)) +R In C, +Q*(O;)/T, where S(02-) is the partial molar entropy of oxide ions, which may be split into vibrational and configurational terms, Q*(O’-) is the enthalpy of transport of oxide ions, v is the Einstein frequency of vibration of ions in a perfect crystal, v’ is the vibrational frequency of ions near vacancies, h is the Planck constant, and C, is the mole fraction of vacancies on the oxygen sublattice : Ca = (x/2)-x for CaO -I- ZrO,, Co = (x/2)+x for Y203 +ZrO,, where x is the mole fraction of the dopant. The entropy of transport of electrons in the platinum leads has a value of 0.58 cal, K-r mol-’ at 1500 K and exhibits a small temperature dependence of 3 x low4 Cal,, Kw2 mol-‘.(4)t F or an electrolyte system such as CaO+Zr02 the variation of the Seebeck coefficient with the composition of the electrolyte is approximately given by the second term on the right-hand side of equation (4), if the oxygen vacancies do not form complexes. While the vibrational term may be approximately constant for each electrolyte system, it may be expected to depend on the nature of the dopant. Ruka et 01.‘~’ have pointed out that while the Seebeck coefficient cannot as yet be calculated with sufficient accuracy, the difference in Seebeck coefficients for two gas mixtures is directly related to the difference in partial entropy of oxygen in the two gas mixtures; d43as I)-ll/(gas 2) = {SW 2, gas 1) - S(O,, gas 2))/4~. (5) In this paper we investigate the possibility of using the above relation for the direct determination of the entropies of formation of oxides. When the mutual solubility of a metal and its oxide is small the relative partial molar entropy of oxygen in the metal + oxide mixture is simply related to the molar entropy of formation of the oxide. For the reaction: Ni(s) +$0,(g) = NiO(s), AS(O,, Ni +NiO) = 2AS”(NiO). -f Throughout
this paper calth = 4.184 J; ml 2= 101.325 kPa.
(6)
(7)
AN ENTROPY
1013
METER
For reactions involving gases the partial entropy of oxygen is a function of the gas composition and standard entropy change for the reaction. For example, the relative partial molar entropy of oxygen in a gas mixture of carbon monoxide and carbon dioxide is given by CO(g) +30,(g) = cwh (8) AS(Oz) = 2AS”(8) -2R In{p(CO,)/p(CO)), (91 where AS”(g) is the standard entropy change for reaction (8). If pure oxygen is used as the atmosphere in one thermocell, and a second cell in the same temperature gradient contains a mixture of Ni-t NiO, then by combining equations (5) and (7) one obtains the expression : AS”(Ni0)
= 2F($(O,)-
+(Ni +NiO)}.
(10)
If a mixture of carbon monoxide and carbon dioxide is used as the atmosphere in the reference thermocell instead of oxygen, the following equation can be applied, AS”(Ni0)
= 2F($(CO +CO,)-$(Ni
+NiO))
+AS”(8)-
R ln(p(CO,)/p(CO)).
(11)
Analogous expressions may be derived for the entropy of formation of NiAl,O*. For an (oxygen + inert gas) mixture the relative partial molar entropy is equal to -R In{p(O,)/p). It may therefore be possible to obtain values for the composition of such a simple gas mixture by measuring the Seebeck coefficient of a solid electrolyte in the gas mixture: ln(p(O,)/p}
= - 4F{ll/(O,) - tj(O, +inert gas))/R.
(121
Similarly the composition of a CO+COz gas mixture may also be obtained from thermoelectric potential measurements. The advantage of such an arrangement over the conventional isothermal galvanic-cell technique for oxygen-potential measurement is that a separate reference electrode is not required once the Seebeck coefficient of the electrolyte has been determined at any known oxygen pressure. Additional information from the mass balance equation is required to derive the composition of a multi-component gas mixture from measurements of the relative partial molar entropy of oxygen of this kind. The accuracy of gas analysis from the thermoelectric potential of “cells without reference electrodes” will also be evaluated in this study. 3. Design of twin thermocell A twin thermocell was designed to provide the information required for the use of equation (5). The difference in the thermoelectric potential of two concentric thermocells, each being equilibrated with a separate gas or condensed phase mixture and placed in the same temperature gradient, was measured by a “Princeton Applied Research” digital electrometer model TM 165. A schematic representation of the cell is shown in figure 1. A metal + oxide (Ni -tNiO or Ni +NiAl,O, +ct-Al,O,) pellet B was placed inside a closed-end calcia-stabilized zirconia tube A. The zirconia tube A was firmly attached to a water-cooled brass head by O-ring seals. The electrode pellet B was covered with a porous platinum foil G and pressed down by a second
1014
C. B. ALCOCK,
K. FITZNER,
a
AND K. T. JACOB
G?
FIGURE 1. Schematicdiagramof the twin thermocellfor the measurement of the entropy of formationof oxides;A and C arecalcia-stabilized zirconiatubesof the samecomposition,B andD aremetal+ oxidepelletsof the samecomposition,G and G’ arethin porousplatinumfoils, F and H are aluminasheaths for platinumleadsE and E’, I is the reactiontube andT1 andTz arePt-to(Pt + 13massper centof Rh) thermocouples. concentric calcia-stabilized
zirconia tube C of smaller diameter, open at both ends and identical in composition to the outer tube A. A second metal + oxide electrode D, with a hole drilled in its centre, was placed on top of the inner calcia-stabilized tube, with a porous platinum foil G’ inserted between the pellet and the tube. Platinum leads B to the lower electrode, insulated by an alumina sheath F, pass through the hole D in the upper electrode. The assembly inside the outer zirconia tube A is pressed down by a spring-loaded twin-bore alumina sheath H. Two thin bands of platinum were coated on the outer surface of the zirconia tube A at levels corresponding to the pellets B and D. Two Pt-to(Pt + 13 mass per cent Rh) thermocouples were attached to these platinized bands. The cell arranged in this manner was lowered into a vertical alumina reaction tube I, placed inside a molybdenum-wound furnace. Oxygen, oxygen + argon, or CO+CO, was passed through the reaction tube I, while a purified argon stream was passed through the assembly inside the zirconia tube A. The cell was placed in the furnace in such a way that the temperature gradient between the upper and lower electrodes was approximately 100 K. The arrangement allowed not only the measurement of the two thermoelectric potentials developed under separately controlled oxygen potentials but also the measurement of the e.m.f.‘s of the two isothermal galvanic cells, one at temperature T1 and the other at temperature T2, each having one metal + oxide electrode and another gas electrode. MATERIALS
Nickel and nickel oxide powders used in this study were 99.98 moles per cent pure and were supplied by Fisher Scientific Company. a-Alumina was supplied by Research Inorganic Chemical Company and was 99.995 moles per cent pure. The NiAl,O,
AN ENTROPY METER
1015
spine1 was prepared by heating (NiO + Al,O,) in air at 1600 K for 12 h. The formation of the spine1 was confirmed by X-ray diffraction analysis. The electrode pellets containing NiAI,O, were prepared by mixing Ni, NiAl,04, and cc-Al,O, in relative amounts 1.5, 1, and 1, compacting and sintering in evacuated silica capsules at 1375 K for 8 h. Pellets were contained in an alumina crucible which was placed inside the silica capsule. All gases and gas mixtures used in this study were obtained from Matheson of Canada. The argon, 99.998 moles per cent pure, was further purified by passing it over copper and titanium at 800 and 1150 K respectively. PROCEDURE
The twin thermocell was constructed as described above; oxygen, oxygen + argon, or CO + CO, was passed through the reaction tube at a flow rate of 200 cm3 min- ‘, and the zirconia tube A was flushed with purified argon at a rate of approximately 100 cm3 min- 1 for 12 h. The furnace was then heated to the required temperature. After a steady-state temperature profile had been attained, the temperature gradient was measured by the thermocouples T1 and T2. The thermoelectric potential of the calcia-stabilized zirconia tube A was then measured between the platinum leads of the two thermocouples. Attempts to measure this thermoelectric potential and thermocouple potential simultaneously on high-impedance digital voltmeters resulted in large fluctuations in the thermoelectric potential. An approximately 30 min interval after each measurement of the thermocouple voltage was required before stable (2 0.5 mV) thermoelectric potentials could be obtained using the common platinum leads. The two isothermal e.m.f.‘s at temperatures Tl and T, between the gas phase in the reaction tube and metal + oxide pellets were recorded. Finally the thermoelectric potential of calcia-stabilized zirconia tube C in contact with metal + oxide electrodes was measured between the platinum leads E and E’. This potential was very sensitive to small departures from thermodynamic equilibrium arising, for example, from polarization or lack of thermal equilibrium at the metal + oxide electrodes. For example, a f 10 mV deviation from equilibrium at these electrodes, indicated by the e.m.f. of the two isothermal galvanic cells, can cause approximately 25 per cent error in the measured thermoelectric potential. The two isothermal galvanic cells are therefore useful indicators of the existence of thermodynamic equilibrium at the metal + oxide electrodes, without which reliable thermoelectric potentials cannot be obtained. 4. Results Due to the permeability of the calcia-stabilized zirconia tube A to oxygen, the metal + oxide electrode was found to polarize by forming an outer coating of oxide, when pure oxygen was used as the reference gas for the thermoelectric potential measurements. This problem was overcome by using a CO +CO1 gas mixture, in which the mole ratio n(CO)/n(CO,) was l/33.5, as the reference gas, and reducing the oxygen potential gradient across the zirconia tube A. In figure 2 the e.m.f.‘s of the
C. B. ALCOCK,
1016 140
K. FITZNER,
I
I
I
AND
I
120-
K. T. JACOB I
I
I
I
I 1300
I
1
./@/
NO-
o/;
SO-
/-
4o:--yp--e, 20
o- 20
-
* I
I 1100
I Qk.\ 1200
I
1400
T/K - 273.15 FIGURE 2. The electromotive force of two isothermal cells at !I”1 and Ta: A, PtlNi + NiOl CaO + ZrO&O + CO@‘t, and B, PtJNi + NiA1204 i uA120&a0 + ZrO$O + COa(Pt with n(CO)/x(COz) = l/33.5 in the gas phase. 0, Reading at temperature T, ; 0, reading at temperature values reported in the literature.‘5*B) Ta; -,
0.2
I
I
----o?I(CO)/n (CO,) = l/33.5 -
*--~-~Q-~~-“~-D~a_--,-~-
O.l0 -r
- OIT; SC
o-b
;“E -O.l-* B
----
a A
I
‘Ni + NiO
-u--u---u--75n--a--O~------a=
Y
.,n
Y
I
Y Y Ni + NiAI,O, + AI,?, -
n (CO>/nCC02)= 9.53 -
----~-----n----~--------~
_____
- 0.2- 0.3- 0.4-f----L-----
*
____
+--------a--.--*=
02
- 0.5 -
0.9999 Ar + 0.ooO10, & ____ ----*-----’ 1 I
- 0.6---p------q---.-----I 1300 1400
1500
1600
1017
AN ENTROPY METER
two isothermal cells at temperatures TI and T2 are compared with those obtained in previous measurements(‘* ‘) with (Ni + NiO) and (Ni f NiA120, + a-Al,O,) electrodes. The good agreement obtained between these measurements and the earlier work indicates that the oxygen potentials over the pellets had attained their equilibrium values. The Seebeck coefficient, $ = E/AT, of the calcia-stabilized zirconia tubes A and C is plotted in figure 3 as a function of the average temperature, (T) = (Tl f T,)/2. The results indicate a small temperature dependence of the Seebeck coefficient. The mean-squares regression equations representing the variation of the Seebeck coefficient with temperature are summarized in table 1. Although the value of the Seebeck coefficient of the zirconia tube equilibrated with the metal + oxide could not be measured, as indicated earlier, directly against that of pure oxygen in this study, the Seebeck coefficients of pure oxygen, an (oxygen + argon) mixture with an oxygen partial pressure of 10e4 atm, and a (CO+CO,) mixture with n(CO)/n(CO,) equal to 9.53, were measured in independent experiments and are plotted in figure 3. Slightly different thermoelectric potentials were obtained TABLE 1. Measured Seebeckcoefficient of zirconia containing 15 moles per cent of calcia. The mean temperature (TI + T,)/Z is denoted by
Electrode Pure oxygen (1 atm) Oxygen + argon {p(OJ = IOU4atmj co + co,{n(co)/n(co,) = l/33.5) co $- co,{n(co)/n(co,) = 9.53) Ni + NiO Ni + NiA1204 $ a-AlzOs
v/mV K-l -0.497 -0.695 $0.102 -0.105 -0.069 -0.08
+ + + + +
5.1 x 10-+(7->/K 5.4 x 10-5
when the zirconia tube A was held in a tilted position relative to the furnace tube. It appears that when the zirconia tube was not coaxial with the furnace tube, the thermoelectric potential did not correspond to the measured temperature gradient. While care was taken to see that the zirconia tube was coaxial with the furnace tube during the measurements reported in this paper, some uncertainty from this source is present in the reported Seebeck coefficients. The relative position of the zirconia tube was less important with the twin thermocell, when the differences in thermoelectric potentials are measured; the effect of position is probably the same on each thermocell. Part of the variation in cell potential with geometry may be caused by changes in gas velocity profiles and circulation patterns. From measurements in the limited temperature interval covered in this study, the small temperature dependence of the Seebeck coefficient cannot be accurately determined, and may be neglected in view of the experimental error (kO.5 mV) in the thermoelectric potential. The entropy of formation of NiO and NiA1204 calculated at a mean temperature of 1500 K are shown in table 2. The entropy change for reaction (8) was taken from JANAF tables.(‘)
C. B. ALCOCK,
1018 TABLE
K. FITZNER,
AND K. T. JACOB
2. Comparison of the entropies of formation of NiO and NiAlaOl obtained from Seebeck coefficient of twin thermocell with values in literature Wta = 4.184 J) ASp(1500 K)/caltr, K-l mol-l from Seebeck coefficients from literature NiO NiA1204 a
-20.46 f 0.45 -17.46 X!K0.5
-20.035 f 0.2 - 17.725 f 0.3
a For the reaction Ni + 40, + a-AlaOa=NiAlzO1.
5. Discussion SEEBECK
COEFFICIENT
Information available in the literature on the Seebeck coefficient of zirconia-based electrolytes is compared with the results obtained in this study in table 3. The values obtained in this study for zirconia containing 15 moles per cent of calcia is in good agreement with the measurements of Fischer,(‘) Ruka et al.,c3) Chebotin et a1.,(” and Pizzini et Al. The values obtained by Stein et al.,(“) and Fischer and Pieper for zirconia containing 15 moles per cent of calcia, and by Goto et a1.(r3) for zirconia containing 8 moles per cent of calcia are not compatible with our measurements. The small, almost negligible, positive temperature dependence of the Seebeck coefficient obtained in this study is supported by the results of Ruka et uL,“~’ and Fischer and Pieper, (12) but is in contrast to the positive temperature dependence suggested by Stein et al. (lr) for calcia + zirconia, and the negative temperature dependence found by Goto et uI.(‘~’ and Chebotin et aLcg’for calcia + zirconia, by Fridman et a1.(r4’ for yittria + zirconia and by Volchenkova et a1.(15) for scandia + zirconia. TABLE
3. Comparison of the Seebeck coefficients of ZrOa based solid electrolytes (atm = 101.325 kPa)
Investigators
~___-___-
Composition of electrolyte
Fischer@) Ruka et ~2.‘~’ Stein et al.“” Goto et ~1.“~’ Chebotin et al.“)
0.12CaO + O.lSCaO + 0.15CaO + O.OSCaO + 0.15CaO +
Pizzini et a[.(lO)
0.208CaO + 0.792ZrOa 0.215CaO + 0.785Zr02 0.255CaO + 0.745ZrOa 0.31CaO + 0.69ZrOa 0.19YaO1 -t 0.81ZrOz 0.1Yz03 + 0.9Zr0, 0.2Y103 -t O.SZrO2 0.3Y203 + 0.7Zr02 0.4YzO3 + 0.6Zr02 0.125Sc203 + 0.875ZrOz 0.13CaO -+ 0.87ZrGz 0.15CaO + 0.85ZrOa
Fridman et a1.“4)
Volchenkova et ~1.“~’ Fischer and Pieper”‘) This study
v/mV K-l
T/K
platm
-0.43 -0.44 -0.26 -0.57 -0.42 -0.45 -0.408 -0.397 -0.389 -0.382 -0.354 -0.47 -0.44 -0.43 -0.42 -0.4 -0.3 -0.43 to -0.41
1273 973 to 1573 1473 1473 1373 1373 1373 1373 1373 1373 1373 1448 1448 1448 1448 1273 1373 to 1923 1300 to 1625
1 1 0.21 1
_
0.88ZrGa 0.85Zr02 0.85Zr02 0.92ZrG2 0.85Zr0,
k.21 1 1 1 1 1 0.21 0.21 0.21 0.21 1 0.21 1
AN ENTROPY ENTROPY
METER
1019
MEASUREMENT
The entropy of formation of NiO and NiAI,O, obtained from the twin thermocell, with a CO-I- CO2 gas containing 2.9 volume per cent of CO as the reference, agrees well (table 2) with those obtained from thermal data on NiO(‘@ and the temperature coefficient of the oxygen potential of Ni+NiAl,O, + cl-Al,O, mixtures.@’ If one combines the information on the oxygen potential of this three-phase mixture with the calorimetric enthalpy of formation of NiAI,O,, (I’) the entropy of formation of NiA120, according to the reaction: NiO+a-Al,O, = NiA1,04 is -(17.73 + 0.3) Cal,, K-’ mol-’ at 1000 K. The Seebeck coefficient measured in this study is plotted as a function of the relative partial molar entropy of oxygen in figure 4. The experimental results, except
s (02)/cal,hK-l ndl FIGURE 4. Variation of the Seebeckcoefficientsof calcia-stabilized zirconia containing 15 moles per cent calcia with partial molar entropy of oxygenat 1500K. 0, Experimental points; -, theoretical slope predicted by equation (5). for a point representing the CO + CO, mixture containing 90.5 per cent by volume of CO, indicate a small deviation from the theoretical slope of 1/4F suggested by equation (5). Presence of impurities in commercial calcia-stabilized zirconia tubes, and larger experimental uncertainty in independently determined Seebeck coefficients under pure oxygen, oxygen + argon, and CO+C02 (90.5 per cent by volume of CO) mixtures, may account for some of this deviation. The results, however, suggest that the term representing the entropy of transport of oxygen in equation (2) varies slightly with oxygen partial pressure. At the oxygen potential corresponding to the CO + CO2 gas mixture containing 90.5 per cent by volume of CO, there may be a small contribution of electrons to the transport number. The numerically smaller Seebeck coefficient for this gas mixture may be a manifestation of this electronic contribution to the conductivity of calcia-stabilized zirconia. By choosing a reference electrode, with a partial molar entropy of oxygen close to that of the test electrode, the probable error in entropy measurement caused by the small deviation from theoretical slope in figure 4 can be minimized. Alternatively an empirical calibration of the entropy
1020
C. B. ALCOCK, K. FITZNER,
AND K. T. JACOB
meter, with a number of electrodes whose partial molar entropies of oxygen are known, may be employed. Based on our experiments the following improvements to the design of the twin thermocell are suggested. (1) The geometric construction of the cell may be altered so that the reference gas is in contact with both the inner and outer surface of the zirconia tube A. The horizontal gradient in oxygen potential across the wall of the tube can thus be eliminated, so that any potential uncertainty arising from the coupling of horizontal and vertical potential gradients in the tube can be avoided. (2) The use of liquid electrodes, saturated in one or more components, would accelerate the attainment of equilibrium by increasing the diffusion coefficients and enabling better contact with the electrolyte. (3) Separate platinum leads may be used for the measurement of the thermoelectric potential of the zirconia tube and for temperature measurement with Pt-to-Pt(Rh) thermocouples. These separate leads may be attached to isolated thin platinized bands on the electrolyte to minimize electrical interference. (4) The reference gas should have values for oxygen potential and partial molar entropy close to that of the experimental electrode. OXYGEN
SENSORS WITHOUT
A REFERENCE
ELECTRODE
From the reproducibility of the thermoelectric potentials obtained in this study, it can be estimated that if the temperature gradient is read with an accuracy of + 1 K over a 100 K interval, the oxygen pressure can be measured within about a factor of 3. Thus the accuracy of the method is poor in comparison to isothermal galvanic cells using the same solid electrolyte where an accuracy of f5 per cent in oxygen partial pressure can readily be obtained. Where the constraints of design of reactors require that no reference electrode be used, it is possible to get a rough estimate of oxygen pressure by Seebeck coefficient measurements. Financial assistance from the National acknowledged.
Research Council of Canada is gratefully
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
Howard, R. E.; Lidiard, A. B. Disc. Faraday Sot. 1957, 23, 113. Pitzer, K. S. J. Phys. Chem. l%l, 65, 147. Ruka, R. J.; Bauerle, J. E., Dykstra, L. J. Electrochem. Sot. lP68, 115, 479. Cusack, N.; Kendall, P. Proc. Phys. Sot. (London) 1958, 72, 898. Steele, B. C. H. Electromotive Force Measurements in High Temperature Systems. Alcock, C. B. ; editor. Inst. Min. Met. (London). 1968. Jacob, K. T.; Alcock, C. B. To be published. Stull, D. R.; Prophet, H. JANAF Thermodynamic Tables 2nd edition, NSRDS-NBS-37. U.S. Government Printing Office: Washington, D.C. 1971. Fischer, W. Z. Naturfirsch. A 1967, 2% 1575. Chebotin. V. N.: Fridman. S. L.: Pal’auev. S. F. Soviet Electrochem. 1970. 6. 1257. Pizzini, S.; Riccardi, C.; Wagner; V.; Sinistri, C. Z. Naturforsch. A 1970, !25; 559. Stein, G.; Lecante, A.; Guillou, M.; Millet, J. C.R. Acad. Sci. Paris 1968, 267, 1660. Fischer, W. A.; Pieper, C. Arch. Eisenhuttenw. 1973, 44, 251. Goto. K.; Ito, T.; Someno, M., Trans. Met. Sot. AIME 1969, 245, 1662. Fridman,.S. L.; Pal’guev, S. F.; Chebotin, V. N., Soveit Electiochem. 1959, 5, 325. Volchenkova .Z. S. :Pal’nuev. S. F. : Fridman.S. L. :Sizintseva.N. F. Soviet Electrochem. 1973.9.33 1. Wicks, C. E.f Block, Fy E. ‘U.S. GUY. Mink Euil. No. 605. U.S. Government Printing ‘O&e: Washington, D.C. 1963. Navrotsky, A.; Kleppa, 0. J. J. Inorg. Nucl. Chem. 1968, 30, 479.