TRANSPORT IN OXIDESNew investigation of oxygen
self-diffusion in Cu2O
F. Perinet, S. Barbezat, C. Monty
To cite this version:
F. Perinet, S. Barbezat, C. Monty. TRANSPORT IN OXIDESNew investigation of oxygen self-diffusion in Cu2O. Journal de Physique Colloques, 1980, 41 (C6), pp.C6-315-C6-318.
<10.1051/jphyscol:1980680>. <jpa-00220118>
HAL Id: jpa-00220118
https://hal.archives-ouvertes.fr/jpa-00220118
Submitted on 1 Jan 1980
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
JOURNAL DE PHYSIQUE
Colloque C6, supplément au n" 7, Tome 41, Juillet 1980, page C6-315
TRANSPORT IN OXIDES.
New investigation of oxygen self-diffusion in CU2O
F. Perinet, S. Barbezat and C. Monty
Laboratoire de Physique des Materiaux, C.N.R.S. Bellevue, 1, place A.-Briand, 92190 Meudon, France
Résumé. — On a effectué de nouvelles mesures des coefficients d'auto-diffusion de l'oxygène dans C u 2 0 monocristallin. Le domaine de stabilité a été exploré sous 2 pressions partielles d'oxygène : 4,6 x 10" 4 atm et 0,26 atm.
L'isotope stable l s O a été utilisé comme traceur. Il a été introduit soit par la méthode du dépôt mince soit par
recuit sous atmosphère de teneur en ' s O constante. On a mesuré les profils de diffusion par spectrométrie de masse
de l'émission ionique secondaire. Ces profils obéissent bien aux solutions de l'équation de Fick. Nous obtenons
comme résultat :
Le défaut responsable de la migration de l'oxygène qui correspond à cette dépendance en pression partielle d'oxygène est l'interstitiel d'oxygène chargé une fois O,'.
Abstract. — New measurements of oxygen self-diffusion coefficients in Cu 2 0 have been performed on single
crystals under two oxygen partial pressures (4.6 x 10"* atm and 0.26 atm) in the stability domain.
The stable isotope l s O has been used as a tracer. It has been introduced by a thin film method or by annealing
under a constant 1 8 0 pressure. The diffusion profiles have been measured by secondary ion mass spectrometry.
They obey quite well the solutions of Fick's equation. The results can be represented by :
The defect responsible for the oxygen migration corresponding to the above oxygen partial pressure dependence
is the singly charged oxygen interstitial OJ.
1. Introduction. — Self-diffusion measurements are
a good tool for studying point defects. In non-stoichiometric oxides, the oxygen partial pressure dependence of the diffusion coefficients enables to identify
the defects responsible for the migration of the studied
species and the temperature dependence provides
information about the enthalpies and entropies of
formation and migration of these defects [1].
Oxygen diffusion in oxides is poorly known because
of various experimental difficulties. However, its
measurements can provide us important information
about the defects in the oxygen sublattice when these
are the minority defects. Measurements of oxygen
self-diffusion are also of importance in the interpretation of phenomena such as sintering and hightemperature creep in which matter transport occurs.
Recent theory predicts that the kinetics of this matter
transport is controlled by the mobility of the less
mobile component of the crystal [2], which, in the
C u 2 0 case, is the oxygen.
C u 2 0 is a metal-deficient oxide. The departure from
stoichiometry can be higher than 10 " 3 [3]. The defects
responsible for this departure from stoichiometry are
neutral and singly-charged copper vacancies. The
structure of C u 2 0 is quite unusual : a face-centered
sublattice for copper but a body-centered sublattice
for oxygen.
In the present work, we have investigated the diffusion of oxygen in C u 2 0 single crystals at two different
oxygen partial pressures : 0.26 atm and 4.6 x 10" 4 atm
in the temperature range of stability. We have measured the temperature dependence at each oxygen
partial pressure and the oxygen partial pressure
dependence.
2. Experimental. — Samples were cut from large
single crystals which were prepared using an arcimage furnace. Their microstructure was investigated
in detail [4, 5].
Diffusion treatments were performed at temperatures ranging between 812 °C and 1 098 °C.
— At a P02 — 0.26 atm the tracer (stable isotope
O) was used in gas phase. A group of zeolitic
pumps was used to obtain vacuum in the chamber
and release the stocked 1 8 0 when the required conditions (T, P0l) of the experiment were reached. Diffusion takes place by isotopic exchange. The initial
ls
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980680
F. PERINET. S. BARBEZAT AND C. MONTY
C6-3 16
-
concentration in 1 8 0 (90 % in the first runs) remains
nearly constant during the experiments (chamber
volume 2 1).
- At a Po, = 4.6 x
atm, the 1 8 0 quantity
available in the chamber would not be sufficient. We
used another method to introduce the tracer : a
C
U thin film
~ was
~ deposited
~
~on the surface of the
sample by a R.F. sputtering technique (C. Sella,
J. C. Martin, to be published). The surface sample
was covered by another pure C u 2 0 crystal to prevent
evaporation during diffusion annealing. The annealing
was done in a flowing mixture 460 ppm O,/Ar.
where A is a constant. Our results obtained a t low
oxygen pressure well fit that solution (Fig. 2).
The concentration profiles were established by
secondary ion emission analysis (CAMECA microanalyser) [6].
3. Results. - 3.1 CONCENTRATION
PROFILES. Due to the fact that we used two different experimental conditions to introduce the tracer, we have considered two different solutions to the Fick's equation.
In the case of samples annealed under 1 8 0 atmosphere, the Fick's solution is :
where x is the penetration, C, is the natural isotopic
concentration, D the self-diffusion coefficient, t the
annealing time. Our results well fit this equation
(Fig. 1).
Fig. 2. - Diffusion profile at Po, :4.6 x
atrn and T = 1 020 OC
obeying the thin-film solution (2). The slope of the line is - 114 Dt.
3.2 TEMPERATURE
AND PRESSURE DEPENDENCE OF
DIFruslvln. - The Arrhenius diagram has been
atrn (Fig. 3)
established separately for Po,=4.6 x
and Po, = 0.26 atrn (Fig. 4). The least-square analysis gives :
- at Po, = 4.6 x
atrn :
-
at Po, = 0.26 atrn
Penetration Ipm)
Fig. 1 . - Diffusion profile at Po, = 0.26 atm and T = 1 055 "C
obeying the solution (1). The c, value in t h ~ sexperiment wasfound
equal to 60 %. The slope of this curve is equal to 112 J D ~ .
When an original thin-film geometry is used, the
solution to the Fick's equation is :
x2
C-C,=Aexp-(2)
4 Dt
Fig. 3. -- Arrhen~us diagram for oxygen selfdiKusion In CuzO
at Po, = 4.6 x
atm.
NEW INVESTIGATION OF OXYGEN SELF-DIFFUSION IN C u 2 0
Fig. 4. - Arrhenius diagram for oxygen self-diffusion in CutO
at Po, = 0.26 atm. Vertical dotted lines show the limits of stability
o f Cu,O.
The difference between the two values of activation
energy is smaller than the experimental error. We
have calculated the pressure dependence of diffusivity
using an average activation energy of 1.55 eV and
obtained :
D x (Po,)" with n = 0.40 T 0.05 .
The combined pressure and temperature dependence of self-diffusion coefficient can be written :
D (cm2.s- ' ) = 3 x 10- 3(~o,)0.4
exp
-
4 . 2 POINT DEFECTS CHARACTERIZATION. - The
oxygen selfdiffusion coefficient is proportional to
the concentration of the defect responsible for the
oxygen migration and to the mobility of that defect.
Using the Kroger-Vink's formalism and the mass
action law it is possible to determine the expected
dependence on oxygen partial pressure of simple
defects in CutO [I].
The formation of a defect can be considered as the
result of an oxygen exchange process between the
oxide and the gas phase.
For a defect V;, which is the most important
charged defect, it can be written
The equilibrium constant is given by :
For a minority defect of the oxygen sublattice, for
example O(, we have :
f 02(g)
-t
0:
+ h.
(9)
with a new reaction constant Kgi given by :
1.55 (eV)
kT
(5)
where Po, is in arm.
4. Discussion. - 4.1 COMPARLSON
WITH OTHER
We have compared our results with previous data of Ebisuzaki et al. [7]. There are slight
discrepancies on the activation energy and oxygen
partial pressure dependence. The authors found
Q = 1.7 T 0.3 eV and n = 0.50 T 0.09; the latter
value was obtained from a very narrow range
- of
pressures at 1 050 O C .
Bretheau [3] measured the influence of temperature
and Po, on steady-state creep rates of c u 2 0 - a t high
temperatures. He found :
1.8 T 0.3 (eV)
= ~ ~ 5 p o. . 42 ~ o . 1
0 2
exp kT
(6)
To obtain explicitly the concentration of a given
defect, one uses the neutrality equation :
[ vAul
DATA. -
where i: is the creep strain rate, A is a constant and 0
is the stress.
These results obtained on the same single crystals
are in good agreement with our diffusion results;
that seems to prove that the matter transport in the
previous creep experiments was controlled by the
diffusion of oxygen which is the less mobile species.
Such a correlation has not often been demonstrated
in oxides.
Table 1.
C6-3 17
-
P
(1 1)
(v&u and holes are the most important charged
species). For the majority defect v:u, it gives
[V;.,] = [K:=,]"2
pAi8
(12)
and for the minority defect 01
[o;]
=
K&(K[~,)-
p3I8
0 2 .
(13)
It is important to point out that the temperature
dependence of the defect concentration given by the
reaction constants is generally a combination of
various constants which do not only characterize the
considered defect but also depend on the majority
defect population through the neutrality equation.
The oxygen partial pressure dependence of a given
defect is also correlated to the majority defects.
Table I [l] gives the value of the exponent associated
with the concentration of oxygen-sublattice defects
and of V i and Vh for an intrinsic M 2 0 oxide obeying
a neutrality equation of the general type : [Vh] p.
C6-3 18
F. PERINET. S. BARBEZAT A N D C. MONTY
We did not consider- the extrinsic case because the
impurity content of' the oxide is certainly much
smaller than the departure from stoichiometry in the
experimental range of T and Po,.
It appears clearly in table I that in our case, oxygen
vacancies are unambiguously excluded and that the
defect giving the oxygen partial pressure dependence
closest to 0.4 f 0.05 is 0:. It is noted that from their
results of the Po, dependence, Ebisuzaki er ul. [7]
proposed that the responsible defect is the neutral
interstitial oxygen 0:. Oxygen interstitial may not
be unexpected in such a structure where the oxygen
sublattice is not compact (B.C.).
Defect complexes are highly improbable considering the low level of concentration of these minority
defects. The possibility for oxygen to migrate by an
exchange mechanism bet ween two oxygen atoms
when a copper vacancy is in the ncighbourhood of
the tracer has been emphasized [7, 81. Such a mechanism should yield a dependence of the selfdiffusion
coefficient on Po, determined by the copper vacancies
with the exponents n given in the last two columns
of table I. The large difference between these values
and the value of n determined in the present work
cannot account for such a mechanism.
The temperature dependence of the oxygen selfdiffusion coefficient gives the sum of the activation
energy of the concentration and of the migration
energy of the defect responsible for the diffusion. It
is possible to deduce the sum of enthalpy AH:;,
associated with the formation process described by
the cquation (9), and of the migration energy AHE.
It is clear through equation (13) that our experiments
give the sum :
where
is associated with the equation (12) and
with the concentration of holes through (11).
From recent results of Maluenda [9] for the electronic conductivity a in Cu,O we can deduce, if we
assume that o is independent of the temperature, a
value of 0.7 eV for A H f c U / 2 .Thus we can write :
It is interesting to compare this result to the same
quantity for V;., (the value of AHp=u has been taken
from [9] and [lo]) :
Experiments which enable us to separate formation
and migration enthalpy terms for minority defects
would be of great interest. However, it is clear from
these results that oxygen interstitials can be created
easily in Cu20, relative to copper vacancies.
5. Conclusion. - Cu,O is the first case of nonstoichiometric oxide in which the oxygen interstitial
has been identified by a phenomenological approach :
it appears singly charged. The original structure of
this covalent oxide where the oxygens are not in a
compact arrangement is perhaps the main reason
for that.
Acknowledgments. -- We want to express our
thanks to M. Doumanis N., who, during a University
post-graduate formation, has had a contribution to
the experimental part of the present work. We are
indebted to M. Lam N. for assistance in language
difficulties.
DISCUSSION
Comment. - Z. MORLIN.
Perhaps it would be of interest to measure the lattice parameter by X-ray diffraction : one may expect
parameter differences depending upon deviation from
stoichiometry.
Replj. - F. PERINET.
Such results would be vcry interesting. Indeed In
our knowledge, there was not any publication of
accurate values of lattice parameter versus oxygen
partial pressure and temperature.
References
Moh I k . C., I)P/clut~ yunc~iuel.~
duns l e ~sulldes, Confolant
1977 (Ed. de Physlquc, Orsay) 1978, Chap. XII.
MONY, C., J Phys~queColloq. 39 (1978) C2-74.
BRETHEAU,
T., The.% d'Etat, Orsay 1978.
BRETIIEAL,
T., MARHIC,C., SPEYDCI,M., CASTAIUG,J.,
Phrlos. Mag. 35 (1977) 1473
R. D . , MARTIKEZ-CLEMENTE,
M . , REV[4] SCHMIDT-WHITLEY,
C O L ~ C H I A,,
,
J . Crysl Gro)s!h 23 (1 974) 1 13.
151 FRIES,E., MARHIC,C , BRETHEAIJ,
T., J. Physique C'olloq
37 (1976) C7-572.
S., J. Mlcrosc Specirosc
[6] MEYER.M., DUBOIS,C., BARBEZAT,
Electron. 3 (1978) 477.
171 EBISUZAKI,
Y., Ph. D. Thesis, lndlana Unlverslty (1962)
MOORE,W. J., EBISUZAKI,
Y., SLUSS,J. A , J. Phys. Chern.
62 (1958) 1438.
[8] S u x ~ s o v N.
, V., ANTOYENKO,
V. M., Zashch. Met. 11 (1974)
361.
[9] MALUENDA,
J., These 3e cycle, Parls-XIII, 1979.
MALUENVA,
J , FAKHI,R . , PETOT-ERVAS,
G , to be published.
[lo] DELI.ACHEKIE,
J., These d'Etat, Nancy 1973.