Study of solid electrolyte polarization by a complex admittance method

J. Phys. Chem. Solids

Pergamon Press 1969. Vol. 30, pp. 2657-2670.

Printed in Great Britain.

STUDY OF SOLID ELECTROLYTE POLARIZATION BY A COMPLEX ADMITTANCE METHOD J. E. BAUERLE Westinghouse Research Laboratories, Pittsburgh, Pa. 15235, U.S.A. (Received4 March 1969; in revisedform 4 June 1969) Abstract-The polarization behavior of zirconia-yttria solid electrolyte specimens with platinum electrodes has been studied over a temperature range of 400” to 800°C and a wide range of oxygen partial pressures. The complex admittance of these specimens was determined over a frequency range from d.c. to 100 kHz. An analysis of these data in the complex admittance plane indicated the presence of three polarizations: (1) an electrode polarization characterized by a double layer capacity and an effective resistance for the overall electrode reaction, mo,(gas) + 2efplatinum) * 02(electrolyte); (2) a capacitive-resistive electrolyte polarization, probably corresponding to a partial blocking of oxvgen ions at the electrolvte grain boundaries by an impurity phase there; and (3) a pure _ _ ohmic eiectroly& polarization. INTRODUCTION

oxygen ion conductivity occurring in zirconia-yttria and similar solid electrolytes at elevated temperatures is well known and has been the subject of numerous experimental studies. In these essentially pure ionic conductors, there have been surprisingly few experimental studies of basic polarization processes at the electrodes and within the electrolyte [ 1,2]. One difhculty has been the lack of an established technique for studying polarization cells of these materials. We require a method in which the current through the cell is kept very low to avoid irreversible electrode changes and heating effects, and which is capable of resolving several polarizations occurring in the same specimen. An obvious solution to these difficulties is to study the impedance (or admittance) of the cell as a function of frequency with low amplitude a.c., but there still remains the awkward problem of analyzing data involving several polarizations which may partially overlap in the frequency domain. The method we have employed eliminates these difficulties and appears not to have been applied previously to solid electrolyte THE LARGE

systems. It is based on measurements of the cell admittance which are taken over a wide range of frequencies and then analyzed in the complex admittance plane. Although analogs of this method have been used in other fields for many years[3-51, its application to electrochemistry is fairly recent. In particular, Sluyters et a1.[6] have used it extensively in their studies of aqueous cell polarization phenomena. There are two purposes to this paper: To suggest on the basis of our experiments which basic polarization processes predominate in cells of zirconia-yttria, and to demonstrate the usefulness of the complex admittance approach in solid electrolyte studies. EXPERIMENTAL PROCEDURE

The specimen material was (Zr02)o.9 from three different (Y2OJo.1, obtained sources: (1) commercial material from Zircoa; (2) material prepared at these Laboratories by standard ceramic procedures; and (3) high purity material sintered under contamination-free conditions in an arc image furnace. Specimens were generally either wafers, approximately lx3X4mm, or approximately 1 X 1 X 12 mm. This bars,

2651

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J. E. BAUERLE

allowed us to vary the area/length factor, A/L, by approximately 100, and the length factor by about 10. All the electrodes were of platinum. Two types of preparation were employed: (1) platinum paste, fired at 1400°C for 1 hr, with weights ranging from 2.5 to 4.5 mg/cm*; and (2) platinum sputtered on by d.c. plasma to weights of O-4 to 2.8 mg/cm*, i.e. 200013,000 A. The porosity of the electrodes (as will be seen later) was a very important variable. Platinum paste electrodes fired at 1400°C were quite non-porous; however, they could be made very porous by passing a heavy current (1 A/cm*) through them for several minutes at 800°C. Presumably, this treatment produced pores by means of the very high oxygen pressures which would be generated at the interface. Sputtered platinum electrodes were reasonably porous as formed and needed no special treatment. The presence of porosity was readily detectable by applying a small drop of liquid to the electrode and observing its disappearance (or lack of it) by capillary action. Specimens were suspended between baffles in the hot zone of a tube furnace (pure alumina tube) with a Pt-Pt 10% Rh thermocouple adjacent to the specimen. Various oxygen partial atmospheres were achieved by flowing calibrated mixtures of oxygen-argon or oxygen-nitrogen through the apparatus. These ranged from 1.5 X low5 to 1 atm of oxygen. The flow rates employed were between 200 and 800 cm3/min for a system having a volume of about 900 cm3. The admittance bridge which we employed in our polarization studies was simple but quite sensitive. A rough schematic is shown in Fig. 1. Some characteristics of this bridge were the following: Voltage across specimen, 13 mV r.m.s.; frequency range, d.c. to 100 kHz; detectable unbalance, 0.1 per cent; balance unaffected by a.c. pickup; nonlinearity in specimen easily detectable by presence of harmonics on scope. The high

Fig. 1. Admittance bridge schematic.

sensitivity was achieved by synchronizing the null detecting scope to the a.c. line frequency. When the bridge was balanced, one observed a sharp steady trace of the residual a.c. pickup in the system; for a very small unbalance, a ‘rippling’ motion could be seen in the trace,* due to the different frequency of the bridge oscillator. Tests were made to determine the effects of residual capacitance and inductance on the bridge accuracy and sensitivity. Corrections for such effects were small and occurred only at the highest frequencies. COMPLEX ADMITTANCE PLOTS

Complex admittance plots are useful for determining an appropriate equivalent circuit for a system and for estimating the values of the circuit parameters. The complex admittance Y (0) of a system at an applied angular frequency o may be written as the sum of a conductance G (CO)and a susceptance B (0) :

Y(w) = G(w) +jl?(o).

(1)

If one plots the imaginary part of the admittance vs. the real part, i.e. B(o) vs. G(w), the resulting locus shows distinctive features for certain combinations of circuit elements. The method is perhaps best illustrated by specific examples of such plots (Figs. 2 and 3) for some simple circuits.? Very roughly, one can say that each semi-circular arc corresponds to a ‘lumped’ R-C combination; each quarter-cir*Tests showed that an unbalance emf of 0.1 mm amplitube could be detected in a trace whose width was 0.5 mm. tWe have excluded inductances from our circuits; in general, the equivalent circuits for electrochemical processes do not require their use.

SOLID

ELECTROLYTE

2659

POLARIZATION

B

R

G

i

(d)

R

I (e)

R

Fig. 2. Admittance plots for some simple R-C circuits.

cular arc corresponds to a combination of a lumped R and a distributed R-C element, such as the Warburg impedance. (The latter element is the analog for a diffusive process.) It is seen in Figs. 2 and 3 that the resistance values are derivable from the circular-arc intercepts on

the G-axis; the capacitance values can be derived from expressions involving the frequencies at the peaks of the circular arcs. The exact equations for these loci can be derived using simple a.c. circuit theory[6, 71; the process is straightforward but tedious and

2660

J. E. BAUERLE A “Warburg

Impedance”

It Is _Approximately

Its Admittance

Is Designated

Equivalent

Is Given WhereA =d-

To The

B

By The

Infinite

Y = A&

Symbol

R-C

tine

+ jAo*,

The equivalent circuit which we shall choose (somewhat arbitrarily at this point) as a representation for our specimens is shown in Fig. 7. It is seen that it satisfies the minimum requirement of yielding the same type of admittance behavior as our specimens. The justification for choosing this particular circuit will become clearer in the sections to follow.

ELECTRODE VS. ELECTROLYTE IN THE EQUIVALENT CIRCUIT

G

ICI

td)

Fig. 3. Admittance plots for some circuits containing a Warburg (diffusional) impedance.

will not be given here. A theoretical discussion of the relationship of these plots to relaxation processes in general has been given by Schrama[& CHOOSING THE EQUIVALENT CIRCUIT

In general, for a given admittance plot there exists more than one possible equivalent circuit (see, for example, Fig. 2(h) and Fig. 7.). One chooses between these on the basis of (1) simplicity, and (2) consistency with what is known about the physical processes of the system. For example, two parallel networks would obviously not be appropriate as analogs for two physical processes that were known to occur in sequence or series [9]. Examples of typical admittance behavior for our zirconia-yttria specimens are shown in Figs. 4-6. To a good approximation, the behavior is that of a lumped parameter system. (Ideally, the angles in the figures would be 0” for lumped parameters or 45” for distributed parameters.)

One of the first questions to be settled experimentally was the following: What portion of the equivalent circuit in Fig. 7 corresponds to the electrode region and what portion corresponds to the bulk of the specimen, i.e. the electrolyte? Two different approaches were tried which led to the same conclusion. The first approach was based on the fact that electrode equivalent circuit parameters should vary with the electrode area A but not the specimen length L, while electrolyte equivalent circuit parameters should vary with the factor A/L. In one test A was increased by a factor of 3 while A/L was increased by a factor of 200. In another test, A was decreased by a factor of 7 while AIL was increased by a factor of 2. It was found that l/R, and C, were proportional to A, while l/Rz, C2, and l/R, were proportional to A/L. A second approach to testing the electrodeelectrolyte question was based on the four-terminal d.c. conductance of a specimen. This type of measurement excludes electrode effects; only the d.c. electrolyte resistance is measured. Such a measurement was carried out on a bar-geometry specimen, and subsequently admittance measurements were made for the same gauge length. The experimental results are shown in Fig. 8. It is seen that the four-terminal conductance coincides with G, on the admittance plot, which is just the d.c. conductance of the equivalent circuit with R, excluded.

SOLID

ELECTROLYTE

POLARIZATION

Fig. 4. Admittance behavior for a specimen with non-emus

These

tests

showed

unambiguously

that

R1 and C1 correspond to electrode polarization processes; R2,C, and R3 correspond to polarization processes in the bulk of the specimen. In terms of admittance plots, the lower frequency dispersion corresponds to the

2461

electrodes @t paste). -..

electrode and the higher frequency dispersion corresponds to the electrolyte. Further evidence for the correctness of the above interpretation will be found in the sections on the effects of various atmospheres and the effects of electrode porosity.

2642

J. E. BAUERLE

1kMz

GllO-

$--‘I

zc&IO%

,’

1 kHz

0

/“’

‘I,ll,~,lllll 0

1

ts.3pY

Pkuz

I,~,‘,,~,,,,~,,,,,,,, 3

4

5

GflO-*f’,

Fig. 5. Admittance

ELECTRODE

POLARIZATION

behavior for a specimen with naturally porous electrodes (sputtered Pt). BEHAVIOR

The electrode behavior of our specimens* *The electrode ~gement on our specimens was symmetrical; hence, the parameters R, and Cr represent the resultant behavior of two nearly identical electrodes, the parameters for one of these being tR, and 2C,. This procedure is legitimate provided that ( 1) we employ only small signal a.c. in the measurements, and (2) we do not employ a d.c. bias voltage. If the two electrodes should diier considerably in their properties, one would obtain a distorted non-circular arc on the admittance plot.

is described in terms of the resistance R, and the capacitance C1, in parallel. Our present hypothesis is that C1 represents the doublelayer capacity of the electrode, and RI represents an effective resistance for the overall electrode reaction &O&as) + 2e(platinum) ~3 02-(electrolyte) (2)

SOLID ELECTROLYTE

2663

POLARIZATION

1*6I*4I-2-

460%

_- PO0.8-

!mttz is I t t I 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3-8 4.0 I,

6-i&-.

mo-3ci-h', 0.8 t

c

6wc

0.6

8UPC 0.6-ap &4a z 0.20 0

,/ I O-2

I 04

I 0.6

I 0.8

I 1.0

I I 1.2 1.4 Gti2n",

, I.6

1.11 f?&O 14.F

2.2

1 2.4

Fig. 6. Admittance behavior for a specimen with artificially porous electrodes (Pt paste + heavy current treatment; see text).

and 13,000 A thickness; temperatures from 400 to 800°C; and oxygen partial pressures from 1.5 x lo+ to 1 atm. Dependence on Electrode capacitance Cl these variables was considered too weak to Most of the experimental values for C1 fell be significant. A calculation of the double-layer capacity in the range of 30-80 pf/cm2, i.e. 60-160 CLfl for (ZrO,),.g(YzOJ,., using conventional cm2 at each electrode. * Included in this range electrostatic theory{1 11 gives a value of 190 were the following: non-porous Pt paste eleci.cflcm2; however, this must be considered as trodes; sputtered Pt electrodes of 2000 only a rough upper limit to the true double*Based on the apparent electrode area. The tree microlayer capacity since it neglects the effect of scopic area could have been either larger or smaller than the compact double layer [ 121. this.

which is known to take place under these conditions[ lo].

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J. E. BAUERLE

Electrode resistance RI Unlike the electrode capacitance, the electrode resistance R, was found to be very sensitive to such parameters as electrode preparation, temperature, and oxygen partial pressure. One may consider the reciprocal of R, to be a measure of the speed of the overall reaction (2). We postulate that this reaction involves the following steps:

* Cl

C2

Equi&nt

Circuit

_

s

Peak

1$/-Jqy” 61 Admittance

G2

G3

Plot for Equivalent

I

Circuit

I

q=+-q

ft.&-+

1’ R3 =q

2 G2

cl=2nfltG2-Gl)

I

‘2=

c,’

2nt21G3-

G2)

Fig. 7. Equivalent circuit for the specimens. for obtaining equivalent circuit parameters mittance plot parameters.

Equations from ad-

Anomalously high experimental values for C, (550 pf/cmz in some cases) were obtained with platinum paste electrodes which had been treated with high currents to make them porous. The origin of these high capacitances is not understood at this time.

(1) Flow of oxygen into the pores of the platinum electrode. (2) Adsorption of molecular oxygen on the pore walls in the electrode. The work of various investigators [ 13, 141 strongly suggests that a platinum surface at these temperatures and pressures would be completely covered with a tightly bound monolayer of oxygen atoms. We are postulating a relatively weak chemisorption of oxygen molecules on this monolayer. (3) Surface diffusion of oxygen molecules to electrode-electrolyte interface. of oxygen molecules. (4) Dissociation (This step might occur before step 3 .) (5) Electron transfer reaction at interface (0 + 2e @ O*-, for example). Let us now consider the experimentally observed behavior of R,. First, we found that

5OOT

0.6

10th

Fig. 8. Admittance plot for a specimen with its 4-terminal d.c. conductance (arrow) marked on the G-axis. The dispersion to the left of this value arises from electrode polarization; the dispersion to the right arises from electrolyte polarization.

SOLID

ELECTROLYTE

POLARIZATION

2665

R~ was reasonably

low only when the electrodes were porous. Qualitatively this behavior may be seen in the admittance plots of Figs. 4-6. This indicates that electrode porosity was essential for the occurrence of reaction (2). Such a result is not too surprising since solid platinum is essentially impermeable to oxygen, even at 1425”C[15]. We do not believe, however, that the pores function only as simple flow channels for gaseous oxygen. Second, we studied the dependence of RI on the oxygen partial pressure (Fig. 11). At 4OO”C, no effect was observed. At 600” and 8OO”C, one can see a strong effect on the electrode dispersion and the complete absence of an effect on the electrolyte dispersion. From plots of this type we obtained data for the dependence of the electrode resistance R, on the oxygen partial pressure P. These data, as shown in Fig. 12, can be fit with either of the empirical expressions -=1 &

- P A ( B+P* >

(3)

or 1 -= RI

P A’ ( B’

cx’ >

(4)

where the A’s, B’s and (Y’S are constants ((Y,cr’ = 0.64). The form of these expressions is that of typical adsorption isotherms[16]. This leads us to hypothesize that at a fixed temperature, the speed of the electrode reaction (measured by l/R,) is a direct function of the concentration of molecular oxygen adsorbed on the platinum pore walls. If this is true, one can deduce that the adsorption process is near its equilibrium (for this temperature), because RI is ohmic over a wide range of currents and depends reversibly on the oxygen partial pressure. Third, we found that the temperature dependence of RI corresponded to a thermally activated process with a rather high activation energy, approximately 2-2-5 eV (see Figs. 9

9

10

11

12

13

14

15

IO4OK-’ -i_, Fig. 9. Temperature dependence of the equivalent circuit resistances. Electrodes were naturally porous (sputtered Pt). Spec. No. 1: 13,OOOA thick. Siei. No. 10:72000A thick. Electrolyte was zirconia-yttria of moderate purity, prepared at this Lab.

and 10). This cannot correspond to the adsorption step (which is near equilibrium) because the temperature dependence is in the wrong direction [ 161. The surface di~sion step also may be ruled out; one would expect to find a relatively small activation energy for this process[l7]. Thus, we are left with either the molecular dissociation step or the electron transfer step as the probable source of the strong temperature dependence of RI. To summarize, our results suggest that the electrode resistance R, depends on the oxygen partial pressure via an adsorption-desorption equilibrium of oxygen molecules on the porous platinum surface, and it depends on tempera-

2666

J. E. BAUERLE 1.

8W

oc

600

I

400

I

I(

I(

IC

E” f a= 10

10

10

1

t I

9

I

10

1

1

/

I

11

12

13

14

15

lo" -1 T 'K

Fig. 10. Temperature dependence of the equivalent circuit resistances. Electrodes were artificially porous (Pt paste+ heavy current treatment). Spec. No. 13: Moderate purity zirconia-yttria prepared at this Lab. Spec. No. 14: Moderate purity commercial zirconia-yttria.

ture via a thermally activated process, most likely either the dissociation of oxygen molecules (on platinum) or an electron-transfer reaction at the electrode interface. ELECTROLYTE

POLARIZATION

BEHAVIOR

The behavior of the electrolyte proper is described by the equivalent circuit parameters RP, Cz and R3. As discussed earlier, the values of these parameters are derivable from the second region of dispersion on the admittance plots. We shah first describe the general behavior of these parameters and then consider the possible physical interpretation of them.

Electrolyte specimens of moderate purity These specimens include both commercially obtained zirconia-yttria and material produced at this Laboratory by standard ceramic techniques. As one might expect, the electrolyte parameters RZ, C, and R3 were insensitive to changes in the oxygen partial pressure. This can be seen quite clearly in Fig. 11 (600°C). The quantities Rz and Rz + R3 show a strong similarity in their temperature dependence (Figs. 9 and 10). This suggests that the resistances R2 and R3 may arise from the same type of physical process, a point which will be mentioned again later. From the standpoint of our equivalent circuit, the quantity R2 + R3 should correspond to the d.c. resistance of the electrolyte. The activation energy of R, + R3 varies slowly from about 1.1 eV at 400°C to about O-9 eV at 800°C. This latter value agrees well with the literature values [18, 191, which are based on conductivity data in the range 600”- 1300°C. The capacitance C, was found to be independent of temperature and quite reproducible for electrolyte material from a given source. For the normalized capacitance, (L/A) CZ, which is numerically independent of the specimen geometry, we obtained values of O-028 pf/cm for zirconia-yttria prepared by standard procedures at these Laboratories and 0.015 pf/cm for the commercially prepared zirconia-yttria. High purity zirconia-yttria A specimen of high purity material was sintered under contamination-free conditions in an arc image furnace. An example of the admittance behavior obtained with this material is seen in Fig. 13. Note that the second dispersion region which we associate with the electrolyte proper, was in this case very small or absent. The location of the 4-terminal d.c. conductance on this plot also suggests that the second dispersion was not present. Qualitatively similar results were obtained at other temperatures and for

SOLID ELECTROLYTE

POLARIZATION

2667

1 ktlz

I

I 10

9 Gl10-5f?,

MkHz

1.6 BapC 1.4

Fig. 11. Admittance behavior for various partial pressm’es of oxygen. PO,= 1.5 x10-5 atm (a); P, = 10-z atm (x); ph = 0.2atm (0). Spec. NO. 10: 400”, 8MW Spec. No. 13: 600°C.

two different specimen geometries. In short, the behavior of the high purity electrolyte appeared to be that of a simple resistance. The d.c. resistivity of this material has been discussed in detail elsewhere [20].

Znterpretation

of electrolyte

polarization

Probably the most plausible explanation of the electrolyte polarization behavior is that the normal oxygen ion conduction of the electrolyte is partially blocked at the grain

2668

J. E. BAUERLE

lo’___.__,,.,1 10-5

1o-4

10-3

10-z

P

10-l

I

atm O2

Fig. 12. Electrode resistance vs. oxygen partial pressure at 800°C. Electrodes were naturally porous, (sputtered Pt, 3 specimens). Equation (3) -, Equation (4). ---------.

Fig. 13. Admittance behavior for a high purity zirconia-yttria specimen. The location of the 4-terminal d.c. conductance (arrow) on the G-axis suggests that no electrolyte dispersion occurs in this material (compare with Fig. 8).

boundaries by an impurity phase there. Electron microprobe analysis of our less pure material indicated the presence of a second phase in the grain boundaries composed chiefly of calcia and silica. This phenomenon has been observed also by Strickler [2 l] and Button [22]. One may picture the effect of such a second phase as shown in

Fig. 14. If one compares this with the electrolyte equivalent circuit, then R, would correspond to the resistance within the grains, R, would correspond to a ‘constriction resistance’ at the contacts between grains, and C, would correspond to the capacity across the impurity phase region. There are some interesting consequences to

SOLID ELECTROLYTE

(al

GD Grain

Grain

Contact

Contact

lb)

m

%

3

POLARIZATION

2669

ductivity at the grain boundaries. This second explanation now appears unlikely since our present work gave no indication of a grain boundary polarization in high purity material. It is possible, then, that the apparent variation in the activation energy of the electrolyte (Zr02),.,(Y20,),., is an intrinsic property of this material which can be understood in terms of the vacancy trapping mechanism. One might hope to detect such trapped vacancies by their dipole relaxation behavior; however, a calculation shows that the capacitive effect would be small (- 20 pf for our specimens) and hence difficult to observe unless other polarizations were completely absent.

R3

Fig. 14. Sketch showing how a second phase in the grain boundaries of an electrolyte might give rise to the observed electrolyte dispersion phenomena (a) actual situation (b) idealized situation.

Acknowledgements-The author wishes to thank Dr. A. J. Panson for his encouraging interest in this work. I am grateful also to Dr. R. J. Ruka and J. Hrizo for helpful discussions.

this hypothesis. First, it explains the experimentally observed similarity in the temperature dependence of R2 and RS. Second, we can obtain an experimental estimate of the capacity per unit area of the grain boundary region. Using our values of (L/A) C, and grain size, one obtains a capacitance/area of 5 pf/cm2. This is a rather large capacity. If one attempted to explain it in terms of a uniform insulating layer of silica, then this layer would have to be 7 A or less in thickness. A more likely possibility is that the impurity layer is blocking to oxygen ion flow, but is a conductor for some other species (electrons or calcium ions, for exirmple). This could give rise to a weak double layer capacity of the magnitude observed. Finally, we should like to comment on the temperature variation of the activation energy for the electrolyte conductivity. This effect was mentioned specifically for our moderate purity material, but it occurs also with high purity material, as discussed in another paper[20]. In that paper, we suggested two possible explanations for the effect, the first involving vacancy trapping, and the second involving a phase of different con-

1. PERFIL’EV M. V., PAL’GUEV S. F. and KARPACHEV S. V., Souier Electrochem. 1,74 (1965). 2. KARPACHEV S. V. and FILYAEV A. T., Soviet Electrochem. 2,576 (1966). 3. COLE K, S. and COLE R. H., J. them. Phys. 9, 341(1941). 4. NOLLE A. W., J. PolymerSci. 5,l (1950). 5. KNESER H. 0.. Koll. Zs. 134,20(1953). 6. SLUYTERS J. k. et al., A series of papers entitled, “The Impedance of Galvanic Cells,” Rec. Trau. Chim. 79, 1092, 1101 (1960); 82, 100, 525, 535, 553 (1963); 83, 217, 581, 967 (1964); 84, 729, 740, 751, 764 (1965); Elecrrochim. Acta 11, 73, 483 (1966); Z. phys. Chem. 52,89 (1967); J. electroanal. Chem. 14,169,181 (1967); 15,151,343 (1967). 7. EULER J. and DEHMELT K.. Z. Elekrrochem. 61. 1200(1957). 8. SCHRAMA J., Thesis, Univ. of Leiden (1957). 9. RALEIGH D. 0.. J. Phvs. Chem. Solids 29, 261 ( 1968). 10. WEISSBART J. and RUKA R. J., Reo. scient. Instrum. 32,593 (1961). 11. MACDONALD J. R., Phys. Reo. 92,4 (1953). 17 1_. VE’ITER K. J.. In Elecrrochemical Kinetics, Theoretical and Experimental Aspects, pp. 73-79. Academic Press, New York (1967). 13. LANGMUIR I., Trans. Faraday Sot. 17, 621 ( 1922). 14. FRYBURG G. C. and PETRUS H. M., J. elecrrothem. Sot. 108,496 (1961). 15. NORTON F. J.,J. appl. Phys. 29,1122 (1958). 16. HAYWARD D. 0. and TRAPNELL B. M. W., In Chemisorption, Chap. 5. Butterworth, Washington (1964).

REFERENCES

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J. E. BAUERLE

17. HAYWARD D. 0. and TRAPNELL B. M. W., In Chemisorption, Chap. 9. Butterworth, Washington (1964). . 18. DIXON J. M., et al.. J. electrochem. Sot. 110. 276(1963). 19. STRICKLER D. W. and CARLSON W. G., J. Am. Ceram. Sot. 47,122 (1964).

20. BAUERLE J. E. and HRIZO J., J. Phys. Chem. Solids 30,565 ( 1969). 21. D. W. STRICKLER, Westinghouse Rep. No. 64-918-273-R6 (1964). 22. BUTTON D. D., bull. Am. Ceram. Sot. 43, 263 ( 1964).