EMSE 312
Final Exam – Solutions
FALL 2010
1. Crystallography:
(10 p)
Explain briefly each of the following (use simple sketches to illustrate
when suitable):
(a) (2 p)
Improper Rotation
(b)
(2 p)
Point Group
(c)
(2 p)
Bravais Lattice
(d)
(2 p)
Screw Axis Symmetry
(e)
(2 p)
Space Group
(a)
A rotation followed by a reflection (roto-reflection) or an inversion (roto-inversion).
(b)
A unique combination of the 10 point symmetry operations (proper rotations 1, 2, 3, 4, and 6,
and improper rotations
1 ,
2
m
=
,
3
,
4and
3
6
m
=
).
(c)
A unique combination of a crystal system (7 crystal systems) and a space lattice (5 space
lattices: P, A (B, C), I , F and R).
(d)
A rotation followed by a partial translation:
;
m
n
m
n
<
and both
and
are integers and
where the partial translation is
n
m
m
t
n
=
. The rotation
can take the values of 1, 2, 3, 4, and 6. For
example, the screw axis symmetry
corresponds to a
rotation followed by a partial
translation of
n
1
4
0
90
1
0.25
4
t
=
=
along the rotation axis.
(e)
A unique combination of one of the 32 Point Groups (which defined the crystal system) and one
of the 5 Space Lattices
(P, A (B, C), I , F and R), where a rotation axis can be a screw axis and a
mirror plane can be a glide plane.
KPDL: 12-15-10
1

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EMSE 312
Final Exam – Solutions
FALL 2010
KPDL: 12-15-10
2
2. Optical Diffraction/Fourier Transforms:
(10 p)
(a)
(5 p)
Draw the most intense features of an optical diffractogram that would be obtained from
one of the square apertures
shown below.
(b)
(5 p)
Draw the most intense features of an optical diffractogram that would be obtained from
all three square apertures
punched out from an opaque screen in an arrangement shown below.
Try to draw the diffractogram to scale, and specify what features of the diffractogram which are
due to the shape of the objects (apertures) and due to interference between the objects, respectively.
(10 p)
3a
a
2a
Solution: a)
b)