130
3 – Transport in ionic solids
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Figure 56 – Electronic conductivity of (CeO 2 ) 1−x (CaO) x with x = 2.8 # 10
−3
as a function of oxygen partial pressure and in logarithmic coordinates.
b. Over the range 10
−5
< P O 2 < 10
−2
bar, we find a linear relationship given
by the expression log σ e = − 0.2857 log P O 2 − 4.1214
The electronic conductivity is a decreasing function of oxygen partial
pressure.
2. Given that the electronic conductivity is a decreasing function of oxygen
partial pressure and considering the following equilibrium reaction of the
solid solution with gaseous oxygen:
O
#
O m 2
1
O 2(g) + 2e ′ + V
••
O
we note that the electronic conductivity is n type.
3. For an oxygen partial pressure of 10
−4
bar,
a. the electronic conductivity is
log σ e = − 2.98 S cm
−1
or
1.05 10 S cm
e
3
1
#
σ =
−
−
b. The expression for ionic transport number is
t
1–
i
t
i
t
e
σ
σ
σ
σ
=
=
Numerical evaluation gives
.
.
t
1 2 26 10
1 05 10
–
i
3
3
#
#
=
−
−
.
t
0535
i =