MSE280: Introduction to Engineering Materials
Homework
5: Solutions
1. (8 points)
The two factors that contribute to the activation energy for substitutional diffusion are the
energies required to break bonds and distort the lattice. Both bond breaking and lattice
distortion are needed to initiate diffusion.
2. Problem 6.2b from Callister
(8 points)
Interstitial diffusion is normally more rapid than vacancy diffusion because:
(1) interstitial
atoms, being smaller, are more mobile;
and (2) the probability of an empty adjacent interstitial
site is greater than for a vacancy adjacent to a host (or substitutional impurity) atom.
Problem 6.5 from Callister
(8 points)
Let us first convert the carbon concentrations from weight percent to kilograms carbon per
meter cubed using Equation 5.12a.
For 0.015 wt% C
C
C
"
=
C
C
C
C
ρ
C
+
C
Fe
ρ
Fe
×
10
3
=
0.015
0.015
2.25 g /cm
3
+
99.985
7.87 g /cm
3
×
10
3
1.18 kg C/m
3
Similarly, for 0.0068 wt% C
C
C
"
=
0.0068
0.0068
2.25 g /cm
3
+
99.9932
7.87 g /cm
3
×
10
3
= 0.535 kg C/m
3
Now, using a rearranged form of Equation 6.3

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