Solutions to exercises
129
4.1 10 s
0
13 1
#
ν =
−
This value is compatible with the hopping frequencies in solids.
Solution 3.3 – Study of electronic conductivity in solid solutions
(CeO 2 ) 1−x (CaO) x
1. a. We use the following relation to determine the electronic conductivity:
σ t = σ i + σ e
where σ t , σ i , and σ e denote the total conductivity, ionic conductivity, and
electronic conductivity, respectively. We assume that the variation in ionic
conductivity with oxygen partial pressure is negligible. The results for
the conductivities are presented in table 36.
Table 36 – Total conductivity and electronic conductivity in solid solution
(CeO 2 ) 1−x (CaO) x with x = 2.8 # 10
−3
and for several oxygen partial pressures.
P O 2 [bar]
1
0.21
10
−2
10
−3
5 # 10
−4
10
−4
10
−5
log P O 2 [bar]
0.00 − 0.68 − 2.00 − 3.00 − 3.30 − 4.00
− 5.00
10
3
σ t [S cm
−1
] 1.096 1.096 1.38
1.66
1.79
2.26
3.14
log σ t [S cm
−1
] − 2.96 − 2.96 − 2.86 − 2.78 − 2.75 − 2.65
− 2.50
10
3
σ e [S cm
−1
]
0
0
0.284 0.564 0.694
1.164
2.044
log σ e [S cm
−1
]
negligible
− 3.55 − 3.25 − 3.16 − 2.93
− 2.69
The curve for the electronic conductivity of (CeO 2 ) 1 −x (CaO) x with
x = 2.8 # 10
−3
as a function of oxygen partial pressure is shown in figure 56 in logarithmic coordinates.