Defect Interactions in Partially Ionic Nonstoichiometric Oxides: A Monte Carlo Investigation.
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DEFECT INTERACTIONS IN PARTIALLY IONIC NONSTOICHIOMETRIC OXIDES: A MONTE CARLO INVESTIGATION. C.MASSOBRIO*, O.MASMOUDI
R.TETOT*, B.NACER*,
* Composds Non Stoechiomdtriques,
and G.BOUREAU
Universit6 Paris-Sud,
91405 Orsay Cedex
(France) **Chimie Physique,
Universit6 Paris VI,
11 rue Pierre et Marie Curie,
75231
Paris Cedex 05 (France) ABSTRACT. We investigate
the
nature
of
the
interactions
between
defects
in
partially nonstoichiometric oxides and their r6le on some thermodynamic and transport properties.
INTRODUCTION In this study, we present an appropriate statistical treatment allowing us to calculate the interaction energies between defects in partially ionic nonstoichiometric oxides from experimental thermodynamic measurements. We show that these interactions may be used to qualitatively explain electronic conductivity. Because of its status of model system for Plutonium dioxide,
a large
amount of experimental data are available for cerium dioxide CeO2 -x (ceria) which is taken as an example in this study. Similar studies are in progress for cubic oxides
such as Co I_x a
large
domain
of
CeO 2 -x
has a fluorite
nonstoichiometry
(0 U 0
0,0
0,1
0.2 X in CeO2O•
0,3 X in CoO
0,2 -X
0.3
Fig 2. Conductivity and mobility at 1000 0 C as a function of nonstoichiometry Experimental results are from [7] for a and from [1] for p
527
and the decrease of p with increasing x.
As analyzed
in ref 1,
this is
probably due to the appearence of a high degree of short range order when x increases, which induces trapping of some of the carriers. The simplest model consists of taking EH constant with x, which is equivalent to consider total disorder of the defects (limit T-)a). In this case, a varies as 2x(1-2x) and p as (1-2x). Therefore, the saturation of a appears at x=0.25 and p is
a linear function of x (see Fig 2).
Obviously
this model does not account for the experimental features. In our model, which is a preliminary one, we assume that the activation energy of
hopping of
location,
therefore
(E1 ) depends
a given polaron
on
its
H
potential
energy.
EiH = E0H _
iIx
only on
Following
its
initial
this
simple
assumption, we may write:
E0
where
HI
is
the
activation
energy
in
complete
disorder
and
E
the
interaction energy of the polaron i with the surrounding charges. In the first part of this study, we have calculated some interaction parameters which allows to estimate the interaction energy of any site of an equilibrium configuration obtained by Monte Carlo simulation for any value of x.
It
is
clear
that
these parameters
do not
permit
to treat
in
a
satisfactory way the vacancy-vacancy interactions because we consider only a repulsion between nearest neighbors. Nevertheless, distribution functions
the calculation of radial
[8] shows that the repartion of the electrons among
the cerium sites depends only slightly on the interaction between oxygen vacancies.
The most important parameters for our purpose are the electron
vacancy interaction a
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