Environmental Engineering Reference
In-Depth Information
where
n
represents number of excess electron in the conduction band per m
3
of
ZnO and [Zn
•
i
] represents concentration of interstitial Zn ions per m
3
of ZnO.
Utilizing validity of the following charge neutrality condition,
2[Zn
•
i
]
one obtains from Eq. 5.83
n
[Zn
•
i
]
P
1/6
O
2
(5.84)
Since ZnO is mainly an electronic conductor,
t
3
1,
t
Zn
i
1, and
t
O
2
0
(almost stationary oxygen sublattice). Therefore, one can write:
σ
Zn
••
i
σ
t
Zn
••
i
σ
Zn
••
i
(
P
O
2
1 atm)
⋅
P
1/6
O
2
(5.85)
The expression for rational rate constant can thus be presented as:
3
2
RT
F
2
1
P
(i)
1/6
O
2
1
P
(o)
1/6
O
2
k
r
0
Zn
••
i
σ
(5.86)
The lattice defect structure of ZnO exhibits the concentration of interstitially
positioned Zn
••
i
ions at the Zn-ZnO phase boundary to be considerably greater
than that at the ZnO-O
2
(g) interface.
Furthermore, it follows from the standard free energy of formation of ZnO
that
P
(i
O
2
P
(o)
O
2
and thus
1
P
(o)
O
2
and this is more true for the sixth root. So the second term in parentheses of Eq.
5.86 can be neglected. Therefore, the expression of rate constant simplifies to:
1
P
(i
O
2
1/6
3
2
RT
F
2
σ
1
P
(i
O
2
0
Zn
••
i
k
r
(5.87)
Since
P
(i
O
2
is constant at a constant temperature,
k
r
should be independent of varia-
tion of oxygen pressure at the outer surface of ZnO film. Actually, Wagner and
Grunewald's [18] experiment on Zn oxidation at 663 K (Fig. 5.16) yielded
the scaling rate constant values lying between 0.72
10
10
g
2
cm
4
S
1
(at
P
O
2
1 atm). Therefore, it is
concluded that for the growth of a compact, adherent, n-type conducting layer
on a metal substrate, the parabolic rate constant becomes almost independent of
variation of oxygen pressure in the environment at a particular temperature.
One can now well appreciate that the oxidation rate of any metal will be largely
dependent on the type and concentration of point defects in the product film/
scale as well as on its transport properties, i.e., electrical conductivity, diffusivity,
0.022 atm) and 0.75
10
10
g
2
cm
4
s
1
(at
P
O
2
