mobile speces in each electrolyte, are coupled together with a common refer- ... By the first method, the emf of the cell is measured with the ... oi the solid solutions till the composite structure. visualised in Fig. l(a) was o b ... The gas, after passing over the Pt mesh electrode, exited through the ...... I< following a change in the.
APPLICATION OF COMPOSITION GRADIENT SOLID ELECTROLYTES IN SENSORS AND THERMODYNAMIC MEASUREMENTS K. T . Jacob and Sukauya Mukhopadhyay Department of Metallurgy, Indian Institute of Science Bangalore 560 012, India
ABSTRACT New compos~tiongradient solid electrolytes are developed which have application in high temperature solid state galvanic sensors and provide a new tool for thermodynamic measurements. The electrolyte consists oi a solid solution between two ionic conductors with a common mobile ion and spatial variation in composition of otber coxup nents. Incorporation of the composite electrolyte in sensors permits the use oi dissimilar gas electrodes. It is demonsuated, both experimentally and theoretically, that the composition gradient of the relativeiy immobile species does not give rise to a diffusion potential. The emi of a cell is determined by the activity of the mobile species at the two eiectrodes. The thermodynamic properties of solid solutions can be measured using the gradient solid electrolyte. The experimental stuay is based on model systems A?(COj)x(S04)l-x (A=Na,K), where S \.aria across the electrolyte. The functionally gradient solid electrolytes used for activity measurements consist of pure carbonate at one ena and the solid solution under stuav at the other. The identical vaiues of activity, obtained h m three different modes of operation of the ceil. indicate unit transport number for the ddi metal ion in the graciient electrolyte. Tlle activities in the solid solutions exhibit moderate positive deviations from Raoult 's law.
1. INTRODUCTION Solid eiectrolytes with gradients in composition have potential use in the design of compact multi-element sensors and thermodynamic studies on macer i b . In muiti-element sensors, a number of soiid electrolytes, with Merent mobile speces in each electrolyte, are coupled together with a common reference electroae. .\laterials compatibility, interfaaal reactions and isolation of the interface born the ambient atmosphere are important faaors in the design of muiti-electrolyte assemblies (1). Interface problems can be avoided by the use of gradient soiid ~lectrolyteswhere composition is varied with distance between speu6c b t i n q values at each electrode. An important theoretical c o n s i d d o n
in the use of gradient solid electrolytes is the v i b l e occurrence of a di&sion potential, analogous to junction potential in the cells involving fused salts. Unequal races of migration of the ions, caused by the presence of the gradient, may result in the development of space charge, m a d s t i n g as d i h i o n potential. To.investigate this phenomena, solid electrolytes am demgzmd with s p d variation in composition. The high-temperature phases of A&Oj and A2S04 (A==Na,K)have the hexagonal structure. with space group P&/mmc (2-5). A cornpieta nrrrge of crysta mdiiicationa of solid solution is formed between the high ternA2C03and A2S04 (W), facilitated by the orientatiod disorder in the ~03' and SO:' sublattice of the allcali carbonates and sulhte~mpectivlaly 4 5). Pure and doped alhli carbonates and sulfates an ionic conductors h.ve been used in galvanic sensors (9-11). To demonstrate the use of a gradient electrolyte with dissimilar gas electrodes, a solid state cell has been d e s i ~ e dwith different gas mixtures flowing over the two electrodes. The electrolyte consists of pure AzCOJ and A2S04at the two ends. with sparial variation in composition between the two boumhy values. A SO?+O?iAr gas mixture, used in contact with A2S04 face of the electrolyte. reacts to form an equilibrium concentration of SO3 in the gas phase at high temperature in the presence of catalysts. The other electrode!, in cont x t with A?C03 , consists of a mixture of C02+02+Ar . The measured emf is compared with values calculated from thermodynamic data to establish the main contributions to the emf and check b r the presence of a di&raion potential (12). An d y t i c a l expression is derived for the difiusion potential using the thermodynamics of irreversible processes (13). The conditions under which the diffusiou potential becomes liegligible are identified. The response time of rhe cell based on the composite electrolyte is investigated. The change in the terminal compositions of the gradient electrolyte as a result of diffusion owr a long period and consequent changes in emf are discussed. solid solutions with The thermodynamic properties of A~(CO~)x(S04)I-x a common cation are measured using a composite gradient solid electrolyte consisting.of pure A2C03at one extremity and the solid solution under study at theother. Gas mixtures containing CO?, 0 2 and Ar are used to fix the chermd potentials of sodium or potassium at the electrodes. The Nernstiaa response of the cells to changes in temperature and partial pressum of C02 and Or at the electrodes is demonstrated. The activities in the solid solutions are measured by three techniques. By the first method, the emf of the cell is measured with the seme CO?+O?+Ar mixture at both electrodes. By the second techniqw, tmo different CO?iOz+Ar gas mixtures are used at the two electrodes. The activities are calculated from the measured emf and the gas compositions using the Xernst equation. By the third approach, the activities are calculated &om the d i k n c e in compositions of CO?+O?+Ar gas mixtures at the two electrodes required to proauce a nuil emf. The null emf technique can be used for activity measurements even when the solid electrolyte exhibits sigdcant electronic conductivity. If these three modes of operation of the cell produce identical results, unit tr-rt number for the dkaii metal ion is confirmed (14, 15).
-
2. EXPENMENTAL PROCEDURE 2.1. hiaterials and Preparation Techniques :
Anhydrous AzC03 and AzS04 (A=Na,K) were obtained h m Johnson Manhey. The gas mixtures were prepared by mb&g metered streams of component gases. Mass flow controllers were used to regulate the flow of the gases. The partiai pressure of oxygen in the resulting gas mixtures was determined by means of an oxygen meter based on stabilized-zirconik Although it is preferable to have a continuous variation in composition aiong the length of the solid electrolyte, in practice it is W c u l t to prepare such a structure in monolithic form. In the present study, pellets were prepared in which the composition was varied in steps. The anhydrous starting salts were hear treated under vacuum to remove adsorbed water vapor. Intimate in the required proportions were mixtures of the dehydrated AICOj and then melted under high purity Ar gas, held at a temperature 50 K below the solidus for 4 hours, and then quenched to room temperature. The crystalline product was ground to a fine powder.
-
The functionally gradient solid electrolyte was prepared by repeated consolidation oi layers, each having a uniform composition. A weighed quantity oi AICOs powder was first pressed in a steel die at 15 MPa, the solid solution of the next composition was then placed over it and consoIidaced again at the same pressure. This procedure was tepeated wrh the successive compositions oi the solid solutions till the composite structure. visualised in Fig. l(a) was o b cained. After the final compaction at 25 MPa, the composite pellet was sintered in oxygen at 1080 K for 5 days. The variation in composition across a sintered gradient eiectrolyte pellet, obtained h m electron probe microanalysis (EPMA), is shown in Fig.l(b). The profile indicates that some intermixing of layers has occurred during consolidation. Also, the diffusion processes that occur during sinrering has resulted in slight smoothening of the sharp composition steps. By the same technique, several composite gradient soiid electrolytes were prepared with difTerent terminal compositions.
-
2.2. A ~ ~ a r a t uand s Procedure :
2.2.a. Sensors with dissimilar gas electrodes : The ceil arrangement for emf measurement using dissimilar gas elecuodes, shown schematically in Fig.2, can be representeci as: Pt. CO; t o , ' I ( N ~ C O ~ ( N ~ ? ( C O ~ ) X ( SlNa?S04 O ~ ) ~ -((SO;' X + SO: X=l X =0
+ O;,
Pt
.. I
!
-"
.,
.
The flat surfaces of the solid electrolyte pellet were polished using diamond paste. Taro gas tight compartments anere created on either side of the electmlyte by spring loading vertical alumina tubes against the electrolyte, with gold Orings inserted in between them. At high temperature, the gold O-rings d h under pressure to form a flat gasket. A retaining ring of alunima was placed around the assembly to prevent lateral displacement of the vertical alumina tubes with respect to the solid electrolyte. Fine P t mesh was placed on the upper and lower surtace of the electrolyte @let and P t leads wwe attached to the mesh. The gas mixtures were passed behween the taro concentric alumina tubes on each side of the solid electrolyte pellet. The SO2 and 0 2 react at high temperature to form SO3. Coiled Pt catalysts, placed in the path of t6e incoming -as mixture. were found to be necessary to ensure equilibrium concentration of :he Merent gas species in the S02+02+Ar g~ mixture. Alrbayh P t catalysts were also placed in the path of C02+02+Ar mixture, their presence wcrs not essential. The gas, after passing over the Pt mesh electrode, exited through the inner alumina tube. The S02+02+Ar mixture was passed through the top half ceil, while CO?+Oz+Ar mixture was flowed through the bottom part of the cell e m b l y . The entire assembly was enclosed in an outer alumina tube through which prepurified Ar gas was passed at a flow rate of 5 ml s--. The top and bottom ends of the outer alumina tube enclosing the cell ,ssembly were closed wlth water-cooled brassheads provided with O-ring to ensure gas-tightness. A grounded Faraday cage, consisting oi stainless steei foil wrapped around the alumina tube, was used to minimize the Inductive pi&-up from the funrace windings on the Pt leads. The cell assembly was situated in the constant-temperature zone of the furnace. The temperature was controlled to xl K.
*
The cell assembly usas illitidly heated to 1050 K. After the gas leakage through the gold O-nnq was foul~dto be negligible, the concroiled gas mixtures were passed over the respective electrodes and the emf of the cell was measured using a high-~mpedance ~ q i t a voltmeter l at Merent temperatures. The steady emi was iounci to be inaependent of the flow rate of the gas mixtures in the ranee of 2 to 6 ml,s - ' The How rate of the gases in the two compartments were matched to irvold the establishment of a thermal gradient across the eiectrolyte by preferent~aicooling. The emf was reproducible on temperature cyclinq. The reversibility oi the emi was checked by microcoulometric titrat~onin both directions. A small quantity oi current (- 100 pA for 200 s) was passed through the ceil using an external potential source. The open circuit emf was then monitored as a function of time. After each such titration, the emf returned to the original raiue before the titratlon. thus ensuring cell reversibility. To determine the response time of cell-I. the emf was monitored as a function of time after rhnnpinp the composition of the gas dowing over each of the electrodes. at different flow rates. 2.2.b. Thermodvnamic Measurements on Solid Solutions -
The ceil arrangement used for thermodynamic measurements can be r e p 109
resented as :
The cell assembly was similar to that shown in Fig.2. Gas mixtures containing CO?,O2 and Ar were passed through both top and bottom ceil assemblies. For testing the Nernstian response, different T a+&+Ar O f t h w gas mixtures were passed over the electrode in contact with: the carbon&+sulface solid solution a d the corresponding emb were recorded, with an equintolar gas mixture flowing past the electrode in contact with pure AICOj . Cell-I1 was operated in three Merent modes for the measurement of activities in the soiia solution. In the most convenient cell arrangement, the same gas musture was used over both electrodes. The need for two gas-tight compmm e w over each eiectrode was thus eliminated. The emf of the cell can then be direcciy related to the activity of A2COj at the solid solution electrode, provided the transport number of A' ions is unity. For measurements on each composition of the solid solution. a specifically designed, separate gradient electroiyte was d. In the secoua mode of operation, au equimolar gas mixture was flowed past the eiectrode in cowact with pure A?CO3 , and another C0?+Q2+Ar mixture was passed over the other electrode, in contact with the carbonate-sulfate soiid soiuc~on.Tile emiof the cell, measured as a function of temperature, w m r e i d to the activity oi =\?COjat the solid soiution electrode and the gas compositions at the two electroaes by the Nernst equation. By the null emf technique, the gas compslcion of the C02+02+Ar mixture over one of the electrodes was MCid unt~ithe ccll regwered zero emf. In another variation of this technique. the emi was measurea as a function of gas composition at one of the electrodes. and the qas composlcion corresponding to zero emf was obtained by interpoiation. The activities were theti calculated by imposing the zeroemf condition on the Xerm quasion.
3. RESULTS AND DISCUSSION \ . Gas Electrodes : 3. I. Sensors with D~~s~miiar
3.1.a High-Temperature Gas Composition :
.at high temperatures, SO? and O2 in the inlet gases react to form SO3, thut chan~~ the q gas composition. The e q d b r i m high temperature composition was caculated h m the standard Gibbs h e energy change (16) for the reaction :
,md the inlet gas corn ition, using a procedure described earlier (17). The ere= C02+02+Ar gas mixtures, used at the carbonate composition of the electrode. is independent of temperature under the expehental conditions of this study.
d$"
I
3.1.b. Interpretation of Cell Emf : If the gradient soiid electrolyte is an ionic conductor, in which the Na+ ions are the only mobile species, the emf developed across the material m a y be expressed by: E=-In-4. , [31
F
4,.
where E is the emf, F is the Faraday constant, and a " ~ and . a'N.are the activities oi the cation at rhe two extremities of the solid electrolyte. In this dxpression. contribution to the emf from ionic migration in the concentration gradient is neglected. Since there are gradients in the chemical potentials of >ulbteand carbonate ions in the solid electrolyte, it is natural to expect M u s i o d transport of these species in opposite directions. The direction of ionic hues in the qradieut soiid electrolyte cue shown in Fig.3. Because of the greater -t;rbiity oi Ne?S04 compased to Na2COa (16), the activity of the cation at the carbonate electrode wiil 'oe liglrer than that of the sulfate electrode. In view of their ionic radii, the rates of diffusional t r w p o n for the carbonate and sulfate ions are e-xpected to be unequal and orders of magnitude lower than that for Na' ion. Unequal rates oi migration of sulfate and carbonate ions can result in the deveiopment of space charge, manifesting as a diffusion potential. In this i t udy, che magnitude oi rhe diffusion potential is assessed. I11 ceii-I. the acti~ityof sodium a t each electrolyte/electrode interface is 5xed bv the composition of the gas phase. At the sulfate electrode. the sodium .ictivity is a d n e d by the reaction :
If the Na?S04 is present at unit activity, and the partial pressures of SO3 and O? are fixed by the flomng gas mixture consisting of SO3+SO2+0?tAr , then the sodium activity is gven by the expression :
*whereti'!';; is the equiiiorium constant corresponding to reaction 14). Similarly, at the carooliate electrode. ttie sodium activity is established by the reaction :
.
where K(6) is the equilibrium consfant correspond.to r d o n [6]. By combining Eqs. [3], [S] and [7], one obtains,
4) and AG"(6) ate the standard free energy changes (16, 18) for and (61, and p" and pfor are the partial pressures of O2 at the sui4rte and carbonate electro es respectively.
2
The measured emf of cell-I at 973 K is shown as a function of ID(^"^^. PI'),,) in the gas phase at equilibrium with the sulfate electrode in Fig.4, while an equimolar mixture of CO? and O2WBS f l o d over the carbonate electrode. As requmd by Eq.[&],emf increases linearly with In (d;o,.P'1~2) over several decades. The emfof the cell can be calculated from the thermodynamic data and the partial pressures established at the electrodes. Calculations were done using data horn ma compilations. JANAF (16) and Pankratz et ai (18). The measured emf lies bemeen the caiculated values, but is closer to the computed values based on more recent evaluation by Pankratz et al (18). The deviation bemeen the calculated and experimental values is independent of lnlp",o,. ptl&,) to a k t approximation. When the partial pressures in the gas phase around the sulfate elecrrolyce wen held constant, the emf decreased linearly with ~ n ( p ' ~ ~ . p ' & as ) , indicated by Eq.iB]. The calculated temperature dependence of the emf based on the ma sets of thermodynamic data (16, 18) is compared with measurements in Fig.5. The noniinearity of the curves arises from the change in equilibrium partial pressures in the SOJ+SO?+O?+A~mixture with temperature. The measured emfs lie becween the calculated curves. Since the small deviation between the experimental and calculated emf is independent of piutial pressures at both electrodes and temperature (Figs. 4. 5). it may be attributed to the inaccuracy of thermodynamic data rather than to d h i o n potential. The emf measurements thus appear to suggest the absence of sigmhcant diffusion potential. This is possible only if the highly mobile Na' ions can destroy the incipient development of space charge due to unequal rates of migration of sulfate and carbonate ions. 3.l.c. Theoretical Analysis : An anaiyticai expression can be derived for diffusion potential o, using the thermodylwnics oi irreversible processes. The electrons in the chemically identical platinum electrodes of cell-I possess different electrochemical potentials.
112
Pt' and r$", due to the electrochemical equilibria established at each elec%trode/electmlyte inmhce. By definition, the electromotive force (E) of the cell
isgivenby:
E =
1 "' - ,,PI) -F(%-
[91
When the electrodes behave reversibly, the e1ectrochemic.d potential of the electrom are established by reactions similar to Eqs.[4] and [6],and are given by,
respectively, when the gradient electrolyte in cell-I is based on A?(C03)*(SO4) - x solid solution. By appropriate substitution in Eq.[9], and assuming that the electrochemical potencud of electrons in platinum is the same as that in the solid electrolyte at the electrade/electrolyte interface ('I? = qC-),
If the h t term on the right is negligible, then the simplified expression is identical with the conventional Nernst expression given by Eq.[8]. This last term represents the diffusion potential, the magnitude of which can be calculat using the thermodynamics of irreversible processes. in
Eq.i!3
The fiw of the mobile ions, A'. COZ-, SO:- and e-, designated by numbers 1to 4. in a chemical potential gradient can be described by the phenomenological
flux equations of irreversible t hennodynamics
:
where L,,'s are the Onsager coefficients relating the generalised forces 2,'s with the corresponding fluxes Ji's in the y-direction. The forces are defined in such a way that the rate oi entropy production per unit volume is equal to C;',, J, 2,:
5
=
d --( ). dtj ?; 'Ij
where qj's are the electrochemical potentials of the ions and electrons, and T is the absolute temperature.
The condition for zero net electric current, that
exists when tbe 0- of positim and q a t i m chPrges balance each other at steady state, is given by
where
is the charge of ion i. Combining Eq.[13] to [IS] one obtains,
Addition of the term -(dqA+/dy) Ci
C,
z, Lij to both
sides of Eq.[16] givw :
x.
where t; = ( ; C ;L,) / ( & I.z, L,,,)is the transport number of ion j (19). Integrating the above expression between the limits y ' and y", which mark the extremities of the solid electrolyte, one obtains,
The advantage of using the above integral is that the ionic elecvochemical potentials which appear within brackets do so in the correct linear combination to ailow their replacement by the chemical potential of the relenrrrr neutral molecules. Therefore, the diffusion potewal # of cell-I under isothermal condition can be expressed by :
This integral, and therefore the magnitude of the diffusion potential. can only be evaiuated if all relevant ionic transference numbers are available as a function of cornpaition. Eq.[l9) indicates that the diffusion potential becomes negligible as the transport numbers of carbonate and sulfate ions and elmrons approach zero. in agreement with experiment. If the electrolyte contains two mobile species with gradients in concen~11tion. as in the case of (AYBI-y)PCOjw ~ t hspatial variation in Y, there is a diffusion potential that develops across the elmtrolyte. A theoretical analysis. simiiar to that outlined above for the case of the gradient solid eiectmlyte wich one mobile species, indicates that the *ion potential zb is given by (13):
'
*
when gas mixcures containing C02 and 0 2 are used to fix the chemical potentials of metals A and 0 ac the electrodes, and the transport number of the carbonact? ions and elecuons approach zero. In the above expression, tA. and t ~ are + the transport numbers of the ions A and B. Thus, in general there is always a &&ion potential that develops across a grdeut electrolyte with two mobile ionic species with unequal transport numbers. The presence of the diffusional potential will add a finite contribution to the ceU emf. The diffitsion-potend approaches zero only when the transport numben of the two mobile species are equal. In general, transport numbers are functions of the chemical potential of the mobile s p i e s ana temperature. Thus it is &1y that the term (tA+- tB+) will be zero over a m g e of partial pressures of C02 and O2established a t the two electrodes. Therefore. the gradient electrolyte involving two mobile ions may not find immediate application in solid state sensors. The analysis of the emf of a non-isothermal cell incorporating a composition gratiient solid eiectroiyte indicates that the cell emf can be expressed in terms of the thermodynamic parameters at the electrodes and the Seebeck coefficient of the gradient eiectrolyre under standard conditions, when the transport number o i one of the ions approaches uuity (13). Under other conditions, the emf is a complex function oi a number of parameters, many of which are difficuit to meanue.
-
.
of sodium or potass~uma c the electrodes is established by reactions simiiar t; Eq.$l. When the rrausport number of alkali ion is unity, the corresponding expression for emf miuces to.
1Vhen the gas c o m p ~ t i o nover the left hand electrode is kept invariant. the emi should vary lineariy with t he logarithm of WC,, .pllz:) over t he right hand electrode, as ~mpileciby Eq.i21). The experimental results shown in Fiq.6, for K' ion conauctinq saciient solid electrolyte a t 973 K, confirm chis Nernstian behavior. An equimoiar minure of C O ? and 0 2 was used at the left electrode. Sirmlar resuits were obtained at other temperatures between 925 to 1150 K. Incerpolation oi the mmsureci data shown in Fig.6 gives the value of In(p",,,.p ,?I12) for null emf. When the emi is zero, Eq.1211 can be rearranged to give :
,,
I
'
Thus. the activity of K?C03 in the solid solution containing 30 mol% of KKlC03is obtained as 0.402 at 973 K.
'
3.2.b. Activity hleasurements with a Common Gas Phase :
The variation of the reversible emf of the K' ion conducting cell, using equimolar C02+02 gas mixture over both electrodes is shown in Fig.7 as a function of temperature. Each set of data points corresponds to a Mereat right Band terminal composition of the gradient elecmlyte. For each tenninai c o m p sition. the emf is a linear function of temperature. The partial- thermodynamic mixing properties of AzC03 in the solid solution with hexagonal structure can be directly obtained from the emf :
The activity of K-CO1 at 1073 K, calculated from the emf, is shown in Fig.8 as a function of composition. The value for X = 0.30 is identical with that obtained in the previous section. The activity oi K2S04is obtaned from the GibbsDuhem relation. X similar procedure was followed for the Na'-ion conducting cell. and in both the cases, the activities exhibit moderate positive deviations from h u l t ' s law. 3.2.c. Xctivitv Xlemurements Using Different C02+01+Ar Gas Electrodes : For a given gradient electrolyte with different CO+O?+Ar gas mixtures at the eiectrodes. the reversible emf of the cell is a linear function of temperature. The activity of K?CO1 at the solid solution electrode at 1073 K. calculated from Eq.!211, using two differelit gas electrodes. is shown in Fig.8 for ,Y = 0.3.
3.2.6. Xctivitv Sleasurements Using Null Emf Technique : By the null emi technique, the composition of C 0 2 + 0 ? mixture over the right hand electrode in contact with carbonate-sulfate solid solution was varied graaually uutil the emf became zero alld the gas composition corresponding to the zero emi was recorded. The experiment has been done with gradient solid eiectrolytes having different right-hand terminal compositions a t 973 and 1073 K. An equunoiar gas mixture was passed over the electrode in contact with pure A1C03 . The activities of K2C03shown in Fiq.8. calculated bom the ratlo of partiai pressures at the two eiectrodes using Eq.[22), are identical with results obtained in the previous sections. This technique can be used for actlvlty measurements even in presence of a s i g h c a n t electronic conductivity in the gaaient eiectroiyte. When electronic conductivity is present. the magnitude o f the cell emi \muid be lower than that predicted by the Nernst equation. When the emi is zero. panial electronic conductivity does not d e c t the measurement.
,
'
3.2.e. Thermodynamic,Mixing Properties of the Solid Solutions :
The variation of the function, ~ g , ~ , / ( X)? l - calculatd h m the emf, with composition of the solid solution is shown in Fig.9. The function is iedependent of temperature within experimental uncertainty limits, indicating that the entropy of mixing is close to the ideal value. The same conclusion is derived Irom the temperature dependence of the emf.The functions A ~ , / ( I X)' and AC&,,/ (1 .Y)' vary linearly with composition, suggesting that the t h r modyaamic mixing properties for both the solid solutions can be represented by the subregular solution model (20). The respective integral mixing properties of the Na2C03-Na2S04and K2COj -K2S04sdid solutions are given by the equations.
-
-
- X) (6500X + 3320(1- X)] LC& = AH = X ( l - S )[503UdY+ 4715(1 - X)] LC& = AH = X ( l
J mol-I
.
J mol-'
.
.[24] [25j
3.3. Response Time To cietemue the response time of cell-I, the emf is monitored as a function of time after changing the composition of the gas flowing over each of the electrodes. at different How rates. A variation of the cell emf with time at 973 K following ii change in the gas composition at the sulfate electrode of cell-I is shown in Fiq.10. A rapid response is obtained after an initial incubation period. which is related to the replacement of the gas initially present In the apparatus by a uew composition. Reduction in the gas volume over the electrode or increase in How rate would enhance the response in this gas-transport controlled regime. The other part of the emf response, after the new gas composition tias been established over the electrode. is of electrochemical nature and can be expressed by (211 : Et - Eo = 1 - exp ( t / r )I ] ,
Em
- Eo
[-
where En,Ec and E, are the voltages at time t = 0,t = t and t = oc respectively, and r is a corresponding time constant. which f~llowsthe Arrhenius' law. Plots
ze)ll p'fz)
(1 of ; ~ n
as a function of t at 973 K, for an increase in the d u e
of (p at the sulfate electrode of cell-I for two different flow rates of the gas. and also for a aecrease in the value of (p'lso,.p"q1/1 ), is shown in Fig.11. The vaiue u i t for electrochemical response is obtained by subtracting the incubation perioa from the total time elapsed after switching to a new gas mixture. The plots are linear ma the corresponding slopes are related to r. The value of r. characterising the eiectrochemical response. is independent of flow rate over the sulfate electrode. The response was faster for an increase in partial pressure of I,,.
SOx, than for a corresponding decrease in partial pressure. For a step in gas composition in the carbonate electrode, the incubation period bar emf response is approximately the same, but the subsequent electrochemical-r is faster than for a similar change at the sulfate elmrode.
A comparison of the response characteristics of cell-I with those of cells using pure Na2S04as the solid electrolyte, or Nasicon I Na2S04 (22) or 3 -alumina ( Na?S04 (23) couples, indicates that the response time of the d l based on the composite electrolyte appears to be determined by t h tvsponse time of each separate electrode, at least to a 6rst approximation. Thus the presence of a composition gradient inside the electrolyte does not appear to influence the response time of the cell. 3.4. Long-term Stability : Over a very iarge period of time, the diffusion of anions may contibinate the puie carbonate and sulfate b e at the extremities of the gradient electrolyte used in ceil-I. A 10 mol o contamination of the pure compound at one 5 mV, assuming of the electrodes .rv~llresult a theoretical change in emf of ideal mixing in the solid solution. However, the effect of composition changes at each extremic?: caused by diffuon will partly compensate each other. The overall ceU reactlon can be represented as :
8
-
For an ideal solid solution. equal molar composition changes at the extremities of the electrolyte will exactly compensate, leaving the emf d e c t e d . In the absence of diffusiondata for the anions, it is difficult to estimate the time beyond which a perceptibie change in composition will occur in the cells used in the present study. However. no decay in emf wm o b s e n d for operational periods extending up to tj00 ks for both cell arrangements.
-
4. CONCLUSIONS Systematic measurements on isothermal gradient solid electrolyte cells have been undertaken to establish the main contributions to emf. The gradient electrolyte permits the use of dissimilar electrodes. Gradient electrolytes can be used in multielement sensors to avoid the problems oi achieving perfect matching of separate electrolytes at the interfaces and isolation of the interface horn the ambient atmosphere. In gradient electrolytes, unequal rates of migration of the ions caused by che presence of concentration gradient can result in the development of space charge, manifesting as diffusion potential. The results of this study indicate that composition gradients in relatively immobile components do not result in a siqnrricant diffusion potential. The space charge is dissipated by the migration oi rhe mobile ion when the diffusion coefficients of the species migrating under the gradient are sigtuficantly lower than that of the principal
1 I
.
mobile species. In such cases, emf is primarily determined by the a r e n c e in chemical potential of the principal mobile species a t the two electrodes. It the electrolyte contains two mobile species with gradients in concentration, then w u l d generally be a diffusion potential that develops across the electrolyte. Therefare, the gradient electrolyte involving two mobile ions may not find immediate application in solid state sensors. The thermodynamic properties of solid solutions.can be measured using composite gradient solid electrolytes, consisting of a pure component at one end and the solid solution tuider study at the other. Although some indications are given on the behavior of gradient solid electrlolytes under non-isothermal condition, further experimental research is needed to explore the potential of such configurations. These studies on functionally gradient materials open up new vistas in solid state ionics.
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2. B. N. Mehrotra Zeit. Krist., 164; 285 (1983).
4
3. H. Y. Becht and R. Struikmann, Acta Cryst., B32, 3344 (1976). 1. W. Eysel. H. H. Hofer, K. L. Keester and T. Hann. Acta Cryst., B41, 5 . (1985). . 5. H. h o l d . W. Kurtz, A. Richter-Zinnius and J. Bethke, Acta Cryst., B37.
1643 (1961). 6. H. F. Fischmeister, h4h. Chem. 9% 420 (1W2). 7. C. W. Bale anti A.
D. Pelton. CALPHAD. 6,255 (1962).
R. L. P. Cook and H. F. Mcklurdie. Phase Diagrams for Ceramists, VII, p. M. 70, Am. Ceram. Soc., IVesterville. Ohio (1989). 9. Ii. T. Jacob and D. B. Rao, J. Electrochem. Soc., 126, 1842 (1979).
10. hl. Gauthier and A. Chamberland, J. Elecrmchem. Sac., 134. 1579 (1977). 11.
R Cote, C. IV. B a l e - d h l . Gauthier. J. Electrochem. Soc.,
131. 63
( 1984).
12.
K. T. Jacob. S. Jlukhopadhyav and A. K. Shukla Solid State Ionics, 62. 27 (1993).
13. S. JIukhopaihyay and K. T. Jacob. Proc. Royal Soc., Lond.. A, (submitted for pubiicacion). 14. S. Bfukhopaihyay and K. T. Jacob, Jletallurgcal Transactions, 24A, (in press).
/
S. MuLhopadhyay d K. T. Jacob, J. Electrochem.
Soc., 140, 2629 (1993). 16. M. W. Chese, Jr., C. A. Davis, J. R. Downey, Jr., D. J. Frurip, R A. blcDonald and A N. Syverud, JANAF Themmhemical Tables, Third edition, J. Phys. Chem. Ref. Data, 14, Supp-1, Parts I and I1 (1985).
15.
I
17. K. T. Jacob, M. Iwase and Y. Waseda, Solid State Ionics, 23, 245 (1987). !
18. L. B. Pankratz, J. M. Stuve and N. A. Gokcen, Thennodynamic Data for hlineral Technology, Bulletin 677, U.S. Department of the Interior, Bureau of Mines,Washington (1984). 19. S. R De G m t , Thermodynamics of hversible Processes, North Holland Publ. Comp., Amsterdam (1951). 20. H. R. Hardy, Acta. Metall., 1, 202 (1953). 21. J. Fauletier, H. Seinera and M. Kleitz, J. Appl. Electrochem., 4, 305 (1974). 22. R Akila and K. T. Jacob, J. Appl. Electrochem., 18, 245 (1988). 23.
R Akila and K. T. Jacob, Sensors and Actuators, 16, 311 (1989).
'
-Distance, mm
----,
Fig. 1 (a). Conceptuai variation of anionic fraction (X) of the carbonate ions across the gradient solid electrolyte used in cell-I.
(1.
Concentration profile across the gradient eiecrrolyte pellet after sinterinq for 450 ks a 1080 K obtained horn electroll probe microanalysis (EPMA).
Alumina tubes Platinum lead S02+02+Ar Plati nurn catalyst Gold '0' r in9 Gradient solid etectrotyte Retaining ring (Al203) Argon gas '
thermocoupte
Fig. 2.
Fig. 3.
Plat i num lead
Schcmi~cicrcpresenracion o f the trell assembly for use with ciissimilar %iselectrories.
X= 1 X= 0 Flux direcrio~sinside the Na'-ion conducting gradient solid clccrrolvte.
Fig.4. Variation of the emf with partial pressures of SO, and O2 in cell-I at 973 K. An quimoilrr gas m ~ ~ t u of r eC02iOz was e m p l o y ~at the other elect rode.
-
0.92
Fig.5. Temperature dependence or the emi oi cell-I ,it !)73 K. X 50:-0:-.4r mixture :11 the ratio 0.44 : 2.4 : 97.16 by volume dna ill1 ec/urnoiar rmsture c,i C02 -0: were used to fix the chemcai porent~ai of sodium at the eiectroaes.
-
I
I
x
Experimental Calculated
-
4
-
-
1 E,V I 0.88
0.84
-
-
I
t
-
80
v
I
i
I
I
-
~~~~+u~/~'c03&(S01)l-X/ 40
-
H
x=1
xnaj d
-
-
I
t
Fig.6. Xernstian respome of cell-I1 incorparatiq tho dient dectralyte to change in #Ic4 at the right hand ekctrodt at 973 K. .An equimolar gas mixture of C02+02 was employed at the other elect rode.
w&
I
1
#'by
E,mV I
I
(Ref)
I
I
-1.95
-160,
I I I
I
/
'
'
-5
I
I
I
-4
-3
-
1
I
b
-.
I
tl
rl
-2
0
-1
-1" (6ioi i$), atm%
-4 h
I
120 -
140
1
1
I
1
I1
, ~ q ~ 4 ~ ~ ~ f i 0 3 (50444 l ~ z ( ~ 0 3 ~ Xtl X=XcO2+0pet -'+a Xdxd x x X=O.O5 ' 'x 0.10
Fiq.7. Temperature dependence of the emf of ceilI1 incorporat~nrrthe gradient electrolyte. Each line cor- E mv -xcx /x-. responds to a different com- 7 position of the solid solution pa-~aa 0.20 . 80at the right hand electrode. xx~xUX-=\nequimolar gas mixture of 60 4CO? O2 was employed at Aex-x~ax 0.30 both electrodes. ex-x
-
-*-
-
I
+
-
40
--
-- & + x - x ~ n
0.45
'
t60
.
-rx-,x2-x----
20 0
--
L x 4-x-x-x-x-x -x-x-x-
-xX-x-
x-x-x-x-xI
x-x-x40.7? ~-1-x-x-~090
-
Fig.8. Activity-composition relation in the KISOl K&O3 solid solution a 1073 K.
-
-
Emf lcommon gas a m . AEmtldiffwent gas atm.
Fig.3. V'ariation of the -6 function. -\Gr,,-+,,/( 1 - S j 2 . with cornpositlon of the carbonate-sulfate solid solut ion with h e x ~ o n a lst ructure. The functton is iadependent of temperature.
Fig. 10. Variation of the emf of cell-I with time at 973 I< following a change in the gas composition at the sulfate electrode for two different flow rates of the gas mixture.
\kriarion tii .he ionction :ln (1 :vit h time ( t ) loilow~ng q:hanqe ol gas composition at .he sulfate electrode oi ceii-I ? t !I73 1.;
Fig. 1I.
e;. -
r
k
7
