electrotransport in oxides

Solid State Ionics 12 (1984) 407-418 North-Holland, Amsterdam

ELECTROTRANSPORT IN OXIDES

Fragois MORIN Istiiuto di Elettrochimica e Metallurgia, Universitd! di Milano, Via G. Venerian 21, 20133 Milan, Italy

At high temperatures, an electrical current flowing through an oxide with prevailing electronic conduction generally exerts two different effects. Firstly, an overwhelming number of electrical charges are carried by electrons and electron holes. Secondly, there is a net migration of the most mobile ions within the crystal lattice. That second effect is rather small in terms of electrical charge displacement because the ionic transference number generally lies between lob5 and 10m4. Nonetheless, the corresponding mass transfer is quite measurable and it has already been observed in the following oxides: Cu,O, NiO, MnO, FeO, Co0 and TiO,. Experimental procedures for the ionic transference number determination in those oxides are described. Starting with the theoretical significance of such measurements, emphasis is placed on the improved knowledge of defect nature and defect migration which is achieved by electrotransport measurements.

Le passage d’un courant Blectrique dans les oxydes semiconducteurs port6s a haute temperature s’accompagne, gtntralement, de deux effets distincts: tout d’abord, la presque totalitt des charges tlCctriques est vehiculee par les electrons ou les trous Clectroniques; le second effet se manifeste par une migration des ions les plus mobiles du rtseau. Ce second effet, quoique beaucoup plus faible en terme de deplacement des charges tlectriques (ri- 1O-s-1O-3), donne lieu a une modification tout-&fait mesurable de la gkomttrie de l’oxyde. Un tel phCnomene a 6tt plus particulibrement dtudiC dans le cas des oxydes MnO, FeO, COO, NiO, Cu,O et TiO,. Nous discutons non seulement des mtthodes expirimentales actuellement disponibles mais aussi des mecanismes fondamentaux mis en cause et de l’eclairage distinct que les essais d’electrotransport apportent a la comprehension globale des phenomtnes de migration dans lcs oxydes. Les resultats les plus concluants portent sur un petit nombre d’oxydes binaires mais le phCnom&ne lui mZme est susceptible de se manifester dans la plupart des oxydes.

Semiconducting oxides may have vastly different electrical conductivities from one to the other but they all have in common that their electrical conductivity increases with temperature. They also generally exhibit a non-negligible departure from stoichiometry. At high temperatures, the defect concentration equilibrium as a function of oxygen partial pressure is rapidly attained. Those features are part of the overall semiconducting properties which make those materials attractive for several technical applications like chemical sensors [l-3], electrode materials for fuel cells [4-S], intercalation electrodes [6] and others. The electrical conductivity is, of course, the most obvious property of semiconducting oxides and conduction is almost entirely supported by the migration

of electrons and electron holes. Nonetheless, electrotransport of ionic species becomes a non-negligible phenomenon as the temperature rises. Electrotrans- port is here defined as the migration of these species under the effect of an applied electric field on the crystal. In certain technical applications, electrotransport becomes an important feature of the electro- chemical processes. Above all, its understanding is essential to the fundamental description of defect nature and defect migration in semiconducting oxides. Quite significantly, electrotransport has been applied to the description of migration processes in oxides long before tracer diffusion could be measured [7]. However, limited efforts have been pursued since, on this approach. Besides, there is a steadily increasing availability of radiotracer data. In fact, the best insight into the diffusion mechanisms in oxides is

408 F. Morin / Elecirotransport in oxides

obtained by a combination of radiotracer and electrotransport experiments. That should become apparent through this paper as the theory is reviewed in conjunction with specific experimental cases.

2. Electrotransport theory

There is a strong analogy between the effect of both the chemical and the electric potential gradients on the migration of chemical species. The Nernst- Einstein relation which quantitatively describes that relationship, can also be applied to solids [8]. Several equivalent demonstrations of it exist with minor differences in the type of formalism being used. The basic statement underlying the Nernst-Einstein relation concerns the perfect equivalence between both the chemical and the electrical potential gradients. In other words, the work required to move a charged particle a certain distance against a chemical potential variation is the same as if the work was done against an equal electrical potential variation. Accordingly,

ij =-Li(al.Li/aX + Ziqe a~/aX). (I)

Particle i is conveniently considered as an elementary defect, being either an interstitial ion or a vacancy. It has a chemical potential pi and an electrical potential &. ii is the number of elementary defects flowing per unit surface and unit time. Li is the usual phenomenological coefficient and zi is the equilibrium valency of the elementary defects according to Kroger and Vink’s notation. With moving defects, the effective charge for migration is better defined for interstitials than it would be for some types of vacancies [9]. One may already ask what would happen with a vacancy associated to an electron hole. Strictly speaking, Vb in MO or VL in MzO must be considered as associated defects whether that distinction is usually made or not. The migration of such an associated defect represents a limited type of coupled motion compared to generalized descriptions of coupled motion between various species. Nevertheless, zi cannot be thought of as being always entirely representative of the actual effect of the electric field and it is substituted by zd:

ii=-Li(alLi/aX+zdqea~/aX). (2)

td stands for the effective valency of the diffusing

defect in contradistinction with Zi which is the equilibrium valency of the same defect in accordance with Kroger and Vink’s notation. A priori, zd is purely a phenomenological factor. Its usefulness will appear furthermore with the establishment of transference number formula and with the following analysis of experimental data.

Hereafter, the classical procedure of considering the effect of the electric field in the absence of any chemical potential gradient and vice versa for the chemical gradient is performed. The mobility per unit field Ui is defined by Ui = jiJ%E and 07, the self- diffusion coefficient of species i, is defined by Fick’s first law. n, is the number of elementary defects per unit volume and E is the electric field. It is assumed that pi obeys the ideal solution law. Consequently, Li vanishes and

(3)

Eq. (3) is a first form of the Nernst-Einstein relation. T represents the absolute temperature and k is Boltzmann’s constant. Dt is experimentally obtained through DT, the radiotracer self-diffusion coefficient. Both coefficients are related by

0: =(DT/f)n/ni, (4)

where f is the correlation factor and n, the number of normal sites for i per unit volume. In turn to DT, the mobility Ui is experimentally determined through the ionic conductivity vi or, more currently, by the transference number ti and c, the total electric conductivity of the oxide. ti is defined as ti = Ui/Cr. Finally,

kT u ti DT

f -& Zd;’

zi is normally cancelled out within the ratio ti/Zi and therefore, it should normally not affect the overall results from eq. (5). This second version of the Nernst-Einstein equation leads to a direct comparison between tracer diffusion and electrotransport data. An approximate comparison between the actual value of 0” and its value theoretically calculated from eq. (5), has limited usefulness. From a fundamental stand- point, the main interest in eq. (5), lies in either the determination of f or zd or a combination of both.

F. Morin / Electrotransport in oxides 409

Consequently

f nq: D” z. __=--1

zd kT ~ ti’

A very simple situation stems from the existence of unassociated vacancies or from the existence of a single type of interstitial defects. The actual value of zd is accordingly in coincidence with Zi and the correlation factor can thus be directly determined. Reciprocally, calculations can be directly performed on zd if the correlation factor is already well estab- lished. Three different points of view can alternatively be adopted concerning the determination of zd. The first case is rather trivial in the sense that zd would strictly be considered as a fitness parameter between different experimental data. Excessive values of z, would indicate a lack of precision on some of these experimental data and the need for further error analysis. Where sufficient precision on experimental data is achieved, further consideration may be given to more fundamental points of view. With enough evidence for the existence of a single type of associated vacancies, zd tells about the net effect of the electric field on the migration of these defects. Finally, zd can be used to verify the eventual assumption of a single unassociated type of defect in a specific oxide. The departure of zd from the theoretical value of Zi

would thus become indicative of secondary defects or coupled motion between different species.

Except for the introduction of zd, eq. (5) has been derived within the usual framework and with more or less the same limitations. Defects are considered to form an ideal solution within the crystal lattice. Single types of defects are considered at a time and the tracer atoms and the ionic charges must follow equivalent paths in contradistinction to the inter- stitialcy mechanism; various fluxes should also be independent from one another. Despite these limitations, the preceding type of relation is most currently applied to the description of diffusion processes in ionic crystals. A more generalized approach by Wagner [lo], still based on the thermodynamics of irreversible processes, takes into detailed consideration the coupled motion of species. The atomistic approach also provides an alternative theoretical description of ion migration in highly defective solids [ll]. Finally, a theoretical validation of the Nernst-

Einstein relation in highly defective solids has been provided recently by combining both phenomenological and atomistic approaches [12].

3. Interfacial reactions and transference number

The electrotransport phenomenon occurs through the whole volume of the crystal lattice but, except for Chemla’s experiments [13], its effect is observed rather at the interfaces. The interfacial reactions may be classified according to the electrode solubility and to the type of migration, either cationic or anionic. The anodic reactions for a mobile cationic sublattice are first considered. For a soluble anode, the ionization reaction is

M+M’++ze-, (7)

where z is the cation normal state of ionization. Eq. (7) is not complete since crystal sites are not yet taken into account. A more correct description of the interfacial reaction would be

M+V;+M;. (8)

Alternatively, an unsoluble anode would give

o;+v;+$o,. (9)

Both eqs. (8) and (9) are a first step towards a complete description of the reaction processes actually involved at the interface. Vacancies may alternatively be replaced by interstitial defects in these reactions. Secondary equilibrium reactions in the crystal close to the electrode are also likely to occur. The essential feature of eq. (8) is the preservation of the crystal lattice integrity. In eq. (9), a chemical structure unit is destroyed and gaseous oxygen is formed.

For a mobile anionic sublattice, a soluble anode would give

M+M;+V;. (IO)

For an unsoluble anode, it would be

o;+;o,+v;. (II)

The remarks for reactions (8) and (9) also apply here except for the interface transformation. Cystal lattice growth occurs at reaction (10) while crystal lattice remains constant and gaseous oxygen is evolved at reaction (11).

410 F. Morin / Electrotransport in oxides

In the case of semiconducting oxides, the mass transfer across the interface may be considered simply as a means of avoiding defect concentration build-up at the interface. Otherwise, polarisation would occur. The interface formed by a semiconducting oxide and a soluble electrode is not likely prone to polarisation. The gaseous exchanges which characterize unsoluble electrodes require that both anode and cathode be sufficiently permeable to gases. With due experimental attention, this condition can be directly satis- fied at the anode.

using z from the ionization reaction represented by eq. (7). But this last convention must be clearly specified and also maintained when applying eqs. (5) or (6). By combining eq. (13) with (6), one gets

f2&-M D” IAt

.zd N,kT OXAmoX u ’ (15)

In eq. (15), all experimental parameters appear in more direct evidence. The only valency term left is the preceedingly defined phenomenological factor zd.

4. Experimental methods in electrotransport 3.1. Determination of the transference number

The mass transfer at the electrodes leads to the determination of the ionic transference number. ti has already been defined as the ratio of the ionic conductivity over the total conductivity. When an electric current I is passed through the oxide sample for a certain time A?, ti can also be described by

ti = (AQi/ZAt), (12)

AQi stands for the total electric charge transported by species i during the time Ar. Depending on whether an oxide weight variation or an oxide displacement is measured, ti is written

t, = A% ziF -- ’ MO, IAt

or

(13)

fi = PoxSAe,, ZiF

MO, ZAt’ (14)

AmoX stands for the weight variation either at the cathode or at the anode, MO, is the molar weight of the oxide and F is Faraday’s constant. S is the area corresponding to the electrode interface, AeoX, the interface displacement pox, the oxide specific weight. With metal deposit or metal consumption measure- ment Am,,, MO,, heox and pox are replaced in eqs. (13) and (14) by analogous parameters now related to the metal. In the same equations, Zi when multiplied by qe is the net electric charge carried out by the defect through the crystal lattice and it is similar to the defect charge at equilibrium. An arbitrary transference number is sometimes calculated by rather

In the sense of the preceding definition of electrotransport, the determination of transference numbers is performed in the absence of any concentration gradient, at least for compounds with electronically prevailing conduction. Generally speaking, the interfacial reaction is followed at either one or at both electrodes. Chemla’s experiments [13] are one excep- tion to that rule; diffusion of a radiotracer in an electric field has also been applied to Fe0 [14] and to Be0 [15] with a resulting observable effect but these experiments will not be further reviewed here. The first direct determination of transference numbers in solids were obtained by Tubandt’s classical experiments [16-181 performed mostly on halides. The principle behind his method is illustrated in fig. 1. Three pellets having an equal weight are pressed together between an inert cathode and a soluble anode. As the current is passed through the pellets, the geometry of the whole set-up is modified according to the type of diffusion involved. After completion of the experiment, pellets are weighted separately. Fig. lb is typical of cationic conduction and fig. lc occurs with anionic migration. The center pellet has been omitted in these two sketches. It is used as a reference weight in practical experiments. For these experiments, the outside atmosphere is a non-reactive gas.

The principle behind Tubandt’s experiments should be applicable to most solid ionic compounds. In practice, several factors need to be controlled. Pellets should separate easily, i.e. sintering must not occur extensively. Metal deposit should not become too uneven. Reaction between the samples and the outer atmosphere must be negligible. Lacombe et al. [14,19] performed the first successful applications of

F, Morin / Elecirotransport in oxides 411

(b)

Fig. 1. Schematic representation of Tubandt’s experiments

on solid electrolytes.

electrolysis on semiconducting oxides. For these experiments, pellets are replaced by a single ferrous oxide sample, either coarse-grained or monocrystal- line, which is pressed between two iron electrodes. The chemical composition within the sample is fixed by the metal/metal oxide equilibrium. The outer atmosphere is argon. Oxide indentation or iron deposit are both easily measured. Weight measurements can also be performed by separating the oxide interfaces, especially at the anode. In the case of manganous oxide, the allowable current intensity without any appreciable heating effect, is much less. Partly, due to that limitation, a platinum cathode is used to dissolve manganese and the amount of manganese dissolved in platinum is measured by a microprobe [20].

The most typical experiment with inert electrodes on semiconducting oxides was designed originally by Diinwald and Wagner [7] on cuprous oxide. Their experimental set-up is illustrated in fig. 2. A pure copper foil, 20 X 5 X 0.02 mm3 in dimensions is precisely engraved at half way of its total length. Platinum electrodes are fixed at both ends and the foil is then suspended vertically in a furnace and fully oxi- dized to cuprous oxide. Following metal oxidation, an

I j 1,.y+

Fig. 2. Original sample arrangement for the first electrotran-

sport experiments on Cu,O [7].

electric current is passed through the sample for a certain time. Afterwards, the sample is broken in two halves along the center notch and each half is weighted separately. The transference number is calculated from the oxide weight shift from the anode to the cathode. One remarkable feature of this experiment is that the oxide composition is fixed by the outer atmosphere and it can thus be varied in order to study different oxide compositions [21]. At the lowest oxygen pressures, copper may dissolve into the inert electrodes. This effect has been successfully counteracted by longer experiment durations [21]. Other efficient means of counteracting this effect are either to use a metal solid solution equivalent to the outer oxygen partial pressure or, more simply, to pre- anneal the sample for a long enough time before applying the electric current. With unsoluble electrodes, cationic migration is the only observable type of migration but it still includes a very large number of semiconducting oxides.

In fig. 3, other set-ups for measuring the oxide displacement are described. The dilatometric determination of ti was first developed bu Gauthier [22] for MgO and later used for NiO [23]. The oxide sample is machined in a very peculiar form in order to con- centrate the displacement on one electrode. Fig. 3b relates to electrotransport experiments in TiO,? [24]. Weight measurements are used and the oxygen pressure is varied between different runs. Fig. 3c illus- trates the experimental set-up for electrotransport.in cobaltous oxide [25]. The anode is a platinum finger which exerts as small a pressure as possible. The cross section of the oxide indentation is very well defined. The anodic displacement is enhanced compared to the average electric current density through the oxide sample.

The choice of a specific experimental arrangement depends on several factors. For example, there is an


(cl

Fig. 3. Alternative ways of measuring cation transference number in semiconducting oxides.

upper temperature limit for electrotransport experiments in TiOz because of pellet sintering [24]. Gas evolvement is also to be taken into account. Rela- tively long and thin samples are more favourable to the oxide equilibrium with the outer atmosphere. Cobalt has not been observed to dissolve appreciably in platinum electrodes. The cathodic interface is rather impervious to oxygen and any increase in cobalt ion concentration is relaxed through oxide thickening in the vicinity of the cathode as shown in fig. 4. On the counterpart, no thinning of the oxide

Fig. 4. Typical cathode thickening during electrotransport experiments on COO. Specific conditions: 0.22 A/mm* for 165 h.

cross section is observed at the anode. Instead, micro- channeling of oxygen occurs at this interface. This last phenomenon would certainly be be less efficient with oxidizing-reducing atmospheres or unsufficiently buffered gas mixtures. In such conditions, weight measurements should be favoured in place of anodic displacement.

5. Experimental case studies

The usefulness of electrotransport experiments in semiconducting oxides becomes evident as specific cases are analyzed. The main oxides to be studied are CuZO, NiO, TiO;?, Fe0 and COO. As much as possible, discussion should be based on the f/zd ratio from eq. (6). The use of a linear scale for this purpose is a rather stringent criterion since any incongruity in f/q thus becomes obvious. On the counterpart, this procedure is thought to be more fruitful than a mere comparison between experimental and calculated values of 0” on a logarithmic scale as it may alternatively be done.

5.1. Electrotransport in cuprous oxide

As mentioned before, the first electrotransport experiments on semiconducting oxides were performed on Cu20 [7,21]. Wagner’s rational constant could thus be computed and compared to the experimental rate of oxidation of copper [26]. Gundermann and Wagner’s results [21] are illustrated in fig. 5. They replace Diinwald and Wagner’s former results and they are greater than those by about 25%. The dependency of t,,+ on oxygen partial pressure was also found to be unsignificant in the oxygen pressure range from 9 X 10m4 to 6 X lo-’ atm corresponding to a defect concentration variation of less than a factor 3. The activation energy of the slope in fig. 5 is 12 kcal/mole. At first, it may be compared to the activation energy of the experimental ratio

D&J%cUZO and it is quite different from the calculated value of 21 kcal/mole for that last ratio.

For the present analysis, the only sufficiently well defined radiotracer data comes from Moore and Selikson [27]. They were obtained between 800 and 1050” C and at a single oxygen pressure equal to


TFC)

6,0 ‘y ’ 600 I

\8 5.0

t\

0 5,7x KY otm. 02 4 e,6xtiotm.02

v $3xlO-3 aim.02 0 7,2X6’Ol(R.o2

I/TPK-‘xlO-‘1

Fig. 5. Gundermann and Wagner’s results on cuprous oxide

[21] plotted versus the reciprocal of temperature (K-l).

1.3 X 10e4 atm. At 1000” C and same PO,, Moore and Selikson found an excellent agreement between their DE, data and the same parameter calculated from the Nernst-Einstein relation, with a resulting devi- ation equal to about 8%. Such a good theoretical agreement is not observed here. This can be explained essentially by the introduction of the correlation factor and by the use of Wagner et al.‘s [28] original data for g,-cuzo. fc,+ is also changed to 5.2 X 10e4 its average value at 1000“ C in ref. [21]. With g,-cu20 equal to 2.5 R-l cm-’ at 1000” C and at PO, = 1.3 X lop4 atm, zd is almost 40% lower than the former theoretical value of one. This result is not totally unexpected because of the eventual existence of neutral vacancies [29].

5.2. Electrorransporr in nickel oxide

The first electrotransport experiments in NiO by Baumbach and Wagner [30] led to the conclusion that fNiz+ was lower than 10 -‘. Recent dilatomeric measurements by Duclot and DCportes [23] cover an extensive range of oxygen partial pressures and temperatures i.e. 10e6 to one atm and 900 to 1350” C respectively. One of their prominent results is the great stability of the nickel ion transference number over the whole range of oxygen partial pressures and

at any temperature. For that case, the average total variation of fNi*+ from 10e6 to one atm, does not exceed 7 to 8%. This is in contradistinction with theoretical considerations derived from the correspondent varying defect model, where n, from (+ = uOPgz”-, takes experimental values from 4.0 to 5.4 [23].

Eq. (6) is easily applied to nickelous oxide. Radio- tracer diffusion in NiO has recently been the subject of very extensive measurements by Atkinson et al. [31-331. These data are in fairly good agreement with earlier data by Volpe and Reddy [34] at somewhat higher temperatures. Within their common temperature range between 1200” C and 1400” C, Atkinson and Taylor’s results [31] are lower than Volpe and Reddy’s data by 22%. In using data from ref. [23] for eq. (6), only transference numbers and electrical conductivities from crystal A are used. Calculated values of f/z, are reported as a function Of temperature in fig. 6. An attempt t0 Calculate zd from a correlation factor equal to 0.78 is also shown in fig. 6. The resulting curve gives largely over- exaggerated values for zd. The material purity may of course play some role on Dki. However, recent measurements by Atkinson et al. [33] have shown that heavy NiO doping by aluminum, at the 0.1% mol level, leads to a markedly lower enhancement than

Fig. 6. Temptative representation of f/.zd and zd versus tem-

perature, at PO, equal to one atm according to presently available data [23, 31, 341.

414 F. Morin I Electrotransport in oxides

what a simple unaccociated defect model would pre- dict. At this point, no clear explanation concerning zd behavior can be provided.

5.3. Electrotransport in ruble

The cationic transference number has been determined in rutile as a function of temperature and oxy-

gen pressure by Singheiser and Auer [24]. Compared to the preceding oxides, diffusion in rutile is compli- cated by the varying effect of crystallographic orientation. In that sense, transference numbers obtained by Singheiser and Auer [24] correspond to averaged values since their electrotransport experiments were performed on pellets quite similarly to Tubandt’s

experimental arrangement. At PO, equal to 3.4x lo-” atm their activation energy for tTi4+ is 42 kcal/mol. Singheiser and Auer’s results for the effect of PO, on tTi’+ are shown in fig. 7. The observed variation for t++ is quite compatible with the already assumed existence of more than one single type of defects [35]; eq. (6) cannot be directly applied to TiOz due to the lack of sufficient radiotracer data.

An indirect attempt to check the validity of present tTi’+ data can be performed in the following way. A theoretical value of @i at 1000” C and PO, = 3.4 x lo-i3 atm is first calculated by means of eq. (5).

0

3.0- \

* 0 X

k,

+?_

.!T 2,0- “\

\ 0

W-

I ’ (oft2 ’

I I I I

10-14 W’O 10-a po2(alm.l

Fig. 7. Variation of the transference number tT:+ versus PO,

according to Singheiser and Auer [24].

The currently available radiotracer data on TiOz at 1000” C, were obtained on rutile single crystals in either air or oxygen and parallel to the c axis [36]. From higher-tyemperature measurements [37], a factor equal to 0.6 compared to the c axis can be deduced for a randomized orientation. Using this D&

value and the preceding theoretical one computed for a largely different oxygen pressure, n, from Dfi = DOP:‘:D is then estimated. nD stands between 5.8 and 6.1. This first estimate on the effect of PO, on D& leads to a quite reasonable figure. It mainly tells that Singheiser and Auer’s [35] measurements are compatible with radiotracer data and with current

defect model on Ti02. Radiotracer data at lower oxygen pressures would nonetheless be essential to further theoretical interpretation of these electrotransport experiments. Variation of the transference number with PO, presently remains the most theoretically significant result of electrotransport experiments in rutile.

5.4. Electrotransport in iron monoxide

Fe,_sO ranks among typical high defect concentration oxides. Consequently, the preceding theoretical treatment can only be considered as a first approxi- mation even if the observation of electrotransport in iron monoxide retains its full phenomenological significance. The first experiments on the electrolysis of solid Fe,_,0 were designed by Desmarescaux and Lacombe [14]. Use is made here of more recent measurements with the same basic method [38,39]. With this method, the only achievable oxide composition is that of Fel_sO in equilibrium with pure iron. It corresponds to the lowest defect concentration in iron monoxide, at any temperature, and it is normally in the order of 6 = 0.04. Such a defect concentration is still relatively high and it helps in making the electrotransport phenomenon more easily measurable.

The diffusion of D& in iron monoxide has been thoroughly investigated by Chen and Peterson [40]. These measurements are combined with transference numbers [38,39] in eq. (6) and the resulting f/zd values are reported in fig. 8. As shown in this figure, a zd value close to unity would not be compatible with the isotopic effect fAK as measured by Chen and Peterson because AK would thus become greater

F. Morin / Electroiransport in oxides 415

f/z

2

I

I I I I

/’ fat zd’t (not compatibk2 wiih;hK=0.46)

I I I I TOO MO 900 toD0

WC)

Fig. 8. Determination of f/z_, and zd at various tem-

peratures for iron monoxide.

-I

f

than unity. A zd value in the vicinity of two is more plausible and the corresponding correlation factor is also in fair agreement with theoretical calculations by Leroy et al. [41]. There is a trend for the estimated correlation factor to increase with temperature but the present theoretical treatment is rather too crude to give it further significance here. At this point, it is worthwhile to mention some strong analogy between the present Fel_sO behavior at S = 0.04 and the recent work by Peterson and Chen on MnlesO [42]. These authors observed a constant D&,/S ratio up to about S = 0.06 which suggests an almost ideal defect behavior within this range. On the counterpart, this phenomenon is largely tempered by the fact that most of the experimentally measured variation of the isotopic effect in Mnl_sO occurs within the same range. A similar situation would not at all be unexpected in iron monoxide for its present defect concentration.

5.5. Electrotransporf in cobaltous oxide

Amongst all semiconducting oxides, cobaltous oxide is certainly the best candidate for diffusion mechanism studies in simple oxides. Transference numbers obtained by indentation measurements [25] are shown as a function of PO, in fig. 9. For comparison, a recent experimental regression of the

Fig. 9. Experimental results on t,-,*+ at 1010” C as a func-

tion of PO,. For comparison, the &, curve from ref. [23]

is also shown.

chemical diffusion coefficient i&, at 1000” C [43] is also reported in fig. 9. There is a striking-resemblance between the tco*+ variation and that of DCOO. The variation of the transference number &-,*+ as a function of PO, leads to conclude to a more or less corresponding variation of vacancy mobility as a function of defect concentration. This statement is somewhat reinfo_rced by the strong similarity between both &-,2+ and DCOO variations with PO,.

Eq. (6) is quite readily applied to cobalt monoxide. In order to get significant zd values, exacting results on DE, and gccoo are essential. At temperatures close to 1000“ C, it has already been stated that Carter and Richardson’s [44] regression on D& is the most satisfactory [43]. Conductivity data come from recent measurements [45] on the same material as that used for electrotransport experiments. In fig. 10, zd is plotted versus PO, for f = 0.78. The present averaged value for zd stands around 1.5 compared to a preceding figure of two [25] mainly because of the more discriminating choice on D&. In any case, zd is greater than the theoretical equilibrium valency, equal to one V&, and it does not seem to vary very significantly with PO,.

6. Summary

The effect of an applied electric field on the migration of ions in semiconducting oxides has been

416 F. Morin / Electrorransport in oxides

185

I I I I I I 10-3 lo-2 lo-’ loo

po2 (otm.1

Fig. 10. Determination of f/q, and z,, at 1010” C for cobalt

monoxide and as a function of oxygen partial pressure.

identified a few decades ago. For most experiments, this effect is normally translated into geometrical modifications of the oxide. Owing perhaps to the very large acceptance of the Nernst-Einstein relation, this phenomenon has received rather limited attention and it has been almost entirely substituted by more modern radiotracer diffusion measurements. Nonethe- less, electrotransport experiments remain a distinctive and powerful investigation tool for studying defect nature and defect diffusion in oxides. Amongst other features, anionic and cationic migrations can be differ- entiated. A direct indication of either the defect mobility variation or the appearance of secondary types of defects stems from electrotransport experiments. By coupling electrotransport measurements with radiotracer data, the correlation factor or the effective valency of the diffusing defects can be estimated. Up to date, the most significant results have been obtained on Cu20, FeO, Co0 and TiOz.

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Discussion

A.T. Chadwick: You report higher ionic transference numbers in

nickel oxide than those calculated from Atkinson and Taylor’s values of tracer diffusivity in the lattice. In the case of sodium chloride, Holt at Imperial College, London, has found quantitative agreement between tracer values for dislocation diffusion, taken together with dislocation density, and electrical conductivity. While his high values for both may result from impurity effects, this demonstrates the possibility of a dislocation mechanism for ionic conductivity. In nickel oxide crystals, dislocations can be the main route for tracer transport. The contribution of dislocation diffusion increases at lower temperatures. The anomaly which you report, varies in the same way with temperature. In view of this, is it possible that the dilatometric measurements which you report, are, in practice, of ionic transport along dislocations?

F. Morin: You are rightly pointing out the effect of short cir-

cuit diffusion. In order to make an approximate calcu-

lation of it in the low-temperature region of dilatometric measurements, one would need at least, a fair estimate of the dislocation density in the material that was used for electrotransport measurements. A second and more trivial point is that the high sensitiv- ity of dilatometric measurements may be somewhat misleading. Large interface displacements must still be used because of artefacts at the one micron scale.

M. Kleitz: If we refer to electromigration in metals, we can

say, grossly, that the ion which feels the electric field is formed of the nucleus and the localized electrons. Electrons delocalized in bands play a separate part. Extrapolation to oxide ions in metal oxides should allow us to conclude, if 2p electrons are delocalized in a valence band, that the ions which feel the electric field, are in fact cations O”+!

F. Morin: In transition metals, electron holes are normally

localized.

J. Schoonman: Do the transference number data Ti4+ in TiOZ,

which you have presented, refer to electromigration of interstitial Ti3+ ions i.e. Ti;“?

F. Morin: At this point, Ti4+ is an arbitrary choice and the

transference number can be easily corrected for a valency equal to 3 + . In fact, according to the most recent experiments by Ait-Younes, Millot and Gerdanian, this valency would be equal to 3 + .

B.C.H. Steele: Can you give some details of your experimental

arrangements? For example, what is the value of the applied dc voltage and current density across the sample?

F. Morin: The highest current density still compatible with a

negligible heating effect of the sample is, of course, the best one to be used. Such an optimum value would be dependent on both the experimental set-up and the specific oxide being studied. A current density of 0.22 A/mm* has already been quoted for COO. It can be greater, without any harmful effect, for Fe0 but it would have to be much smaller for NiO. In any


case, the absence of any effect of the current density on the determination of the ionic transference number

been used in order to have reversible electrodes. Is this the case?

must be experimentally checked. F. Morin:

J.B. Wagner: In the experiments on the transference number of

copper in cuprous oxide, platinum electrodes were used. Accordingly, an oxygen atmosphere must have

An overwhelming portion of the sample is in chemical equilibrium with the outer oxygen atmosphere. Nonetheless, caution must be exerted concerning the reversibility of the cathode at lower oxygen partial pressures because of the eventuality of copper dissolution into platinum.

electrotransport in oxides

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