MSE 605, Crystallography & Crystal Chemistry
Name: _______________________________
Homework 7
Due 3 December 2015
The numbers following each question give the approximate percentage of marks
allocated to that question.
1. Use the diffraction angle to demonstrate why second-order diffraction from (100) is
equivalent to first-order diffraction from (200).
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MSE 605, Crystallography & Crystal Chemistry
2. Given the (110) cross section through the reciprocal lattice below (the [110] zone
axis diffraction pattern), made by 200 kV electrons (λ = 0.025 Å) diffracting through a
thin crystalline material with a face-centered cubic structure (space group Fd 3 m )
484 cm from the viewing screen (page), estimate the lattice constant of the material
and index reflections with the appropriate corresponding hkls out to h2 + k2 + l2 = 32.
NOTE: consult the Fd 3 m class handout or the International Tables (available in
eBook form at http://it.iucr.org.libproxy.boisestate.edu/A/) before you start!
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MSE 605, Crystallography & Crystal Chemistry
3. Use the reciprocal metric tensor to show that the interplanar spacing for an
orthorhombic crystal, d, is related to the lattice constants, a, b, and c, via
1
d2
=
h2
a2
+
k2
b2
+
l2
c2
.
10
hkl
4. Use the reciprocal metric tensor again to calculate the angle between (123) and
(421) planes in a monoclinic unit cell with lattice constants a = 1 Å, b = 2 Å, c = 3 Å,
β = 85°.
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MSE 605, Crystallography & Crystal Chemistry
5. Find the crystallographic direction (zone axis) common to the planes (241) and (331)
in a monoclinic unit cell with a = 4.7 Å, b = 3.2 Å, c = 8.1 Å, β = 92°.
5
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MSE 605, Crystallography & Crystal Chemistry
6. a. Draw a representation of objects with 2/m point symmetry, labeling all the
symmetry elements present. Using this diagram, construct a multiplication table
for this point group using the same labels. HINT: The order of the group is four.
15
b. Draw a representation of objects with 3m point symmetry, labeling all the
symmetry elements present. Using this diagram, construct a multiplication table
for this point group using the same labels. HINT: The order of the group is six.
15
c. Which of these two groups is/are abelian?
5
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