On the electronic conductivity of composite electrolytes

Solid State Ionics 28-30 (1988) 1073-1077 North-Holland, Amsterdam

O N T H E E L E C T R O N I C CONDUCTIVITY OF C O M P O S I T E E L E C I ' R O L ~ E S Joachim MAIER Max-Planck-lnstitut fiir FestkOrperforschung, Heisenbergstrafle l, D- 7000 Stuttgart 80, Fed. Rep. Germany Received 30 August 1987; in revised version 13 November 1987

The general problem of the distribution of minority charge carriers (here electrons) in space charge regmns ~s cl~scussed. It is shown that their profile is, boundary equilibrium supposed, determined by the behavior of the majority charge carriers (here ions). This result also has important implications for semiconductors. The contribution of electrons to the excess conductivity of space charge regions is calculated for one interface as well as for a dispersion. The Wagner-Hebb te~.hnique is ertended to the problem of a non-uniform defect concentration in the quasi-parallel switching approximation. Wagner-Hebb experiments are performed on AgCI:T-AI203 composites. An increase of both ~- and p-type conductivity is found with respect to pure AgCI. Applying the space charge model, the result can be explained by a double effect. Impu,'ities are introduced (homogeneous doping) and enhance the hole concentration in the bulk (detected by the high-T behavior); space clmrge effects (heterogeneous doping) due to the interaction of y-AlaOa surface with the silver cations (indicated by the influence on the ionic conductivity) enhance the n-conductivity in the space charge regions. The homogeneous effect is presumably due to O doping and is consistent with literature results on AgI-, LiI- and CuCl-alumina composites.

1. Introduction

The admixing of insulating surface-active oxides ~""~' ~o T-A!=O; *." 1,,:,,-d~fec rive ion conductors such as Ag-, Cu- and Li-halides gives rise to an enhanced ionic conductivity exhibiting nearly the same activation enthalpy as for the metal vacancy migration in the bulk [ 1-3]. The conductivity effect can be understood by an internal adsorption of the mobile ions at the alumina surface [ 4 ]. In the case of AgCI and AgBr the assumption of a saturation effect yields a quantitative description [ 3-5 ]. Similar effects can be discussed in systems of two ionic co.,Muctors [ 6 ], near grain boundaries and dislocations [ 7 ] and - in a more sophisticated way - in micro-sized :ystems

[8]. The behaviu~ of the e!ectrenic minority charge carriers in composit.z electrolytes is somewhat puzzling. Polarization experiments on Lii: Ai203 [ 9 ] and Ag!" A1.203 [ !0] revo~l~-d an increase of the p4¥pe conductivity. In the case of CuCl" A12Q [ ~ i ] no ef~. . . . . " A1z©~ e,n the electronic conductivity was observed. Recent experiments on AgI "A1203 [ 12] ...... ~,~ ,m~ i~l addition to the increased hole concon?radon the n-carrier concentrztic.". , , . . . . -,,,, ~,,_

hanced. In the following context polarization studies on AgCI" ~-A1203 are presented. In order to provide a precise treatment, the contribution of the electronic minority charge c a l l e r s in space charge regions and the necessary modifications of the WagnerHebb analysis for non--aniform systems is discussed. It is shown that the experiments can be explained by a combined e~ect of homegeneo~s (impurities) and of heterogeneous doping (space charge effects dominated by the interaction between A1203 and the majority charge carriers) en the ~lectroni: minority charge carriers. For the quaatitative evaluation, data ef Mizusaki and Fueki [ 13 ] are used for the bulk defect chemistry of pure AgCI. It is assumed that the incensiste~cie~ in their evaluation by neglecting necessary modifications of the evaluation formulae (Wagner--Hebb, solid state diffusion) due to ionization processes [ 14], do not cause grave errors. Mere, iust an ouLiine u~-~""l--me~cuc~,d v~uv~,.-~ . . . . . . ~*;,~n,'~ a more detailed treatment is in preparation

[15].

0 167-2738/88/$ 03.50 © Elsevier Soence Publishers B.V. (Noah-Holland Physics Publishing Division)

J. Maier/Eiectronicconductivity of composite electrolytes

!'374

2. Minority charge carrier concentration in space charge regions

taking account of eqs. (1) and (2), the integration yields

Applying the transport equilibrium condition (zero gradients for the electrochemical potentials of excess (iadex n) aad defect electrons (index p)), we find for a linear geometry

AY~ = .~. ~U.,p22 (1_+20~ ~ 0,,) Cn.poo •

£p =~-~ =exp[ - F ( ¢ - ¢ o o ) l R T ] ---~".

(1)

Eq. (1) means that the concentration enhancement ~ ( x ) ( ~ c ( x ) / c ® ) at a certain distance x from an interface with respect to the bulk value c~ is completely determined by the space charge potential (O(x) - ¢ ( x = o o ) ) also for the minority defects. The space charge potential itself, however, is fully determined by the majorit~ charge carders ( V ~ denoted by v, Ag~ denoted by i) according to Poisson's equation. As a consequence the distribu,ion of e' and h" is given b~ '.he surface behavior of the silver ions (cf. ~ = ~ 7 " = ~ ' ) . The final result for semi-infinite bouvdary c~nditions is £..={[l+0~exp(-~)l/II-0~exp(-O]}

~.

(2)

0~ (-0~) reflects the interaction with the neighbouring phase and is given by the concentration enhancement of the silver vacancies (interstitial defects) immediately at the interface (x=0) according to ref. [4]. ¢ symbolizes x/2, where 2 is the Debye length (.~2=~oRT/2FZc,,~) th.-t is also de~ermined by the bull< concentration c)f the majority charge carrier concentrations.

If we consider the (strictly) parallel transport along the interfhce AgCI/AI203, the mean extra conductivity due to space charges AcrL.e=AY~/Lx (where AYe is the extra conductance freed of unimportant geo~ - ~ . . . ~ . A , , a

~,t~,~

.~.a X

~

~,aa,tw ~ . ~ a t w ~ , l ~ A % $ % , ~

A~.,,iI~LI[I

For a large positive space charge potential (0~-~ 1 ), as assumed because of*_he effects of ¥-A1203 on the ion conductivity, we find

AY~ ~F(2it) u..(C.oC,~,)t/2-F(22) UpC~,~ .

(5)

If the de#etion influence of the holes is also negligible (as it is fulfilled below), we deduce A Y~ ".,A Y~ = F( 2A ) u. ( CnoC.oo) '/2 = u. ( 2~eoR Tc~o) it2 ( cn~lcv® ) .

(6)

We recognize that in contrast ~o the conductivity of the majority charge carriers, the result depends on the bulk value and thus on the doping level. For a dispersion we find in the quasi-parallelswitching model [ 4 ] (only the continuous pathways are counted) the effective conductivity Orra,e ---- tym - - O'm,io n

=#~(I--¢A)(tr,~+ap~)+#LOAt2AAY~.

(7)

A Y~ is given by eq. (6), fl~ and fit are geometrical factors (~ 1 and ~0.5 in the ideal non-blocking case), g2a is the surface-to-volume ratio of the A1203 panicles and .0A their volume fraction in the dispersion.

4. Wagner-Hebl ~'~olari~fien in non-uniform systems

3. Conductance contributions of minority charge carriers in space charge regions

. . . . . . . . . .

(4)

It,ll

the x-direction) is given by

In the above approximation the mean steady state current density, im.c of the electrons and the total steady state current Ie in a Wagner-Hebb experiment with electronic electrodes (blocking for ions) can be written as a superposition of the contribution of the different regions (co): L/a=im.e= Z ~,,¢,,i,~ .

(8)

oo

ar~ = E ~r~.. = E Fc.,.= f u.,.(~.,. - i ) dx. (3) •a , p

n,p

o

Considering u..~, as constant with respect lo x and

where a is the electrode area. The extra current density, Ai~,~ due to space charges is averaged over the x-coordinate ( ± to the direction of me~.surement, y). We find for one interface

J. Mater/Electronicconductivityof compositeelectrolytes / ~ g oo

Aid.e-

ff LxL~,F 1

6. Results and discussion AO.e(X,,Ag():))dxd~g

'

(9)

pAs 0

where L is the electrode distance and UAgthe chemical potential of silver. The dashes denote the value at the two electrL~cles. For pure parallel transport (cf. 7cro-gradient of the electrochemical potential of the electrons in x-direction) we end up formally with the well-known Wagner-Hebb equations [ 16 ] but with Om,~ of eq. (7) instead of the bulk value:

Oim.dOrt-em,dLy

1075

(blocking electrode),

(10)

where r/is the polarization voltage. Since Om,p according to eq. (7) (=floo(l-OA)epoo) and era,, according to eqs. (6,7) (=O.~oo[floo(l--OA)+const. ×(C~o/C2oo)u2]) are fully determined by their bulk values as far as the PA~dependence is concerned (C~o, c ~ do not depend on he Ag activity, aA~), we also obtain - formally - the well-known integrated form im.o = ( R T / L ~ F ) {*~.. [ 1 - e x p ( - ~lF / R T ) ]

+ ¢ ~ p t e x p ( r l f / R T ) - 1 ]}.

(11 )

,:rAin and a Ag m.~ are the mean conductivity valr.es if the dispeL,on is equilibrated with Ag (aAo'~ ~). Equations. (6)-(11 ) ~epresent the basis ;or the evaluation of our experimental results that we are presenting now.

5. Experimental AgCl : ~/-A1203composites (OA:4V/Oand 10v/o; effective grain size (6/QA ~--2rA) of the A1203 particles: 0.06 ~tm) have been prepared as described in ref. [ 5 ] (T-AI203: MeUer Company). For the Wagner-Hebb analysis, the pellets have been contacted with a graphite pellet on one side and with evaporated silver on the other side. The cell -- Ag!AgCI" T-A1203!C + was then polarized in the indicated directbn with constant dc cu~ems as small as possible (Keith~ey current source) in a quartz cell, filled and washed with dry Ar and protected against light. The few experiments at two "temperatures ( 300 and 215 oC) took one year in total.

Voltage-current data for 300°C (obtained after a waiting period of' ~ 2 weeks per roint) are shown in fig.. for two samples. 300 °C is a ~emperature where two-phase enhancement effects in the composites at least on the ions are n~t important ~ i. The values represent clearly nen~equflibrium values. Obviously the polarization is superposed by a rapid impurity diffusion influencing strongly the electronic charge carrier "oncentration, but not the majority charge carrier concentration [ 3 ]. In view of the fact that the concentrations of the electronic carriers are more than seven orders of magnitude below that of the ionic defects, this result is certainly expected. Since the impurity dh,u~,o,l ""' -" - is hi~her in the 10v/ o sample than in the 4w'o sample an impurity flux frr "a (or along) the AI~O3particles is probable rather thin from the gas phase. The experimental results at 215 ° C, where possible impurity diffusion is low enough for a reasonable r/I characteristic to be recorded, are showy in fig. 2. At this temperature, enhancement effects on a~o. are important [ 3 ] and thus space charge effects must be considered. The shape is indicative for p-type conductivity for the high C1 activities caused by the high overvoltages at the C-electrode. Since under the experimental condffion ~FIRT>> 1, it is natural to plot IdL~F/aRT versus exp(,lF/RT) in order to determine the effective conductivities according to

iLrF /aRT=J~,, +aA~p exp( rIF/RT) .

(i2)

We obtain from the slope in fig. 3 approximately aAgp= 6 X 10- t s ~ - ~ cm- t. Comparing this value

AgC| "y"A[203 {0.L)3 l.l.m } ©

30

0.4vlo

,rl • Io v/ 300 °C

<

ITI

20

0

®

~v

@® 0.1

0~2

l 0.3

TI/V

F~g. 1. (Ntm-stationary) current-voltage data for 300°C after a polarization time of I week.

J. Maier/Electronic conductivity of composite electrolytes

1076

~=x/k

l

AgCl y- Al203(4./,,0.03Ism ) I 3 215"C /

•

2

j

/

2

1

l

3

/#

i

,I

0.6 =

11/V

.... l

'

-2 Oi,

-4

0.4

4

l

AgCI (a~=1)/'y- AI203

t

e"

•,-, -.

1

-6

O

"

OV

-8

Fig. 2. Steady state current-voltagecharacteristicfor 215 °C.

l

On %

AgCI" ~,- At2Os(4v / , , 0.03 I.tm ) 6

215"C

-16

•r E O

.........

L

-18 -20 i

In" 2

|

i

t

t

I

t

t

t

20 i

00

'

2

I

I

i

4

I

6

I

I

I

8

L

I

10-5 exp(R-~T) Fig. 3. Evaluationof the valuesfrom fig. 2 accordingto eq. (12). with the value tor pure Agt51 DmK (extrapolatedfrom ref. [13] o f & ~ = 5 X 10 -~6 f~-* cm -*, we have an enhancement of about one order of magnitud '. This increase of the p-conductivffy should reflect the influence of homogeneous doping, since space charge effects (positive space charge potential 0~>0 [ 3,4]) would depress up. Evaluating the intercept in fig. 3, we find an overall n-conductivity of aamg,=5X 1 0 - t o ~ - t c m - t , which is alao enhanced by about one order of magnitude ( ~ _~5 × 10- t t D - ~c m - ~, extrapolated from ref. [13]). If we ignore space charge effects (and consider the bulk data as reliable, see above) the interpretation (since tim product e ~ c r ~ should be invafiant) would imply distinct structural changes ~e.g. elastic, plastic effects). Taking into account space charge effects, however, the explanation is straightforward. If we assume that the :,rnpurities introduced enhance the p-conductivity in the AgCI bulk of the composites (Crop) anti depress therefore cry,, we find an enhanced overall p-conductivity, but we may find also an enhanced overall

I

t

*

,

|

40 xlnm

I

10 12

l

I

I

I

60 =

Fig. 4. Profiles of the partial conductivities derived from the analysis (see text) for ?.gCl at 215°C. The in,crease ofa. is due to ~he heterogeneous (space charge) effect (adsorption ofAg+ ). (The logarithmicscale is misleadingconcerningthe absolutevalues.) x is the distance from the interface.

n-conductivity due ,o seace charge enhanc~.ment ( . ~ - ~ = > 0!) as shown in fig. 4. This shall be considered in more detail now. Due to the space charge effect, the depletion layer (2(215°C)-- 14 n m ) does not play any important role, so that

This enhancement reflects the influence of homogeneous doping. For the n-type conductivity the space charge effect is very important (see fig. 4) and we have to write Ag O'rn.n

Ag

= O':'on[ | - - ~ A

+ flLC~Af2A(2~CoRTCvo)1/2F -1 cv.]. -

(13)

Assessing the latter part by assuming the Coo value found in ref. [4] (c,o... 1/VM), we obtain (/Yt =0.5. e= 13, VM=26 cm 3 m o l - l ) : ~

ag "--a ~ g ( l + 10 -4 cv~ -l V~ t ) ITI. I'1 ~

(14)

J. Maier/Electronic conductivity of composite electrolytes

where VM is the molar volume. Introducing a bulk mole fraction for the majority charge carriers at 215 °C of 3 X 10 -6 [ 17 ] (no extrinsic effects have to be considered fo* the bulk concentration of the ionic defects at 215 ° c,.. [ ~a1), we end up with a~g,, _~ 350A~. This obviously means that the proper bulk value of the n-conductivity (a,~= 1) is indeed smaller --than the value for pure AgCI (OA~ ~ tO as it should be for impurity doping enhancing the pconcentration. A better quantitative agreement (factor 4 instead of 10) cannot be expected in view of o many uncertainties and approximations. The results for the defect-chemical situation are quantified in fig. 4. Attributing the slight discrepancy to e g. "'structural" effects (that must occur to a certain extent) would be to overstress the evaluation. As far as the impurity effect is concerned, we presume that O-doping according to O+Cla--,O~+h"

(15)

is decisive. Experiments with Ag20 [ 15 ] or Ag2S [ 18 ] (of. also Cu=S in CuCl [ 19 ] ) indicate a sufficient solubility of 0 2- or S2-. The problem of chemical diffusion in non-uniform systems and the evaluation of the dynamics of the polarization will be considered separately.

7. Conclusions

Po'.arization studies on AgCI'AI203 composites, revealing that both n- and p-conductivity are enhanced, can be consistently understood by our adsorption model described earlier. The positive space charge potential due to the attractive interaction of the A1203 surface with respect to the Ag ions can explain tk2 enhancement of the overall n-conductivity. The enhancement of the overall p-conductivity is due to the introduction of imgurities, as shown particularly at higher temperatures. This also applies to literature examples (see above). Particularly in the case of vm-~- A1203 [ 11 ], uuviously an appreciable impurity effect is absent: the depletion of holes in the space charge regions could, of course, not be found in the measurements. In the case of AgI: A1203 [ 12 ] the n-enhancement is larger than for AgCI :.M203; this is consistent with the larger ionic effect [2,3] (cf. eq. (13)).

1077

It was possible to calculate the space charge effect on the concentration and the conductivity of minority charge carriers as well as to extend the Wagner-Hebb evaluation to non-uniform systems. Since the concentration distribution of the minority charge carriers is determined by the defects governing the charge density, particularly in semicondtlctors possible profiles of the majority charge carriers have to be considered carefullv. Brouwer diagrams for boundary regions can be constructed now in order to explain the partial pressure dependence of boundary conduction in oxides or to help optimizing the processing of semiconductive sensors [201.

References

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