Environmental Engineering Reference
In-Depth Information
Table 5.2
Ratios of linear coefficient of expansion of some metal-oxide systems
(in general valid up to
1173 K)
Fe/FeO
Ni/NiO
Co/CoO
Cr/Cr
2
O
3
Cu/Cu
2
O
1.25
1.03
0.93
1.30
4.32
Ti/TiO
2
Al/Al
2
O
3
Si/SiO
2
Zr/ZrO
2
Hf/HfO
2
1.30
3.22
0.475
0.91
1.03
various metal-metal oxide systems, which are presented in Table 5.2, will be
very useful.
It is important to point out that during the 1920s Tammann [6] for the first
time provided experimental evidences for obeyance of a definite mathematical
relation between the extent of reaction and exposure time. Such a relation was
found to be parabolic in nature. His experimental results inspired a large number
of investigators to derive a variety of mathematical relations to be obeyed during
the progress of oxidation, depending on the individuality of the systems and pre-
vailing experimental conditions.
Broadly speaking, two types of oxide growth rate have been observed, i.e.,
thick-layer growth and thin-film growth where the demarcation between the two
is a thickness of
10,000
˚
(1000 nm), as suggested by Cabrera and Mott [7].
In both cases, the oxide film formed increases in its thickness with time but the
rate laws obeyed in the two cases are different. For the thin-film growth, four
kinetic laws have been proposed and experimentally verified for a number of
metal-oxidant systems. These are presented below in their integral forms:
1.
Inverse logarithmic law: 1/
ζ
k
1
k
2
ln
t
2.
Normal logarithmic law:
ζ
k
1
k
2
ln
t
3.
Cubic law:
ζ
3
k
c
t
, and
4.
Parabolic law:
ζ
2
k
p
t
where
ζ
instantaneous thickness of the oxide film at any time (
t
), and
k
1
,
k
2
,
k
p
are constants in the corresponding kinetic equations. For thick
layer growth or scaling processes, two possible rate laws are observed: (1) para-
bolic law (
1
,
k
2
,
k
c
, and
k
ζ
2
k
p
t
) and linear law (
ζ
k
1
t
), where
k
p
and
k
1
are parabolic and
linear rate constants, respectively.
The above rate expressions could also be presented in their differential forms.
Instead of thickness, the extent of reaction can be expressed in terms of mass
gain per unit area as a function of time [8]. The various oxidation-time relation-
ships are presented in Fig. 5.7.
One must realize that in the study of ambient or near-ambient temperature
