Electrochemical cell for composition dependent measurements of electronic and ionic conductivities of mixed conductors and application to silver telluride

Solid State Ionics 76 (1995) 5-14

SOLID STATE lowlcs

Electrochemical cell for composition dependent measurements of electronic and ionic conductivities of mixed conductors

and application to silver telluride*

W. Preis, W. Sitte Institut ftir Physikalische und Theoretische Chemie, Technische Universitiit Graz, A-801 0 Graz, Austria

Received 3 July 1993; accepted for publication 7 November 1994

Abstract

An electrochemical cell is described which allows measurements of ionic and electronic conductivities of mixed conductors as a function of composition. On one side of the disc-shaped sample four peripheral, roughly equidistant electronic contacts are mounted; on the other side four ionic contacts are positioned in the same manner. As the cell is based on the van der Pauw geometry, only the thickness of the sample and not the spacings between the electronic and ionic contacts needs to be determined. The composition of the sample can thus be altered by means of coulometric titration. For conductivity measurements on mixed conductors the composition gradient of the sample, arising from the flow of electrons and ions in the mixed conductor, is considered in detail. To demonstrate the high stoichiometric resolution the cell has been applied to study the composition dependence of ionic and electronic conductivities of a-Ag,Te at 300°C within the homogeneity range and with high stoichiometric resolution. Experimental details as well as an interpretation of the composition dependence of the electronic conductivity are given.

Keywords: Conductivity measurement; Electronic conductivity; Ionic conductivity; Mixed conductor; van der Pauw method

1. Introduction

For the investigation of transport properties of polycrystalline mixed conductors usually bar-shaped samples are used. Two ionic or electronic electrodes together with two ionic or electronic probes in between allow the measurement of ionic or electronic conductivities. An additional contact on the sample allows EMF measurements and the in-situ variation of the composition by means of the coulometric titration technique [ 11.

Actually, this linear four-point arrangement can

* Presented at the 9th International Conference on Solid State Ionics, 12-l 7 September, 1993, The Hague, The Netherlands.

cause problems if, e.g., in the case of ionic conductivity measurements soft electrolyte edges have to be mounted on the bar-shaped sample a certain distance apart. To avoid geometrical errors and to obtain rea- sonable probe voltages the probe spacing should be as large as possible. On the other hand, however, errors caused by imperfect current contacts at the ends of the sample bar decrease rapidly if the probe spacing/bar length ratio as well as the bar width/bar length ratio is reduced. Dudley and Steele [ 2 ] therefore recommend one third of the bar length as an op- timum probe spacing. As a consequence a large amount of material is needed in the form of a pressed sample bar.

Alternatively the van der Pauw method [ 31 allows

0167-2738/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDZO167-2738(94)00246-O

6 W. Preis, W. Sitte /Solid State Ionics 76 (1995) 5-14

conductivity measurements on arbitrarily shaped, but flat and isotropic samples. Only the thickness of the sample needs to be known. If the thickness of the sample is much smaller than its in-plane dimensions, point contacts on one surface of the sample may be used instead of the originally proposed line contacts.

The aim of this paper is to present an electrochemical cell based on the van der Pauw method, allowing independent dc measurements of ionic and electronic conductivities of mixed conductors as a function of composition, employing peripheral ionic contacts on one surface and electronic contacts on the other surface of a thin sample produced by pressing powder of polycrystalline material.

An essential feature of conductivity measurements on mixed conductors is the fact that a composition gradient is created due to the flowing ionic or electronic current in the sample. Therefore it is essential to find a relationship between the measured probe voltage for defined contact sizes and the composition gradient created in the sample and to express the composition gradient as an EMF interval of the coulometric titration curve.

2. Theory

2.1. Cell geometry

As the geometry for measuring the electronic and ionic conductivities of mixed conductors is based on the van der Pauw method, some theoretical princi- ples of this four-point method are given. A van der Pauw arrangement for conductivity measurements is shown schematically in Fig. 1. The sample must be homogeneous and free of holes. Only the thickness of

Fig. 1. Van der Pauw arrangement for conductivity measurements with contacts of finite size.

the sample needs to be known, whereas its shape can be chosen almost arbitrarily.

The electric current I,, is first fed through the ad- joining contacts Q and R and the potential difference Vsp is measured between the opposite probes S and P (Fig. 1). Thus the resistance RQR,SP is defined as the quotient of the potential difference Vs, between S and P and the electric current IoR. After interchanging the connections the resistance RPQ,RS is obtained, which is given by the ratio of the potential difference V, between R and S and the current IpQ through P and Q. Van der Pauw showed that the electric conductivity (T of the sample is related to these resistances by the following equation:

exP(- ~RQR,sP@+ exP(- ~RPQ,RvJ~)=~ , (1)

where d is the thickness of the sample. In the case of a slightly irregular arrangement of the contacts the conductivity can be calculated from Eq. ( 1) by iteration. Writing (Y,, for exp ( - nR,,,o,,d) and pn for exp ( - TcRQR,SPcT~d) the following iteration formula may be used [ 4 ]

Gz+1 =&I + %+Pn-l

~~(~~,R~Q,R~+P~RQR,sP) ' (2)

In this case it is useful to start the iteration from

2ln2 00 =

nd(&o,Rs + RQR,SP ) ' (3)

For an examination of the error due to the finite size of the contacts instead of being pointlike we take a circular sample with equally spaced perfectly conducting contacts in the shape of semicircles. A current IQR flows through the electrodes Q and R and a voltage Vsp between the potential probes S and P can be measured (Fig. 1). The radius of the contacts should not exceed one fifth of the sample’s radius. For this set-up we can estimate from investigations using other arrangements [ 5,6] that the error in the present case must be less than approximately 10%.

If a mixed conductor is used as sample, major variations of the conductivity occur in the vicinity of the current carrying contacts, as will be discussed below. Taking this aspect into account, we can in good approximation regard the potential probes as being pointlike. In this case the maximum error of the measurement is only half as large as in the case of four finite sized contacts, e.g. 5%. This is due to the fact

W. Preis, W. Sitte /Solid State Ionics 76 (1995) 5-14 7

that the contributions of the individual finite sized contacts are approximately additive and that these contributions do not depend on whether the contact is employed as a potential probe or an electrode in the two resistance measurements performed according to van der Pauw [ 3 1.

2.2. Conductivity measurements on mixed conductors

When a direct current is fed to a mixed conductor through electronic or ionic electrodes, the current densities of the electrons and ions of the mixed conductor are given by

ji=_ _!?!__I!!!!3 ZF ax ’

with j,, ji, &, ,i&, gee, Oi being the current densities, electrochemical potentials and partial conductivities of the electrons and ions, respectively. The chemical potential of the mobile component “a” may be split up into the electrochemical potentials of the ions of “a” and the electrons

/tL,=/!Ti+Zpe. (5)

In the case of ionic electrodes no electronic current is present in the steady state, because pure ionic electrodes completely block the flux of the electrons. Otherwise, if electronic electrodes are used, the ionic current will drop to zero in the steady state. Using electronic or ionic electrodes we therefore have due to Eqs. (4a) and (4b) in the mixed conductor and in the steady state

44 o -= ax ’

aI-& - =o ax f

(6a)

Additionally, on application of Eqs. (4)-( 6) we get in the steady state

a.k ZFj, -=- (7a) dX 0, ’

aha ZFji -=-- ax gi ’

(7b)

If we consider an electrochemical cell of the mobile component “a” with the latter in its standard state as the reference electrode, we obtain a relationship between the chemical potential of component “a” in the sample and the measured electrochemical force E of this cell

E=- $(fi.-r:). (8)

Inserting Eq. (8) into Eqs. (7a) and (7b) we get

aE Je=-G,x>

aE

Ji = Oi ax .

As the EMF E is related to the composition of the sample by the coulometric titration curve, the above Eqs. (9a) and (9b) show that the composition (EMF) gradients in the steady state are proportional to the electronic or ionic current densities. In our case the largest deviation from the initial composition will therefore be found around the current carrying electronic or ionic contacts.

In order to measure the EMF difference between two points xi and x2 of the mixed conductor, we place there two probes of identical material. The voltage I’{;) between two electronic probes in the positions x1 and x,, measured by a high impedance voltmeter with virtually no current flowing, is given by

I%? = - ; [/%(xz) -L(X,) 1 * (loa)

On the same lines we measure the voltage Vlf,’ between two ionic probes in the same positions

F19= $ [i&i(XZ)-!&i(X1)1 . (lob)

On application of Eqs. ( 5 ), ( 6 ) and ( 8 ) we get

I’[;’ =,5(x2) -E(x, ) , (Ila)

Vi;)= - [,7(x2)-E(xl)] . (lib)

Since, as already mentioned, the EMF is related to the composition of the sample by the coulometric titration curve, the measured voltage between the ionic

8 W. Preis, W. Sitte /Solid State Ionics 76 (I 995) 5-14

or electronic probes makes it possible to monitor the inhomogeneity of the sample during the conductivity measurement.

As already mentioned, a composition gradient is created in the mixed conductor if a direct current is fed through electronic or ionic electrodes. This aspect has to be looked at in detail.

Riess and Tannhauser [ 71 examined the application of the van der Pauw method to mixed ionic- electronic conductors some years ago. The authors concentrate on systems with reversible gas electrodes, but their results can also be applied to systems with reversible solid electrodes. In order to avoid sig- nificant variations of the charge carrier density of the mixed conductor in the vicinity of the current carrying electrodes, they give a relation limiting the voltage between the current carrying contacts as a function of temperature. This relation reads

eV”<< kT, (12)

with e being the elementary charge, k the Boltzmann constant and T the temperature, respectively. This relation means that the voltage applied to the electrodes has to be quite small.

Riess [ 8 ] gives an alternative approach to the four- point conductivity measurement of mixed conductors of linear or circular configuration. He employs three blocking and one reversible electrodes. By the use of the reversible electrode the chemical potential of the mobile ionic defect of the mixed conductor can be fixed in the vicinity of this electrode and adequate relations given enable the calculation of the conductivity at defined chemical potentials using arbitrarily high voltages (of course also limited by the decomposition voltage of the sample or the formation of new phases at the electrodes).

In the following we consider the situation that the voltage between the current-carrying electrodes is limited to an extent that no irreversible change of the sample in the vicinity of the current-carrying contacts occurs, e.g. decomposition of the mixed conductor or solid electrolyte (in the case of ionic electrodes) or formation of a new phase. Two cases must be considered. Firstly, the composition gradient is highest in the vicinity of the current-carrying contacts and the conductivity in these regions may de- viate considerably from that in the rest of the sample, see Eqs. (9a) and (9b). Secondly, the composition

gradient outside the current-carrying contacts has to be examined in detail. Regarding the first case we have to direct attention to the fact that the above es- timation of the maximum error arising from the size of the contacts is valid in the extreme case of perfectly conducting contact areas and therefore this maximum error holds true for contact areas of any conductivity. Composition and therefore conductivity changes of the sample within defined semicircles around the current-carrying electrodes can therefore be neglected if we accept an error depending on the size of these semicircles. In our case the radius of these semicircles amounts to one fifth of the sample’s radius and therefore the maximum error is equal to approximately 5%, as already discussed. In practice the errors will be smaller than 5% because the conductivity in most cases changes gradually with the composition reducing the deviation of the conductivity in the vicinity of the electrodes. Although these consid- erations refer to a sample with equally spaced contacts, the error in good approximation is the same for a slightly irregular arrangement [ 3,4,8,9]. In the sec- ond case the composition gradient created in the mixed conductor outside of the current-carrying contacts by the flow of electrons or ions has to be examined in detail. The maximum voltage VSIP, between two probes S’ and P’ located anywhere on these semicircles of the two current-carrying contacts can be determined in relation to the probe voltage V,, between S and P converting the circular sample on a semi-infinite plane by means of conformal mapping [ lo]. General relations of this kind as a function of the contact size can be found in [ 9 1. In our case, with the radius of the current-carrying contacts amount- ing to one fifth of the sample radius, the result is that the voltage VssIp, is larger than the probe voltage V,, by approximately factor 6. This means that e.g. for a given EMF interval U of the coulometric titration curve the current flowing through the current contacts should be ascertained, so that the probe voltage V,, does not exceed U/6:

vs, 2 ;AE . (13)

It should be mentioned that in the vicinity of the stoichiometric point the coulometric titration curve is exclusively determined by the chemical potential of the electrons in structurally disordered compounds like a-Ag,Te but dominated by the chemical

W. Preis, W. Sitte /Solid State Ionics 76 (I 995) 5- 14

potential of the silver ions in compounds like f3-Ag2Te with Frenkel disorder with almost totally ionized de- fects [ 111.

Summing up we can state that conductivity measurements on mixed conductors by the van der Pauw method can successfully be performed if the voltage between the current-carrying electrodes as well as the voltage between the probes are monitored carefully. If we introduce current-carrying contacts of finite size instead of pointlike ones, e.g. contacts which are located within semicircles of fixed size, a distinct maximum error of the measurement arises due to this geometry (this maximum error amounts to e.g. approximately 5% in our case with electrodes having a radius which amounts to one fifth of the sample’s radius). Keeping in mind that the voltage between the current-carrying electrodes has to be limited to an extent that irreversible changes of the sample in the vicinity of the two current-carrying contacts are avoided, composition (conductivity) gradients within these semicircles can be neglected and only the variation of the composition of the mixed conductor outside these semicircles ( = relevant part of the sample) has to be considered. Relations like our Eq. ( 13) between the probe voltage and an EMF interval AZ? of the corresponding coulometric titration curve of the mobile ion, valid for fixed contact/sample dimensions, then enable the limitation of the composition gradient created in this relevant part of the mixed conductor. This EMF interval bE should be chosen sufficiently small (e.g. AZ?= 1 mV) in order to obtain conductivity results with high stoichiometric resolution.

3. Experimental

Fig. 2 shows a schematic view of the electrochemical cell for simultaneous measurements of the electronic and ionic conductivities of a-Ag,Te as a function of composition. On the sample’s upper surface four roughly equidistant platinum strips serve as electronic contacts. On the bottom four ionic contacts are mounted in the same manner.

The ionic contacts are composed of molten silver iodide, pressed (but non-molten) silver iodide bars and silver plates as silver sources and sinks. The silver plates are covered with molten silver iodide in

ceramic stamp

silica disc

platinum wires

platinum atrip

disc-shaped sample

silver iodide (molten)

silver iodide (non-molten)

\ m silica disc

silver plate

’ platinum wires

Fig. 2. Electrochemical cell for composition dependent ionic and

electronic conductivity measurements.

order to improve the contact between Ag and AgI. It was observed that during the melting process some silver dissolved in the AgI melt (the solubility of silver in a AgI melt amounts to 0.01 wt% at 580°C [ 121)) and the electronic conductivity of AgI in- creased, thus making conductivity measurements as well as coulometric titrations impossible. These problems could be solved by pressing non-molten AgI bars onto the upper surface of the molten AgI units. The four ionic contacts are equidistantly arranged on a silica disc as shown in Fig. 2. The several parts (platinum strips, sample and ionic contacts) of the assembly are pressed together by a ceramic stamp by the help of light spring action between two silica discs (located at the upper and lower end of the cell).

All experiments were carried out in a sealed quartz apparatus under a constant helium flow to prevent traces of oxygen from contaminating the sample. The EMF of the electrochemical cell was measured between the four short-circuited electronic contacts on the top face of the sample and the four short-circuited ionic electrodes on the bottom face by a high- impedance digital multimeter (Keithley 199). In this case the arrangement is a galvanic cell of the type

Agl AgI I a-Ag,+,Te I Pt (1)

allowing EMF measurements as well as coulometric titrations. For the electronic and ionic conductivity measurements we used a precision current source (Knick 5152) and a digital multimeter/scanner (Keithley 199) connected to a dc voltage amplifier (Knick C3050). The temperature was held constant


within 0.2”C by means of a precision temperature controller (Eurotherm 8 18 ).

The computer-controlled data acquisition system permits elimination of thermoelectric voltages by performing two voltage measurements with opposite current directions. The probe voltage is calculated from the difference of the measured voltages by halv- ing them. Due to the composition gradient occurring in the sample during each conductivity measurement, some time (between seconds and minutes, depending on the chemical diffusion coefficient) is needed for the steady state voltage between the probes to build up. If the current applied is too large and the chosen maximum value of A,? of Eq. ( 13) is ex- ceeded, a suitable current is calculated by the computer and the conductivity measurement is repeated.

As an application of the method proposed we performed conductivity measurements on a-Ag,Te at 300°C using commercially available silver telluride (99.99%, Johnson Matthey) which was pressed into a disc-shaped powder compact with a thickness of 0.876 mm and a diameter of 10 mm. The EMF limit AE of Eq. ( 13) for electronic and ionic conductivity measurements was chosen to amount to 1 mV corresponding to a probe voltage of 160 WV.

4. Results and discussion

Fig. 3 shows the electronic and ionic conductivities measured simultaneously as a function of the EMF of the galvanic cell Ag 1 AgI 1 a-Ag,+,Te 1 Pt at 300°C. The ionic conductivities can be converted into component diffusion coefficients of the silver ions Dig by

applying [ 111

(14)

where V, denotes the molar volume of a-Ag,+,Te (4 1 cm3 mol-’ ). The measured ionic conductivity 4 (Fig. 3) as well as the calculated component diffusion coefficient of silver D& (Fig. 4) are practically constant within the whole range of composition due to the structural cationic disorder of a-Agz+sTe.

The electronic conductivity decreases with de- creasing silver activity (increasing EMF-values) and shows a minimum at EMF values around 140 mV (Fig. 3). Our results concur well with the results of

Fig. 3. Simultaneously measured electronic (filled circles) and ionic conductivities (filled triangles) of a-Ag,+,Te versus the

EMF of the galvanic cell Ag 1 AgI 1 a-Ag*+&Te 1 Pt at 300°C.

2.0 /

IA E / mV

Fig. 4. Component diffusion coeffkient of silver D& of a-Ag2+aTe

versus the EMF of the galvanic cell Agl AgIl a-Ag,+,TelPt at

300°C.

Refs. [ 13,14 1. A detailed interpretation of the composition dependence of the electronic conductivity follows.

For the electronic conductivity both the hole concentration nh and electron concentration n, have to be taken into account

(15)

where b, and b, are the electron and hole mobilities. The electron and hole concentrations, i.e. the number densities of electrons and holes, are described in

W Preis, W. Sitte /Solid State Ionics 76 (1995) 5-14 11

terms of the two-band-model applying Fermi-Dirac statistics [ 15 ] :

F,/z(vle) > (16a)

F,,,(-ve--glkT) . (16b)

m,*, rng, q,=,uJkTand eg denote the effective masses of electrons and holes, the reduced chemical potential of the electrons and the bandgap, respectively. The zero-reference level for the electron energy is chosen at the lower edge of the conduction band. Fi,2 is the Fermi integral which is defined as

Fl/2(V’)= 7

u1J2

1 +exp(u--) du ,

0

(17)

u being the kinetic energy of the electrons or holes. The EMF is related to the reduced chemical potential of the electrons by

FE -.T=wl:r (18)

where qz is the reduced chemical potential of the electrons in equilibrium with silver. Since the holes (in view of their high effective mass and low concentration) may be regarded as nondegenerate, their number density can be transformed into the following expression [ 16 ]

nh= $x,“exp(F(:TEo)), (19)

where NA, E” and x,” are Avogadro’s number, the EMF of the galvanic cell (I) at the stoichiometric point and the mole fraction of electrons at the stoichiometric point, respectively. Combining Eq. ( 15) with Eqs. (16a) and ( 19) one obtains

~ =4n 2m:kT 3’2 e

( ) Fl~2~r~-FEIRT~b,e

+ $ x2:x pr ‘:;“‘I b,, . (20)

The unknown parameters rn:, r$, x$exp( -FE’/ RT), b, and b, will be determined from the coulometric titration curve of Ref. [ 171 by the following procedure.

The non-stoichiometry parameter 6 is given by

116,181

6=&-x,, xh =x,0 exp[F(<yEo)] , (21)

where x, and xh denote the mole fractions of the electrons and holes, respectively. At high EMF values of the cell (I), i.e. low silver activities, the influence of the mole fraction of the electrons may be neglected. Thus in a 6 versus exp (FE/RT) plot a straight line results at high EMF values (Fig. 5). Its slope corre- sponds to the expression xzexp( -FE’/RT) of Eq. (20) and amounts to -8.5 x 10P5. As the ratio between electron and hole mobilities is considerably high, the contribution of the holes to the electronic conductivity at low EMF values (in the case of u- Ag,Te between 0 and 50 mV) may be disregarded, due to their low concentration. Since the electron mobility b, can be regarded as independent of the sample’s composition, we may write

This can be modified into an expression for b,

b,= V+$,F($$).

(22)

(23)

At low EMF values the electronic conductivity varies linearly with E (Fig. 6) and do,/ti (slope k, of the straight line in Fig. 6) amounts to approximately -4.25 x lo5 Sm-’ V-‘. According to Eq. (21) x, is found to be

I

“0 slope: -8.510-5 4

Co -40.

.

-701 0 30 60

explFE/RT)

Fig. 5. Determination of the parameter xEexp( -FE”/RT) of a-

Ag,+6Te at 300°C.

12 W Preis, W Sitte /Solid State Ionics 76 (199.5) 5-14

.

40000- l

7

6

-1

.

\

b” 30000 1 \ i k :,

: k,=-4.25.IO5 Srn-‘V-’

20000 0 25 50

E / mV

Fig. 6. Electronic conductivity of u-Agz+8Te in the regime of small

EMF values of the galvanic cell Ag 1 AgI 1 a-Ag,+,Te 1 Pt at 300°C.

3.0

x” 2.5

“0

E / mV

Fig. 7. Mole fraction of the electrons of a-Ag,+,Te in the regime

of small EMF values of the galvanic cell Ag 1 AgI j a-Ag,+,Te 1 Pt

at 300°C.

X,=6+ [x:exP( - g)]ex*(g). (24)

As the values for 6(E) are obtained from the coulometric titration curve, the right part of Eq. (24) is calculated and plotted as a function of the EMF by applying the above determined value for x:exp ( - FE’IRT), see Fig. 7. Again, at EMF values ranging from 0 mV to 50 mV the curve is a straight line with the slope k2 = - 3.0 x 1 Oe3 V- ’ corresponding to dxJdE. Using these results b, is obtained from Eq. (23) and amounts to 0.060 m2 V-’ s-l.

The parameters rn: and q: are determined from the coulometric titration curve with the help of meth- ods introduced by Kellers et al. [ 191. According to Eq. (16a) and Eq. ( 18) the logarithmic mole fraction of the electrons In(&) is expressed as

ln(x,) =lnpn (yr2 $1

+ln[Fl,2(rX -FE/W 1 . (25)

Consequently, m: and ?e* can be obtained by shifting the ln[Fi,2(qe)] versus --qe curve taken from the McDougall-Stoner tables [ 201 both horizontally and vertically until it fits the ln(x,) versus FE/RTcurve, obtained from the coulometric titration curve by cal- culating the x, values from Eq. (24). The value for rn: is obtained from the horizontal shift given by ln[4n(2m:kT/h2)3/2V,/NAJ and was found to be approximately 1.04X 10L3’ kg. The vertical shift represents r: and amounts to approximately 1.25.

The hole mobility b, can be expressed as

Xexp[“(T,“)] (26)

by transforming Eq. (20), Using the measured values of the electronic conductivity, the suitable fitting parameters m:, r:, xzexp( -FE’IRT) and b, determined above and the Fermi integrals FI12 (q) taken from the McDougall-Stoner tables, the hole mobilities can be calculated as a function of the EMF of the galvanic cell Ag 1 AgI 1 cl-Ag, +aTe I Pt according to Eq. (26), see Fig. 8. The hole mobility is almost independent of E, showing values around 0.00 14-0.00 16 m2 v-i s-1.

With the help of this set of parameters we are able to predict the EMF-dependence of the electronic conductivities by applying Eq. (20). Fig. 9 shows the theoretically calculated electronic conductivities (solid line) compared with the conductivity values calculated according to Valverde’s treatment [ 2 1 ] (dashed line) and the experimentally determined

4, I

-01 ” ” , I 140 170 200

E / mV

Fig. 8. Hole mob&y of a-Ag,,, Te as a function of the EMF of

the galvanic cell Agl AgI 1 a-Ag,+,Te 1 Pt at 300°C.

W. Preis. W. Sitte /SolidState Ionics 76 (1995) 5-14 13

E / mV

Fig. 9. Experimentally determined electronic conductivities (tilled

circles) compared with the values calculated from Eq. (20) (solid

line) and the conductivities calculated from Eq. (27) by Val-

Verde [ 211 (dashed line) for a-Ag,+sTe as a function of the EMF

of the galvanic cell Ag 1 AgI 1 a-Agz+aTe 1 Pt at 300°C.

values (filled circles). Valverde assumed that both the electrons and holes may be regarded as nondegenerate and he obtained the following expression for the electronic conductivity as a function of the EMF:

(27)

Ge(minj and Emin denote the electronic conductivity and the EMF at the minimum (Ge<min) = 104 S cm-‘; Emin= 138 mV). The conductivities calculated according to Eq. (27) coincide well with our measured as well as calculated data at high emf values because the holes are actually nondegenerate. At high silver activities (low EMF values), however, the values calculated according to Valverde differ considerably from our results. This can be regarded as a proof that degeneracy of the electrons must be taken into account at least at high EMF values.

5. Conclusions

The presented electrochemical cell allows for composition dependent measurements of electronic and ionic conductivities with high stoichiometric resolution. In contrast to the most widely used linear four- point configuration, our cell makes use of the van der Pauw geometry with the main advantage that only the thickness of the sample and not the exact positions of the contacts on the periphery of the disc-shaped sam-

ple needs to be known. This makes experimental work easier, especially if e.g. ionic electrolytes are employed as electrodes and probes for ionic conductivity measurements. Additionally, much less material in the form of a powder compact is needed. If a mixed conducting sample is employed in this cell, coulometric titrations and therefore composition dependent dc measurements of the electronic and ionic conductivity are possible.

Concerning the conductivity measurements on pure electronic or ionic conductors no precautions are necessary, except for the errors introduced by the finite size of the contacts. In the case of a mixed conductor a composition gradient is created in the mixed conductor, unless the chemical diffusion coefficient is so small that practically no polarization of the sample occurs due to the flow of the electrons or ions. In order to increase the stoichiometric resolution of the conductivity measurements, a relationship between this composition gradient, formulated as an EMF interval AE of the coulometric titration curve, and the voltage of the electronic or ionic probes has been given for defined contact sizes. This is advantageous for materials with high chemical diffusion coefficients and small homogeneity ranges, especially when electronic and ionic conductivities are of the same order of magnitude.

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Documents

Electrochemical cell for composition dependent measurements of electronic and ionic conductivities of mixed conductors and application to silver telluride