Environmental Engineering Reference
In-Depth Information
dm
dt
D
O
N
(s
O
ξ
J
(mol cm
2
s
1
)
(6.20)
V
m
where
N
(s
O
is the oxygen solubility in A (atom fraction),
V
m
is the molar volume
of the solvent metal or alloy (cm
3
mol
1
),
D
O
is the diffusivity of oxygen in A
(cm
2
is the instantaneous thickness of IOZ. If counterdiffusion of
solute B is assumed to be negligible, the amount of oxygen accumulated in the
IOZ per unit area of reaction front is given by
s
1
), and
ξ
N
(O)
B
νξ
V
m
m
(mol cm
2
)
(6.21)
where
N
(O
B
is the initial solute concentration in the A-B bulk alloy.
Differentiating Eq. (6.21) with respect to time, one obtains an alternative ex-
pression for the flux as
dm
dt
N
(O)
B
ν
d
dt
(6.22)
V
m
Equating (6.20) and (6.22), one can write
N
(s
O
ξ
N
(O)
B
ν
d
dt
V
m
D
O
(6.23)
V
m
On rearrangement of Eq. (6.23), one obtains
N
(s
O
D
O
ν
ξ
d
ξ
dt
(6.24)
N
(O)
B
ξ
Integration of Eq. (6.24), assuming
0at
t
0, yields
1
2
ξ
N
(s
O
D
O
ν
2
t
(6.25)
N
(O)
B
or
1/2
2
N
(s
O
D
O
ν
ξ
t
(6.26)
N
(O)
B
Equation (6.26) gives the penetration depth of the IOZ as a function of oxida-
tion time. The following points emerge from the consideration of Eq. (6.26):
1.
The penetration depth has a parabolic time dependence:
ξ
t
1/2
.
2.
The penetration depth for a fixed time is inversely proportional to the square
root of the atom fraction of solute in the bulk alloy.
