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Materials Science and Engineering
MIME 1650
Lecture 6
1
1
Chapter 3 
MIME 1650 Materials Science and
Engineering
Lecture 6: Crystalline Structure and Miller
Indices
2
Chapter 3 
ex:
linear density of Al in [110]
direction
a
= 0.405 nm
Linear Density
• Linear Density of Atoms
≡
LD =
a
[110]
Unit length of direction vector
Number of atoms*
# atoms
length
1
3.5 nm
a
2
2
LD

=
=
*The sharing of atoms with adjacent unit cells must be considered
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MIME 1650
Lecture 6
2
3
Chapter 3 
Linear Density
• Linear Density of Atoms
≡
LD =
Unit length of direction vector
Number of repeat distances
Repeat distance:
distance between adjacent atoms along the direction.
In general
LD = 1/r where r is the repeat distance between adjacent atoms
4
Chapter 3 
Planar Density
• Planar Density of Atoms
≡
PD =
area of plane
# of atoms centered on a plane*
*The sharing of atoms with adjacent unit cells must be considered
Materials Science and Engineering
MIME 1650
Lecture 6
3
5
Chapter 3 
Crystallographic Planes
•
We want to examine the atomic packing of
crystallographic planes
•
Iron foil can be used as a catalyst. The
atomic packing of the exposed planes is
important.
a) Draw (100) and (111) crystallographic planes
for Fe.
b)
Calculate the planar density for each of these
planes.
6
Chapter 3 
Planar Density of (100) Iron
Solution: At T < 912
°
C iron has the BCC structure.
(100)
Radius of iron
R
= 0.1241 nm
R
3
3
4
a
=
Adapted from Fig. 3.2(c),
Callister 7e.
2D repeat unit
=
Planar Density =
a
2
1
atoms
2D repeat unit
=
nm
2
atoms
12.1
m
2
atoms
= 1.2 x 10
19
1
2
R
3
3
4
area
2D repeat unit
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MIME 1650
Lecture 6
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Chapter 3 
Planar Density of (111) Iron
Solution (cont): (111) plane
1 atom in plane/ unit surface cell
3
3
3
2
2
R
3
16
R
3
4
2
a
3
ah
2
area
=
=
=
=
atoms in plane
atoms above plane
atoms below plane
a
h
2
3
=
a
2
2
D
r
e
p
a
t
u
n
i
1
=
=
nm
2
atoms
7.0
m
2
atoms
0.70 x 10
19
3
2
R
3
16
Planar Density =
atoms
2D repeat unit
area
2D repeat unit
8
Chapter 3 
Single Crystals
Single crystal – material in which
periodic arrangement of atoms
extends uninterrupted
over the
entire specimen
Without external constraint, crystal
assumes a regular geometric shape
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This note was uploaded on 04/18/2008 for the course MIME 1650 taught by Professor Burham during the Spring '08 term at Toledo.
 Spring '08
 Burham

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