Environmental Engineering Reference
In-Depth Information
pressure in the gas phase for p-type oxides, whereas defect concentration or non-
stoichiometry increases with decrease of oxygen potential in the gas phase for
n-type semiconductors.
On the basis of defect equilibria, the dependence of theoretical electrical con-
ductivity on oxygen pressure can be predicted. For a large number of systems,
such estimated values match fairly well with the experimental data, lending sup-
port to the defect models proposed by Wagner and Schottky [14], Hauffe [15],
Verway [16], Kr
¨
ger [11,17], and others.
Examples:
1
2
O
2
(g)
Cu
2
O
2V
Cu
2h
•
(5.44)
for which
[V
′
Cu
]
2
⋅
p
2
K
(
T
)
(5.45)
P
1/2
O
2
According to the following electroneutrality condition:
[V
Cu
]
p
(5.46)
therefore, one obtains,
p
σ
h
•
P
1/8
O
2
(5.47)
P
1/7
The experimentally found relation is
O
2
, which supports the defect model
proposed by Wagner and Gr
¨
newald [18]. Similarly,
σ
h
•
1
2
O
2
(g)
NiO
V
Ni
2h
•
(5.48)
for which
[V
Ni
]
⋅
p
2
K
(
T
)
(5.49)
P
1/2
O
2
When the electroneutrality condition becomes
2[V
Ni
]
p
(5.50)
one would be able to write the following from Equation 5.49:
P
1/6
O
2
p
σ
h
•
(5.51)
