Environmental Engineering Reference
In-Depth Information
On the other hand, at extremely low oxygen pressures,
n
[M
i
]
or
log
n
log[M
i
]
(5.27)
At intermediate
P
O
2
, the electroneutrality condition may be
n
p
(5.28)
where
K
i
K
F
,or
[V
′
M
]
[M
i
]
(5.29)
when
K
′
M
][M
i
]).
All five sets of above-mentioned equations, together with either of the equa-
tions representing simplified charge neutrality condition, will result two types of
graphical presentation of concentrations of defect as a function of
P
O
2
, which are
known as Kr¨ ger-Vink diagrams [11] as depicted in Fig. 5.13a [for
n
F
K
i
(
K
F
[V
p
] and
5.13b (for [V
[M
i
]), respectively. These are the most simplified diagrams
and they obviously become more complicated if there are mixtures of Schottky-
Wagner and Frenkel disorders along with some foreign aliovalent ions. Figure
5.13a and b clearly exhibits that a compound, MX, would behave either as an
n-type or p-type conductor at log
P
X
2
less or greater than stoichiometric composi-
tions.
′
M
]
5.4.6 Defect Formation Reaction in Nonstoichiometric
Compounds
Oxygen-Deficient Oxides
An oxygen vacancy formation is favored by the transfer of an oxygen atom from
a normal lattice site to the gas phase, or by transfer of a metal atom from the
gaseous state to the normal cation site, or by moving a metal atom from the
normal lattice site to an interstitial site with corresponding release of electronega-
tive component to the gas phase. Such situations can be presented in the following
manner:
1
2
O
2
(g)
O
O
V
O
;
K
r
[V
O
]
⋅
P
1/2
O
2
(5.30)
or
[V
O
]
P
M
(g)
M(g)
M
x
M
V
O
;
K
r
(5.31)
or
1
2
O
2
(g);
M
x
M
O
O
M
i
K
r
[M
i
]
P
1/2
O
2
⋅
(5.32)
