MSE 102 Fall 2011
Problem Set 4 Solutions
James Mastandrea
Problem Set 4 Due Date: 9/22/2011
1
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Question 1
For this problem we are told that the crystal has symmetry described by plane group 9, c2mm. This plane
group describes rectangular systems. Since the system is rectangular, one might usually select
~a
and
~
b
vectors
such that
k
~a
k 6
=
k
~
b
k
. However, since a square is a type of rectangle, selecting your
~a
and
~
b
vectors such that
k
~a
k
=
k
~
b
k
is also a valid approach to this problem. The choice of
~a
and
~
b
will affect the solutions to this
problem set. Consequently, I will provide the solutions to this problem set for both of these conditions.
First Case:
k
~a
k 6
=
k
~
b
k
Part A
I selected
~
b
= 2
~
e
x
and
~a
=

1
~
e
y
.
I first plotted all of the Ga atoms at wyckoff letter
a
for the (0,0)
coordinate reference. Then I added (
1
2
~
b
,
1
2
~a
) to each of the atom locations previously found to plot the Ga
atoms at wyckoff letter
a
for the (
1
2
,
1
2
) coordinate reference. A unit cell is indicated by the thin black lines.
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 Fall '08
 Staff
 Geometry, Plane Group, Ga atoms

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