Electrical conductivity and chemical diffusion coefficient measurements in single crystalline nickel oxide at high temperatures

1. Phys. Chm. Sdids Vd. 39. pi. 1169-I 173 @perclmmRwLfd..I578. PtintedinGmtBriuin

ELECTRICAL CONDUCTIVITY AND CHEMICAL DIFFUSION COEFFICIENT MEASUREMENTS IN SINGLE CRYSTALLINE NICKEL OXIDE AT HIGH TEMPERATURES R. FARHI and G. PETWT-ERVAS C.N.R.S., Laboratoire des PropriMs Wcardqucs et Thermodynamiqucsdes Matiriaux 93430, Villctaneuse, FranCe (Receioed 31 OcM~er 1977;accepted in mised form IOApril 1978) Abstract-Ekctrical conductivity measurements on nickel oxide have been performed at high temperatures (I273 K < T < 1673K) and in partial pressures of oxygen ran&~ from Ps = 1.89x IO-‘atm to Pti = I atm. The P*“” dependence of the conductivity decreases from about l/4 for PO,= 1 atm to smallervalues for lower partial pressures of oxygen. The activation enthalpy for conduction increases for decreasing oxygen partial pressures (from 22.5kcal mol-’ at PO2= I atm to 26.0kcal mol-’ for P& = 1.89x IO4 atm). This behaviourcan be explained by the simultaneous presence of singly and doubly ionized nickel vacancies, with differentenerg& of formation. Furthermore,chemicaldi!Tusioncoefficientmeasurementshave been performedin the same temperaturerange, using the conductivitytechnique.and leadinglo the result:

nickel vacancies can be written:

The physic0 chemical properties of transition metal oxides are mainly related to their deviations from stoichiometry. These deviations themselves depend on two important parameters: the temperature and the partial pressure of oxygen in equilibrium with the oxide. Nickel oxide seems to be one of the transition metal oxides which have been the subject of the numerous studies. It appears from the existing results that the predominant defect in this oxide is the nickel vacancy, electrically compensated by electronic holes, which confers to this oxide the properties of a p-type semiconductor. According to the Kriiger-Vink notation[l], the formation of a nickel vacancy whose ionization degree is a can be written:

Oo, V& and /I’ represent respectively an oxygen atom on its normal lattice site, an a times ionized nickel vacancy, and an electronic hole. With the assumption that Viii is the predominant defect in the lattice, the simplified condition for electrical neutrality is: p=

a[VpN’i]

(2)

where p is the molar fraction of electron holes h; and [ V$] the molar fraction of nickel vacancies, which is equal lo the deviation from stoichiometry. The electrical properties of an oxide crystal are therefore strongly connected to the nature, the ionization degree and the concentration of the predominant point defects. Taking into account the electroneutrality condition (2). the eqdibrium constant for the formation of

=1 pa+'

K P

(3)

apqlR

Consequently, the carrier concentration is expressed by the relation:

I

,/2&X+,, PO,

(4)

in which AH,’ is the enthalpy of formation of the considered defect. It can be seen that the carrier concentration is a function of two thermodynamic parameters, temperature T and oxygen partial pressure Pg. Therefore, the electrical conductivity may be expressed by the relation: I/z(P+I) .

(5)

Under these conditions, the degree of ionization a of the nickel vacancy can be directly determined by studying the P, dependencies of the conductivity. Since the carrier mobility, c(p.generally depends on temperature, it is not possible to obtain directly the enthalpy of formation of the defect by studying the variations of conductivity with temperature. For a thermally activated carrier motion, like small polaron hopping mechanism, the current carrier mobility can be expressed by the general formula:

II69

k.=poexp(-g)

(6)

where AH,” is the activation enthaipy for the hole

R. FARHI and G. PETOT-ERVAS

1170

migration. Substitution of eqn (6) into eqn (51 gives:

Table 2. Results

of the analysis of nickel oxide before and after the experiments

AH’ AH” *I)RT++G--

I

Paz

1,2(,a+,)

(71

Then, the activation enthalpy for conductivity AH, corresponds to the sum AH,” + [(AH,?f(a + I)]. Electricat properties of nickel oxide at high temperatures have been the subject of intense studies. However. disagreement still exists concerning many problems related to these properties. More particularly the state of ionization of the cation vacancies remains a subject of discussion. If we express the state of ionization of nickel vacancies by n = 2fa t I), some authors&51 have obtained n = 4 and proposed that the predominant defects are singly ionized nickel vacancies. Others (6-I I] found that n is 6 and consequently explain their results assuming that doubly ionized nickel vacancy is the major defect. The occurrence of both types of vacancies has also been suggested in some studies[l2-171. The published results concerning the atomic transport, and more particularly the activation energy for the self diffusion of nickel in its oxide. exhibit some scatter, since the values of this activation energy range between 44.5 and 6l.OkcaI mot-‘(14, 17-231. Chemical diffusion coefficient measurements have been also performed on nickel oxide at high temperature, but they lead to somewhat different results, as it can be seen in Table 1. In order to explain the scatter of the results concerning the ionization degree of nickel vacancies, we have determined the electrical conductivity of nickel oxide single crystals at high temperature, in thermodynamic equilibrium with a given oxygen partial pressure. Furthermore, chemical diffusion coefficients have been deduced from the electrical conductivity measurements performed as a function of time when one of the two parameters PO2or T was changed to a new value. I. EWtRlM5’lTAL

T?XHNIQUE

The used samples were single crystals of nickel oxide prepared from high purity powder. The concentrations of impurities in the initial powder and in the single crystal samples after conductivity measurements are given in Table 2. The nickel oxide powder was cold pressed in small bars and sintered at 1473K. Single crystals were grown along the (100) axis in an arc-image furnace. under air and at a temperature next to 2300K. The single crystals were machined to obtain brick-shaped samples whose dimensions were about 2.5 x 3.0 x 25 mm. Electrical connections were realized by Pt coating of the sample, and through Pt wires, as shown in Fig. 1. This

Element

Before measurements

Si Cr AI Bi Ca CU Pb Fe Mn

5-10 0.5-2.0 0.5-2.0

1273 1373 1473

1573 1673

I

Mg Ag

I8 2

I

arrangement allowed a fine control of the geometrical factor. The effective dimensions were measured using an optical microscope. The sample such provided with electrical contacts was introduced in the cell represented in Fig. 2. Equilibrium atmospheres were established using mixing pumps aflowing to choose oxygen/argon ratios. The temperature was measured with a PtfPt-Rh 10% thermocouple. The 4

electrical leads were connected either to a transformer ratio arm bridge (Wayne Kerr Co.), or to a double Kelvin bridge whose null detector is a phase synchrone amplifier. Measurements were performed in a.c. current, at a frequency of I kHz. We have verified that no appreciable effect on the measured value was introduced when the frequency varied up to 20 kHz. On the other hand, a small influence on the conductivity was detected when gas flow rate was smaller than 5 t h-‘. The laboratory tube was placed in a resistance furnace whose temperature was regulated at 2-I K. Measure-

lkeda and Niil25l Low P, HirJt PO,

8.9 x I@ 2.4 x lo-’

1.5 x lo-’ 3.9 x to-’

8.8 x to-’ 1.8x IO ‘b 3.4 x lo-”


Fig. I. Sample and electrode arrangement

De& ef al. [241

5.4 x lo-’ 1.1 x 10-O 2.2 x IO-h

3
Table I. Chemical diffusion coefficients in nickel oxide (cm’s Temperature. K

After measurements

8.6 x to-” 2.4 x lo-’

5.9 x lo-’ 1.3 x lo-* 2.6 x lo-”

‘)

Morlotti[ZCj

Price and waener (271

Our results

6.7 x IO-’ 1.6 x lo-’

1.3 x lo-’ 2.5 x 1o-7

1.3 x lo-’ 3.6 x IO-’

3.5 x 10“ 6.9 x IO“ 1.3 x 10“

4.2 x lo-’ 6.8 x IO-’ 1.0 x lo-*

9.1 x lo-’ 2.0 x lo+ 4.0 x lo-”

Electricalconductivityand chemical diffusion coefficient measurements in singk crystallinenickel oxide

1171

ments were performed in the temperature range 12731673K and for oxygen partial pressures from Pm= I atm to PO, = 1.89x lOA atm.

tCONDUCTNKY~DURlNG itQuluBRATtoN OF TEE cAsoxum SYSIUk Patton OF ‘IHE rixmlIcALnlFFlIaoNc-

2.1 Principle The determination of the chemical diffusion coefficient in oxides by studying the variation of a physic0 chemical property between two equilibrium states was tirst suggested by IMnwald and Wagner [28]. When one of the parameters, PO, or T, of the thermodynamic equilibrium between the gaseous phase and the oxide is modified, the point defects concentration at the solid/gas interface instantaneously corresponds to the new imposed conditions of temperature and oxygen partial pressure. On the other hand, in the bulk of the sample, thermodynamic equilibrium is only reached after a considerable time lapse, depending on the chemical diffusion coefficient in the oxide. it can be For a brick-shaped sample, demonstrated[27,29] that, after the change of one of the parameters Pg or T, the conductivity u of the sample is related to the time t and to the chemical diffusion coefficient fi by the relation:

Fig. 2. Conductivity cell assembly: (a) feedthrough; (b) gas inlet and outkt; (c) Pt kads; (d) alumina tube: (e) water refrigeration; (f) furnace; (B) alumina radiation shields; (h) alumina sheath; (i) Pt, Pt-Rh thermocouple; (j) NiO single crystal.

u--O, -= uo-0,

(8) with o. = conductivity at the time r = 0 when a thermodynamic parameter is modified: (T, = conductivity when the new equilibrium state is reached; and H, L, I = dimensions of the sample. For a sufficiently large time, the terms corresponding to n, m and p > 0 are rapidly negligible, and the preceding relation becomes: ~~=(~>‘exp_r’(~+~+if)61.

(9)

Thus, the chemical diffusion coefficient can be directly determined, for each temperature, by plotting In [(a - u.4/(u0 - ad] as a function of time. The study of the variations of b as a function of the temperature allows one to deduce the chemical diffusion activation energy.

2.2 Results and discussion The values obtained for the chemical diffusion coefficient fi between 1273 and 1673K are reported in FQ. 3. Within the experimental errors, the same values

6.01 60

Fig. 3. Chemical

7.0 10’/ltKA’)

diffusion coefficient temperature.

00

results as a function

of

of b were obtained when we moditied either PO, or T. The following analytic expression for the chemical diffusion coefficient fi between 1273 and 1673K was obtained by a least squares adjustment: b=0.244exp(-F)cm2s-‘.

(10)

The obtained values of fi are in good agreement with those reported by other authors(26271, except Morlotti[26] who finds much higher values than ours (see Table I). We have compared our results concerning the chemical diffusion activation energy with those obtained by these authors: Price and Wagner[27] have proposed a rather different value (Qd = 21.9 kcal mol-‘), whereas Morlotti[26] and Dertn er al.[24] have obtained results similar to ours (31.0 and 33.7 kcal mol-’ respectively).

1172

R. FARHI and G. PETOT-ERVAS

In the simple case of the predominance of only one type of defect, it may be shown[30] that the chemical diffusion coefficient is related to the diffusion coefficient of nickel vacancy D&, according to: B = (a + I)&,,.

(11)

Taking into account this relation, it is obvious that the activation energies for chemical diffusion and for defect migration are identical. Furthermore, the nickel selfdiffusion coefficient is expressed by the relation: DN;= DO,, exp (12) where AH, is the activation energy for vacancy migration (AH, = Qb if only one type of defect exists). By combining the available values of AH,‘[7,8, I I. 161and the value of the chemical diffusion activation energy QA obtained from our experimental results, one can then determine the activation energy associated with the self

0.0 -

Log Fig.

4. Oxygen

partial

Pollatm)

pressure dependence conductivity.

of the

electrical

diffusion of nickel, Q&,, in nickel oxide. We have obtained a value for Qp,,, of approximately 55 kcal mol-‘, which agrees with those obtained by means of tracer techniques: Volpe and Reddy[ 171,Klotsman et 01.[20] and Lindner and Akerstrom[Zl] have proposed for Qk, the values of 62.7. 48.4 and 56.0 kcal mol-’ respectively. 3. CONWCTtVtTY MEASURBMMTS AT TEElWODYNAMtC EQUtUERIIJM

The crystal was considered to be at thermodynamic equilibrium when the conductivity of the sample no longer varied with time. We have verified that the obtained values were reproducible with the oxygen partial pressure and with temperature. The results are summarized in Figs. 4 and 5, in which log u is plotted as a function of log P, and l/T, respectively. Taking into account the different experimental conditions (oxide purity, electrodes arrangement, and so on) of the various authors[2-9,12-14,171, the measured conductivity values are in good agreement with those given in the literature. It appears, from these results, that the variation of log (T as a function of log P, or of l/T is not linear, as it is expected from relation (7). valid only when one type of defect exists in the crystal. So, the values of II and AH,, defined respectively as:

are not constant. The experimental corresponding values, resulting from a least squares adjustment, are tabulated in Table 3. for some temperatures and oxygen partial pressures. The obtained variations are not consistent with a conductivity regime controlled by impurities, especially when the vacancy concentration decreases, i.e. for the lower oxygen pressures. Because of the small deviations from stoichiometry in nickel oxide, the concentration of vacancies is always

--

5 2 b 0” - 1.0 -I

Fig. 5. Temperature

dependence

of the electrical

conductivity.

Electrical conductivity and chemical diRusion coefficient measurements in sin& crystalline nickel oxide

1173

Table 3. Variations of n and AH,, as a function of oxygen partiaJ pressme and temperature

1273 kA

I AH, 0.21

AH,

E

AH, 4.33 x lo-)

AH.,,

mol-’

ki mol-’ k:

I .89 x lo-’ AH,

4.34 4.27 22.5 * 0.2

4.35

4.40

4.28

4.40 4.41 22.8?0.1 4.48 4.64 22.6 23.1 4.54 4.81 23.4 23.9 4.65 5.18 25.5 26.0

4.52

4.61

4.80 23.5 5.01 24.3 5.49 26.5

4.96 23.9 5.24 24.7 5.88 26.9

mol-’ k:

2.1 x lo-’

mol-’

1673

4.28 mol-’

k:

Temperature, K 1373 1473 1573

4.29 22.0 4.29 22.9 4.30 24.9

relatively small (IO-’ < V$ < IO-‘). Thus, the curvatures observed in Figs. 4 and 5 should be interpretedas arising from the presence of both singly and doubly ionized nickel vacancies rather than from the association of these defects. A thermodynamic model has allowed us to determine theoretically the proportion of singly and doubly charged defects as a function of temperatureand oxygen partial pressure for the entiie range of NiO stability, and to study quantitatively the corresponding variations of the conductivity and of activation enthalpy for conductivity. This model will be developed in the next paper(311. 4. CONCLUSlON

Conductivity measurements were performed on single crystals of nickel oxide within the temperature range 1273-1673K and the oxygen pressure range 2x lo-‘I atm. These measurements have allowed us to determine the chemical diffusion coefficient in nickel oxide between 3273 and 1673K. No significant variation of fi with oxygen partial pressure has been detected. The activation energy for chemical diffusion has been found to be 36,600cal mol-‘. in good agreement with the results of other authors. Conductivity measurements at thermodynamic equilibrium have shown that the values of n and AH, varied with PO, and T. These variations have been attributedto the simultaneous presence of singly and doubly ionized nickel vacancies, in proportions depending on PO, and T. This assertion will be tested in the next paper.

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