EGN3365Structure and Properties of Materials
TTR 8:309:45
Instructor: Dr. S. Seal TA: Mr. Himesh Bhatt
Solutions: HomeWork 8
Problem 1:
We are asked to determine the position at which the nitrogen concentration is 2 kg/m
3
.
This
problem is solved by using Equation in the form
J =  D
If we take
C
A
to be the point at which the concentration of nitrogen is 4 kg/m
3
, then it
becomes necessary to solve for
x
B
, as
x
B
= x
A
+ D
Assume
x
A
is zero at the surface, in which case
x
B
= 0 + (6 x 10
11
m
2
/s)
= 1 x 10
3
m = 1 mm
Problem 2:
Using Equation , we set up two simultaneous equations with
Q
d
and
D
o
as unknowns.
Solving for
Q
d
in terms of temperatures
T
1
and
T
2
(1273
K and 1473
K) and
D
1
and
D
2
(9.4x10
16
and 2.4 x 10
14
m
2
/s), we get
Q
d
=  R
= 
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= 252,400 J/mol
Now, solving for
D
o
from Equation
D
o
= D
1
exp
= (9.4 x 10
16
m
2
/s) exp
= 2.2 x 10
5
m
2
/s
(b)
Using these values of
D
o
and
Q
d
,
D
at 1373
K is just
D = (2.2 x 10
5
m
2
/s) exp
= 5.4 x 10
15
m
2
/s
Problem 3:
This problem asks us to determine the values of
Q
d
and
D
o
for the diffusion of Fe in Cr from
the plot of log
D
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 Spring '08
 YongHoSohn
 Derivative, Natural logarithm, Mr. Himesh Bhatt

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