Environmental Engineering Reference
In-Depth Information
W
sum of the energy of solution of a metal ion in the oxide and the activa-
tion energy for the ions to transit from one position to the next site,
expressed in joules
k
Boltzmann constant
1.38
10
23
J
⋅
K
1
q
electronic charge in 1.602
10
19
coulombs
a
lattice constant (cation-cation distance
4
10
10
m in the case of
Cu
2
O lattice)
V
potential developed across the film in volts
V
/
ξ
field strength in V
⋅
m
1
A closer look at the above equation (5.97) suggests that as
ξ
increases the value
of exp(
ξ
1
/
ξ
) goes on decreasing, and after a particular value of
ξ
(i.e., when
ξ
approaches
/d
t
value becomes so small that the rate may be considered
to be negligible and the oxidation process almost comes to a stop. This particular
thickness has been defined as the ''limiting thickness.'' However, this equation
is valid only in the very thin film range over which electron tunneling is possible
requiring almost no activation energy (i.e., thermal activation). It is apparent
from the above equation that the number of migrating species at the metal-oxide
interface will determine the rate. Beyond the limiting thickness, the field-creating
electrons will no longer be available at the outer surface by tunneling mechanism.
At such low temperature, the electron availability by thermoionic emission is
also not possible.
With an increase in temperature to the intermediate range (e.g., for copper,
330-473 K) and the thickness of the film formed being limited to the so-called
thin range, oxidation kinetics becomes different from that followed at low temper-
atures, conforming in many cases, to a normal logarithmic rate law. Theoretical
explanations of this process have mainly been provided by Cabrera and Mott [7],
William and Hayfield [36], and Uhlig [37]. William and Hayfield's equation is
virtually a simplified version of Uhlig and others for which the same is briefly
discussed here.
Emission of electrons from the metal was considered as the rate-limiting step
in the oxidation of copper at least at temperatures below 393 K. This led them
to visualize a mechanism of logarithmic oxidation in which the rate is mainly
controlled by the arrival of electrons at the oxide-oxygen interface. Since the
oxidation rate is controlled by the electron flow from the metal, space charge
effect plays a prominent role in controlling the rate of electron flow and hence
the oxidation process itself. The essential step is then the provision of electrons
at the oxide-oxygen interface in order that the oxygen atoms can be ionized
and incorporated into the oxide lattice according to the following defect equa-
tion:
ξ
1
), d
ξ
O
2
(g)
4e
′→
2O
O
4V
′
Cu
(5.98)
