Solutions to Test 1
MatSc 503  Kinetics of Materials Processes
Test date: February 25,
2002
1.
A 1mmthick sheet of steel at 750
˚
C is subjected to conditions that maintain the carbon
content at zero on one surface and at 3 at% carbon on the other surface.
At 750
˚
C the
carbon contents of ferrite and austenite which are in equilibrium with each other are,
respectively, 0.09 and 2.7at%.
The diffusion coefficients of carbon in ferrite and austenite
at 750
˚
C are 5.5
×
10
11
and 1.1
×
10
12
m
2
/s, respectively.
(a)
(10 points) Schematically draw the concentration profile of carbon.
At steady state:
1mm
h
c
c
0.0
0.09at%
2.7at%
3.0at%
(b)
(10 points) Determine the position of the ferriteaustenite interface at steady state.
At steady state,
x
c
D
x
c
D
∂
∂
−
=
∂
∂
−
γ
γ
α
α
or
h
h
−
−
×
−
=
−
×
−
−
−
1
7
.
2
0
.
3
10
1
.
1
0
09
.
0
10
5
.
5
12
11
Solve for the interface position h at steady state, we have
mm
9375
.
0
16
15
=
=
h
2.
Describe the TYPE of solutions that you will employ to describe the concentration profiles,
or the TYPE of mathematical methods that you will use to obtain the profiles, for the
following nonsteady state diffusion problems: (Assuming a diffusion coefficient of 10

10
cm
2
/s for the diffusing species and the solid is a plate of 1cm thickness)
a.
(7 points) Diffusion of a thin layer of material initially deposited on one of the surfaces
of the plate into the solid for 100 s.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '02
 CHEN
 Thermodynamics, Atom, Steady State, constant surface concentrations

Click to edit the document details