PHYSICO CHEMICAL PROPERTIES OF NICKEL OXIDE AT HIGH TEMPERATURE

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PHYSICO CHEMICAL PROPERTIES OF NICKEL

OXIDE AT HIGH TEMPERATURE

R. Farhi, G. Petot-Ervas

To cite this version:

R. Farhi, G. Petot-Ervas. PHYSICO CHEMICAL PROPERTIES OF NICKEL OXIDE AT

PHYSIC0 CHEMICAL PROPERTIES

OF NICKEL OXIDE AT HIGH TEMPERATURE

R. FARHI and G. PETOT-ERVAS

C. N. R. S., Laboratoire PMTM, Avenue J. B. ClBment, 93430 Villetaneuse, France

Rhum6.

-

Une etude de I'kart A la stoechiometrie dans I'oxyde de nickel pulvkrulent a Ctk effec- t u k par titrage coulomktrique, dans une gamme de pressions d'oxygkne s'ktendant de 0,012 & 0,21 atrn et aux deux temperatures de 8810 et 896 OC. Les rbultats semblent montrer l'existence, dans le domaine Btudie, de lacunes de Nickel ionisks une fois comrne defaut prkdominant. Le coefficient de diffusion chimique dans l'oxyde de nickel monocristallin a 6t6 determine par la m6thode de la conductivitk klectrique entre 1 000° et 1 400 OC, et pour des pressions d'oxygkne sY6tendant depo, = 10-4 atrn &pol = 1 atm. De plus, le comportement anormal de la conductivite klectrique a kt6 explique par la presence simultank, dans le domaine Btudie, de lacunes de Nickel une fois et deux fois ioniskes. Un modble thermodynamique est propose sur cette base.

Abstract. - A study of thedeviation from stoichiometry by coulometric titration has been performed on nickel oxide powder, from po, = 0.012 atrn to po2 = 0.21 atm, at 881° and

896 OC. The results are in agreement with the existence of singly ionized nickel vacancy as the pre- dominant defect in the investigated range. Chemical diffusion coefficient in nickel oxide single crystals has been determined by the electrical conductivity technique, between 1 000° and 1 400 OC, from pol = 10-4 atrn topo, = 1 atm. Moreover, the anomalous behaviour of the electrical conduc- tivity has been explained by the simultaneous presence of singly and doubly ionized nickel vacancies in the investigated range. A thermodynamic model is proposed on this basis.

A study of point defects in nickel oxide has been

made using two different techniques. First, coulo- metric titration has given us results concerning the variations of the deviation from stoichiometry at moderately high temperatures. On the other hand, electrical conductivity measurements have been per- formed in order t o obtain chemical diffusion coefficients and conductivity values at high temperatures. Using these later results, a point defect model has been built which gives informations about the simultaneous presence of singly and doubly ionized nickel vacancies.

1 . Coulometric titration.

-

The oxygen pressure in equilibrium with non stoichiometric nickel oxide has been measured by means of electrochemical cells of the type :

Pt, ~o,,,olZr02, 15

%

C a O l ~ o Z,,,

,

Pt

.

The crucible containing the nickel oxide powder is separated from the reference gas by a tight pyrex seal, as shown on figure 1.

When the thermodynamic equilibrium is reached, FIG. 1. - Electrochemical cell for the coulometric titrations :

the measured electromotive force is expressed by the 1) reference gas ; 2) Pt/~t-Rh thermocouple ; 3) alumina rod ;

Nernst relation : 4) silica container ; 5) silica tube ; 6) painted Pt electrodes ; 7) stabilized zirconia electrolyte ; 8) quartz crucible ; 9) pyrex (1) seal ; 10) Pt electrical junctions ; 11) alumina radiation shield ;

12) oxide specimen ; 13) alumina crucible.

NICKEL OXIDE AT HIGH TEMPERATURE C7-439

The imposed variations of the sample stoichiometry are controled by coulometric titration. Then, the variation Ay of the stoichiometry can be expressed as follows :

with :

M : molecular weight of the oxide, m : sample's weight,

i : current passing through the cell during the time t,

F : Faraday's constant,

: number of moles of oxygen in the gaseous phase above the sample.

n : depends on the ionization degree of nickel vacancies.

2. Electrical conductivity measurements.

-

The used technique is a four-probes classical one. Figures 3 and 4 respectively show the sample device and the whole assembly. The total amount of impurities in the used single crystals has been found to be less than 20 and 45 ppm respectively before and after the runs.

Measurements have been performed at 8810 and 896 OC, in the oxygen pressure range from 0.012 to 0.21 atm. The results are reported on figure 2. It can be seen that the value n = 4 fits the results better than the value n = 6. Thus, it can be assumed that, in the investigated range, singly ionized nickel vacancy is the predominant defect.

FIG. 3.

-

Conductivity sample : two arrangements have been used, but we have verified that the case (a) is the better, because equipotentials are always perpendicular to the sample axis. This is not the case for (b). (The hatched areas are'Pt coatings.)

FIG. 2. - Variations of the deviation from stoichiometry versus

-pAcrel,. (relation (2)) for n = 4 and n = 6 and for the two ~nvestigated temperatures, 881 and 896 oC.

On the other hand, the proportionality constant k* has been calculated from the slopes of the straight lines obtained (see Fig. 2), and consequently, the departure from stoichiometry has been found to be :

2.1 DIFFUSION RESULTS.

-

In a first step, chemical diffusion coefficients in nickel oxide between 1 0000

and 1 400 OC have been determined by investigating the conductivity variations of the sample as a function of time, when the equilibrium conditions of the oxide are changed. The diffusion equations for a brick-shaped sample are given by :

3 m 0-

-

'Jm

C

e x p - ( 2 n + l ) ' x 'Jo

-

'Jm n=o (2 n

+

112 7c2

-

m 1 7c2

-

x - D t exp - ( 2 m

+

I ) ~ - - Dt

n2

m = o (2 m

+

1)' L~

5

1 7c2 exp -(2 p

+

1)'- Dt p=O (2 p

+

1)2 l2 where (4)

H,

L

and I are the dimensions of the sample,

5

is the chemical diffusion coefficient,

t is the time,

oo is the conductivity at time t = 0 (when the equilibrium conditions are changed),

o, is the conductivity at time t = c~ (when the new equilibrium state is reached). For a sufficiently large time, the following appro- ximation is made : 3 1 1

-

+

-

+

L)

5t]

.

'J

-

=

(5)

[-

"2 (H"P 12 'Jo

-

'Jm ( 5 )

Thus, the chemical diffusion coefficient can be directly determined by plotting the logarithm of the conductivity variation versus time. Chemical diffusion coefficients are shown on figure 5, as a function of 1/T. The activation energy for the vacancy migration has been found to be AH,,, 21 36 600 cal.mo1-l.

2.2 CONDUCTIVITY RESULTS.

-

Measurements have been performed between 1 0000 and 1 400 O C from

to 1 atm of oxygen. The results as a function

of the oxygen pressure are reported on figure 6.

The

value of n, defined as

L o g Poz(atm)

varies with oxygen pressure and temperature, and we shall explain this phenomenon later. The same beha- viour is observed for the conductivity activation ener- gies, as can be seen on figure 7 : the activation energies are function of temperature and oxygen pressure, and the variations are important mainly at low oxygen pressures.

These considerations can be explained by assuming the simultaneous presence of singly and doubly ionized nickel vacancies.

The classical equations for non stoichiometric oxides where predominant defects are metal vacancies are given by :

NICKEL OXIDE AT HIGH TEMPERATURE C7-441

K,, K, are the equilibrium constants for the formation

of singly and doubly ionized vacancies, respectively, and AH; and AH: are the corresponding enthalpies

of formation. The electroneutrality condition must take into account the two types of vacancies :

By care of simplicity, we have introduced a new variable, k, which is the ratio of the concentrations of the two types of vacancies :

It can be demonstrated that the derivatives of k with respect to po2 and T are given by the following expressions : If we define E, by :

a

In o E = - = 8 - 1 - R AHo

,

(1 2 )

a

-

T R : gas constant,

AHo : activation enthalpy for conductivity. We can calculate

as functions of k, provided that the mobility of holes does not vary with p,,. The following expressions are derived :

aE,

= -

A H : - ~ A H , O

k ( 2 k + 1 )

a

In Po, 2 R 4(1

+

3 k)3 (15) AH: is the activation enthalpy for the mobility of

holes (I).

Taking into account the variations of k with po2

and T (relations (10) and ( l l ) ) , it can be seen that E, (and consequently AH,) varies with po2 and T.

The same calculus can be made for n. The following expressions are obtained :

an

--

-

- k

a

In Po, (1

+

2 k) (1

+

3 k ) ' (18)

It may be remarked that, in relation (16), the

limiting conditions are respected (n = 6 when k + oo

and n = 4 when k = 0). These two cases correspond to the predominance of doubly and singly ionized nickel vacancy, respectively.

Log Po,(atm)

FIG. 8. - Comparison of the experimental values with the ana- lytical representation of log o vs l o g ~ ~ , : experimental points ;

-

analytical representation. The thinner lines represent the conductivity behaviour if n were constant and equal to n(0)

(i. e, the value of n for po2 = 1 atm). The value n(0) has been experimentaly determined by small step measurements perform-

ed in the rangepo, = 10-1 to 1 atm.

(1) In this calculus, the conduction mechanism has been L o g PO, ( a t m )

By integrating relation (18) with respect to In p,,, diagram gives the proportion of one type of defect we obtained the analytical representation of log o as a (for example Vhi) with respect to the other. It can be function of logp,, for a given temperature. We have seen on this figure that, at low temperatures and relati- compared in figure 8 the experimental values with this vely high oxygen pressures, singly ionized nickel analytical representation. vacancy is the predominant defect. This qualitative In conclusion to this work, we have drawn in result k i n good agreement with those of coulometric figure 9 the iso-k lines as a function of p,, and T. This titration.

DISCUSSION

C. R. A. CATLOW. - I am doubtful as to the ade- quacy of the very simple models you have used to describe defect clustering in non-stoichiometric NiO. Our calculations suggest that clustering is far more extensive in such oxides (a result supported by e. g. the experimental diffraction data on Fe,-, 0). More- over we find that the binding energy of the larger vacancy aggregates is so much greater than that for the simple clusters that the former should not be significant over any concentration range. The good fit you obtained of your data to simple cluster models does not, I believe, prove the existence of such models ;

in your analysis the simple clustering could simulate the effect of the actual defect interactions which are, I believe, far more complex.