1
ECE331 Homework #2 Solutions
1.
Direction
A
is a [
1 10] direction
Direction
B
is a [121] direction
Direction
C
is a [0
1
2 ] direction
Direction
D
is a [1
2 1] direction
2.
For plane
A
this is a
)
0
1
1
(
plane. For plane
B
, this is a (122) plane.
3
.
(a) (1
2 11) plane (b) a (2
1
1 2) plane
4
. Compute and compare the linear densities of the [100], [110], and [111] directions for FCC.
1) In the figure below is shown a [100] direction within an FCC unit cell.
For this [100] direction there is one atom at each of the two unit cell corners, and, thus, there is
the equivalent of 1 atom that is centered on the direction vector.
The length of this direction vector is just
the unit cell edge length, 2
R
2
[Equation (3.1)].
Therefore, the expression for the linear density of this
plane is
LD
100
=
number of atoms centered on [100] direction vector
length of [100] direction vector
=
1atom
2R 2
=
1
2) [110] direction
vector
direction
[110]
of
length
vector
direction
[110]
on
centered
atoms
of
number
=
110
LD
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R
R
atoms
2
1
4
2
=
=
3) An FCC unit cell within which is drawn a [111] direction is shown below.
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 Spring '09
 RAJAN
 Atom, Crystallography, Crystal

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