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Influence of oxygen pressure on oxygen self-diffusion in NiO
Solid State Ionics 12 (1984) 75-78 North-Holland, Amsterdam
INFLUENCE OF OXYGEN PRESSURE ON OXYGEN SELF-DIFFUSION IN NiO
C. DUBOIS, C. MONTY and J. PHILIBERT Laboratoire de Physique des Matkriaux, CNRS, 1, place Aristide-Briand,
Bellevue, 92195 Meudon Cedex, France
In a previous work oxygen self-diffusion in NiO has been measured under 0.21 atm oxygen pressure. The results are well described by: D,,(cm2s-1) = 50 exp [-5.6(eV)/k7’]. A new series of experiments under PO, = 1O-4 atm has been performed to study the influence of oxygen pressure. The samples have been annealed under an argon flow containing 100 ppm of oxygen-18. The diffusion profiles have been obtained by secondary ion mass spectrometry; they are consistent with a solution of Fick’s laws considering an effect of evaporation/condensation at the surface of the samples. The measurements have shown that near 1300” C the dependence on P O2 is very small. On the contrary the change in Dc with PO, is significant at 1555” C (II,= P& with a = OS), (I varies regularly between these two temperatures. That leads to a small effective activation energy under 10m4atm. This behaviour can be explained assuming that besides two different charge states for majority defects (Vbi and VLJ, they are two types of minority defects in the oxygen sublattice: oxygen vacancies and oxygen interstitials. L’autodiffusion de l’oxygene dans NiO a et6 mesuree sous une pression d’oxygtne de 0.21 atm dans un travail anterieur. Les resultats sont bien decrits par: &(cm2 s-‘) = 50 exp [-5,6(eV)/kT]. Une nouvelle serie d’exptriences sous une PO, de 10m4atm a et& faite pour etudier l’influence de la pression d’oxygene. Les Cchantillons ont CtCrecuits sous un flux d’argon contenant 100 ppm d’oxygene-18. Les profils de diffusion ont ttt obtenus par spectrometrie de masse de l’emission ionique secondaire; ils obeissent a une solution des lois de Fick obtenue en considtrant un effet d’evaporation ou de condensation a la surface des Cchantillons. Les mesures ont montre que prbs de 1300” C la dependance en PO, est tres faible. Au contraire la variation de D, avec PO, est importante B 1550” C (Do= P& avec (Y= 0,5), a varie regulibrement entre ces deux temperatures. Ceci conduit a une energie d’activation apparente faible sous 10d4 atm. Ce comportement peut Gtre expliqut en supposant que, a c&t de dtfauts majoritaires presentant deux Ctats de charge (Vk et Vki) il y a deux types de defauts minoritaires dans le sous reseau de l’oxygbne: des lacunes d’oxygene et des interstitiels d’oxygtne.
1. Introduction
In our previous work [l], we have measured the oxygen self-diffusion under an oxygen pressure PO, = 0.21 atm, between 1200 and 1600” C. It was found that the diffusion coefficients can be represented by Do(cm2 s-l) = 50 exp [-56(eV)/kT].
transport and related properties such as creep [2] or sintering. High-temperature creep tests on the same crystals have been performed as a function of temperature and oxygen partial pressure [3], they suggest that the main defects of the oxygen sublattice are oxygen vacancies.
(1)
In this work the oxygen self-diffusion was measured under PO, = low4 atm and in a temperature range of 1300-1550” C. The aim of these studies is to identify and characterize the point defects of the oxygen sublattice. These defects are minority defects and their concentrations are low, nevertheless they influence matter
2. Experiments The experimental details of the sample preparation are the same as those given before [l]. However the annealing treatments were performed in a new way: the samples were treated under a constant oxy-
C. Dubois et al. / Oxygen self-dijiision in NiO
76
gen-18 partial pressure PO, = 10e4 atm, annealing them under a flowing mixture (argon + 0.01% oxygen18). Previously, they were equilibrated under a flowing mixture with oxygen-16. Diffusion annealing times ranged between 25 and 90 h. Diffusion profiles were obtained using SIMS (CAMECA EM1 300).
NiO TX 1914 C t : 41.71 h.
\,io“&rn.
~~-7.8
3. Results
D:
tP
cm e-’
3.7 IO-“Clllk’
The diffusion profiles were analysed using the solution of Fick’s law assuming a constant 180 concentration, C,, at the sample surface and an evaporation (or condensation) process which produces a migration of the surface with a rate u. The solution can be written:
+exp (-ux/D) erfc[(x-
vt)/2(Dt)“*]}+ C,,
(2)
where C is the I80 concentration at penetration x, C, is the natural 180 concentration (0.2%), f is the annealing time and D is the diffusion coefficient. When vt is much smaller than (Dt)“‘, this equation is equivalent to the classical solution: (C,-C)/(C,-C,)=erf[x/2(Dr)“‘]
Fig. 1. Concentration-penetration profile for oxygen diffusion in NiO at PO, = 10d4 atm, T = 1314” C, t = 42 h. The theoretical fit is given by the full line; full circles are experimental points measured by SIMS.
(3)
obtained assuming o = 0. Two examples of the results are given in figs. 1 and 2. We have used eq. (2) to fit the data and the “best fit” values of t, and D have been obtained. Table 1 gives tr and D computed for each diffusion profile. D values are plotted on an Arrhenius diagram as log D versus l/T in fig. 3 at two PO, (0.21 atm and 10m4atm).
154Col~
NiO
.
T= 1548c
4. Discussion of the results The pentrations (=( Df)l”) obtained in these experiments are small and allow large uncertainties in the results. Nevertheless all the Do values measured under PO, = 10e4 atm are smaller than those obtained under 0.21 atm. Around 1300” C Do values are very close. The PO, exponent is positiye at high temperatures (135~1500” C), and it is nil or slightly positive around 1300” C
Fig. 2. Concentration-penetration profile for oxygen diffusion in NiO at Po, = 10m4atm, T = 1548” C, t = 69 h.
C. Lhbois et al. / Oxygen self-difusion in NiO
Table 1 Experimental
Majority defects in NiO are (Ytimes charged nickel vacancies V$ [5] whose formation is described by:
results, PO, = 10e4 atm
Temperature (“C)
Annealing time (h)
1314
41.75
1346
28.42
1398
27.50
1405
27.50
1440 1501 1548
74.75 68.66 69.00
77
Fit to eq. (2)
40,(g)+V;;+ah’+00, (4)
[V&][h’]” = K;;Pb/:.
D (cm’s_‘)
u (A s-l)
5.68 x 10-t’ 2.50 x 10-r’ 3.70 x 10-l’ 5.28 x 10-l’ 1.46 x lo-l6 7.30x 10-l’ 2.30 x lo-l6 1.07x lo-l6 7.90x 10-l’ 1.28 x lo-l6 8.58 x 10-l’ 4.86x 10-l’ 2.86 x 10-l’ 2.07 x 10-l’ 1.53 x lo-l6
1.66 x 1o-4 -8.64 x 1O-4 -7.87 x 1O-4 3.31 x 1o-3 1.32x 1O-2 5.01 x10-s -1.33 x 1o-3 4.50 x 1o-3 1.24~ 1O-3 4.60 x 10-s 3.4 x 10-s -3.2x 1O-4 2.77 x 1O-4 -2.05 x lo-’ -3.26 x 10-s
The electroneutrality equation can be written
LY[V&]= [h’],
(5)
which leads to [V;a&
*-“(“+‘)(~~~)l/(“+l)~~~:(~+‘). (6)
In the same way, the formation of V{’ and 0:’ is described by the following: Oo+ Vg +pe’+lOJg),
(7)
[V$J[e’lP = I&P& l/Z,, ;Oz(g) + O:‘+ yh’,
(8)
[O;‘][h’]’ = K&Pg;. Several defects can be imagined to describe the results, they can be simple or complex. Considering only simple defects: oxygen vacancies /3 times charged Vg or oxygen interstitials y times charged Oy’, their concentration can be related to the parameters PO, and i?
I
log
-13 :
[h'l[e'l
= KG,
(9)
the concentration [Vg] and [OY’]can be deduced: [vg] = (YP/(“l+l)(K~M)P/(U+l)(KG)--P(KFVO)
NiO
Do (~““8)
Adding to eqs. (4)-(7) the intrinsic equilibrium of electronic carriers:
xp~;2(~+1w2 (10) [O;‘]=
n-‘/‘“+l~(Ht,)-‘/‘““~~K~~~
~p-Y/2(a+l)+‘/2 02 (11)
-17 i
1
a
a.5
lSO0
1100
T-“d 1300
K-’ ‘Ic
Fig. 3. Experimental points plotted on an Arrhenius diagram. The full line was obtained by a least mean squares fit on the high-pressure results [l].
a, /I, y are positive, l/2(& + 1) is the PO, exponent of the majority defects concentration. There is only a change of sign of the PO, exponent when one considers an oxygen vacancy or an oxygen interstitial with the same charge state. In our experimental range, 1/2(a + 1) varies between l/4.8 and l/5.3 [6] when the temperature increases, which means that (Yis between 1 and 2 (majority defects can be considered as a mixing of VX, VI;, and holes). We have two possibilities to explain the observed PO, exponents (0 to 4): (1) 0: ( y = 0) at high temperatures, 0: at about 1300” C.
C. Dubois et al. / Oxygen self-diffusion
78
in NiO
).
4_
5..
6.
L
Fig. 4. Schematic view of the suggested coefficient of the defects.
point defect
population.
(2) Of at high temperatures, VG at about 1300” C. Such a change of defect charge state of interstitials seems unlikely as it would mean that, at constant oxygen pressure, the ionisation degree of interstitials would decrease with increasing T A mixing of Ol and V, with a predominancy of Of above 1500” C and a predominancy of V, below 1350” C looks better. That implies an activation energy for diffusion much higher in the case of 0: that it is in the case of V,. A schematic view of the suggested defect population is given in fig. 4.
D is the product
and the migration
probable but they can be present with other defects, free or associated. Discrepancies between creep and diffusion experiments are not understood. Some new experiments, particularly on doped samples are suggested.
References [l] [2] [3]
5. Conclusion The minority defects of the oxygen sublattice in NiO are not well known at present. The diffusion experiments show that oxygen interstitials are highly
of the concentration
[4] [5] [6]
C. Dubois, C. Monty and J. Philibert, Phil. Mag. A 46 (1982) 419. J. Philibert, Solid State Ionics 12 (1984), this volume. J. Cabrera-Cano, A. Dominguez-Rodriguez, R. Marque J. Castaing and J. Philibert, Phil Mag. A46 (1982) 397. I. I. Kucher, Sov. Phys. Solid State 3 (1961) 401. R. Gomri, H. Boussetta, C. Bahezre and C. Monty, Solid State Ionics 12 (1984), this volume. R. Farhi and G. Petot-Ervas, J. Phys. Chem. Solids 39 (1978) 1169.
INFLUENCE OF OXYGEN PRESSURE ON OXYGEN SELF-DIFFUSION IN NiO
C. DUBOIS, C. MONTY and J. PHILIBERT Laboratoire de Physique des Matkriaux, CNRS, 1, place Aristide-Briand,
Bellevue, 92195 Meudon Cedex, France
In a previous work oxygen self-diffusion in NiO has been measured under 0.21 atm oxygen pressure. The results are well described by: D,,(cm2s-1) = 50 exp [-5.6(eV)/k7’]. A new series of experiments under PO, = 1O-4 atm has been performed to study the influence of oxygen pressure. The samples have been annealed under an argon flow containing 100 ppm of oxygen-18. The diffusion profiles have been obtained by secondary ion mass spectrometry; they are consistent with a solution of Fick’s laws considering an effect of evaporation/condensation at the surface of the samples. The measurements have shown that near 1300” C the dependence on P O2 is very small. On the contrary the change in Dc with PO, is significant at 1555” C (II,= P& with a = OS), (I varies regularly between these two temperatures. That leads to a small effective activation energy under 10m4atm. This behaviour can be explained assuming that besides two different charge states for majority defects (Vbi and VLJ, they are two types of minority defects in the oxygen sublattice: oxygen vacancies and oxygen interstitials. L’autodiffusion de l’oxygene dans NiO a et6 mesuree sous une pression d’oxygtne de 0.21 atm dans un travail anterieur. Les resultats sont bien decrits par: &(cm2 s-‘) = 50 exp [-5,6(eV)/kT]. Une nouvelle serie d’exptriences sous une PO, de 10m4atm a et& faite pour etudier l’influence de la pression d’oxygene. Les Cchantillons ont CtCrecuits sous un flux d’argon contenant 100 ppm d’oxygene-18. Les profils de diffusion ont ttt obtenus par spectrometrie de masse de l’emission ionique secondaire; ils obeissent a une solution des lois de Fick obtenue en considtrant un effet d’evaporation ou de condensation a la surface des Cchantillons. Les mesures ont montre que prbs de 1300” C la dependance en PO, est tres faible. Au contraire la variation de D, avec PO, est importante B 1550” C (Do= P& avec (Y= 0,5), a varie regulibrement entre ces deux temperatures. Ceci conduit a une energie d’activation apparente faible sous 10d4 atm. Ce comportement peut Gtre expliqut en supposant que, a c&t de dtfauts majoritaires presentant deux Ctats de charge (Vk et Vki) il y a deux types de defauts minoritaires dans le sous reseau de l’oxygbne: des lacunes d’oxygene et des interstitiels d’oxygtne.
1. Introduction
In our previous work [l], we have measured the oxygen self-diffusion under an oxygen pressure PO, = 0.21 atm, between 1200 and 1600” C. It was found that the diffusion coefficients can be represented by Do(cm2 s-l) = 50 exp [-56(eV)/kT].
transport and related properties such as creep [2] or sintering. High-temperature creep tests on the same crystals have been performed as a function of temperature and oxygen partial pressure [3], they suggest that the main defects of the oxygen sublattice are oxygen vacancies.
(1)
In this work the oxygen self-diffusion was measured under PO, = low4 atm and in a temperature range of 1300-1550” C. The aim of these studies is to identify and characterize the point defects of the oxygen sublattice. These defects are minority defects and their concentrations are low, nevertheless they influence matter
2. Experiments The experimental details of the sample preparation are the same as those given before [l]. However the annealing treatments were performed in a new way: the samples were treated under a constant oxy-
C. Dubois et al. / Oxygen self-dijiision in NiO
76
gen-18 partial pressure PO, = 10e4 atm, annealing them under a flowing mixture (argon + 0.01% oxygen18). Previously, they were equilibrated under a flowing mixture with oxygen-16. Diffusion annealing times ranged between 25 and 90 h. Diffusion profiles were obtained using SIMS (CAMECA EM1 300).
NiO TX 1914 C t : 41.71 h.
\,io“&rn.
~~-7.8
3. Results
D:
tP
cm e-’
3.7 IO-“Clllk’
The diffusion profiles were analysed using the solution of Fick’s law assuming a constant 180 concentration, C,, at the sample surface and an evaporation (or condensation) process which produces a migration of the surface with a rate u. The solution can be written:
+exp (-ux/D) erfc[(x-
vt)/2(Dt)“*]}+ C,,
(2)
where C is the I80 concentration at penetration x, C, is the natural 180 concentration (0.2%), f is the annealing time and D is the diffusion coefficient. When vt is much smaller than (Dt)“‘, this equation is equivalent to the classical solution: (C,-C)/(C,-C,)=erf[x/2(Dr)“‘]
Fig. 1. Concentration-penetration profile for oxygen diffusion in NiO at PO, = 10d4 atm, T = 1314” C, t = 42 h. The theoretical fit is given by the full line; full circles are experimental points measured by SIMS.
(3)
obtained assuming o = 0. Two examples of the results are given in figs. 1 and 2. We have used eq. (2) to fit the data and the “best fit” values of t, and D have been obtained. Table 1 gives tr and D computed for each diffusion profile. D values are plotted on an Arrhenius diagram as log D versus l/T in fig. 3 at two PO, (0.21 atm and 10m4atm).
154Col~
NiO
.
T= 1548c
4. Discussion of the results The pentrations (=( Df)l”) obtained in these experiments are small and allow large uncertainties in the results. Nevertheless all the Do values measured under PO, = 10e4 atm are smaller than those obtained under 0.21 atm. Around 1300” C Do values are very close. The PO, exponent is positiye at high temperatures (135~1500” C), and it is nil or slightly positive around 1300” C
Fig. 2. Concentration-penetration profile for oxygen diffusion in NiO at Po, = 10m4atm, T = 1548” C, t = 69 h.
C. Lhbois et al. / Oxygen self-difusion in NiO
Table 1 Experimental
Majority defects in NiO are (Ytimes charged nickel vacancies V$ [5] whose formation is described by:
results, PO, = 10e4 atm
Temperature (“C)
Annealing time (h)
1314
41.75
1346
28.42
1398
27.50
1405
27.50
1440 1501 1548
74.75 68.66 69.00
77
Fit to eq. (2)
40,(g)+V;;+ah’+00, (4)
[V&][h’]” = K;;Pb/:.
D (cm’s_‘)
u (A s-l)
5.68 x 10-t’ 2.50 x 10-r’ 3.70 x 10-l’ 5.28 x 10-l’ 1.46 x lo-l6 7.30x 10-l’ 2.30 x lo-l6 1.07x lo-l6 7.90x 10-l’ 1.28 x lo-l6 8.58 x 10-l’ 4.86x 10-l’ 2.86 x 10-l’ 2.07 x 10-l’ 1.53 x lo-l6
1.66 x 1o-4 -8.64 x 1O-4 -7.87 x 1O-4 3.31 x 1o-3 1.32x 1O-2 5.01 x10-s -1.33 x 1o-3 4.50 x 1o-3 1.24~ 1O-3 4.60 x 10-s 3.4 x 10-s -3.2x 1O-4 2.77 x 1O-4 -2.05 x lo-’ -3.26 x 10-s
The electroneutrality equation can be written
LY[V&]= [h’],
(5)
which leads to [V;a&
*-“(“+‘)(~~~)l/(“+l)~~~:(~+‘). (6)
In the same way, the formation of V{’ and 0:’ is described by the following: Oo+ Vg +pe’+lOJg),
(7)
[V$J[e’lP = I&P& l/Z,, ;Oz(g) + O:‘+ yh’,
(8)
[O;‘][h’]’ = K&Pg;. Several defects can be imagined to describe the results, they can be simple or complex. Considering only simple defects: oxygen vacancies /3 times charged Vg or oxygen interstitials y times charged Oy’, their concentration can be related to the parameters PO, and i?
I
log
-13 :
[h'l[e'l
= KG,
(9)
the concentration [Vg] and [OY’]can be deduced: [vg] = (YP/(“l+l)(K~M)P/(U+l)(KG)--P(KFVO)
NiO
Do (~““8)
Adding to eqs. (4)-(7) the intrinsic equilibrium of electronic carriers:
xp~;2(~+1w2 (10) [O;‘]=
n-‘/‘“+l~(Ht,)-‘/‘““~~K~~~
~p-Y/2(a+l)+‘/2 02 (11)
-17 i
1
a
a.5
lSO0
1100
T-“d 1300
K-’ ‘Ic
Fig. 3. Experimental points plotted on an Arrhenius diagram. The full line was obtained by a least mean squares fit on the high-pressure results [l].
a, /I, y are positive, l/2(& + 1) is the PO, exponent of the majority defects concentration. There is only a change of sign of the PO, exponent when one considers an oxygen vacancy or an oxygen interstitial with the same charge state. In our experimental range, 1/2(a + 1) varies between l/4.8 and l/5.3 [6] when the temperature increases, which means that (Yis between 1 and 2 (majority defects can be considered as a mixing of VX, VI;, and holes). We have two possibilities to explain the observed PO, exponents (0 to 4): (1) 0: ( y = 0) at high temperatures, 0: at about 1300” C.
C. Dubois et al. / Oxygen self-diffusion
78
in NiO
).
4_
5..
6.
L
Fig. 4. Schematic view of the suggested coefficient of the defects.
point defect
population.
(2) Of at high temperatures, VG at about 1300” C. Such a change of defect charge state of interstitials seems unlikely as it would mean that, at constant oxygen pressure, the ionisation degree of interstitials would decrease with increasing T A mixing of Ol and V, with a predominancy of Of above 1500” C and a predominancy of V, below 1350” C looks better. That implies an activation energy for diffusion much higher in the case of 0: that it is in the case of V,. A schematic view of the suggested defect population is given in fig. 4.
D is the product
and the migration
probable but they can be present with other defects, free or associated. Discrepancies between creep and diffusion experiments are not understood. Some new experiments, particularly on doped samples are suggested.
References [l] [2] [3]
5. Conclusion The minority defects of the oxygen sublattice in NiO are not well known at present. The diffusion experiments show that oxygen interstitials are highly
of the concentration
[4] [5] [6]
C. Dubois, C. Monty and J. Philibert, Phil. Mag. A 46 (1982) 419. J. Philibert, Solid State Ionics 12 (1984), this volume. J. Cabrera-Cano, A. Dominguez-Rodriguez, R. Marque J. Castaing and J. Philibert, Phil Mag. A46 (1982) 397. I. I. Kucher, Sov. Phys. Solid State 3 (1961) 401. R. Gomri, H. Boussetta, C. Bahezre and C. Monty, Solid State Ionics 12 (1984), this volume. R. Farhi and G. Petot-Ervas, J. Phys. Chem. Solids 39 (1978) 1169.