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Assignment 1

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Central University of Tamil Nadu
Department of Materials Science
MST19E32 Crystallography and Materials Design
Assignment I
Answer all the questions:
1. Identify the primitive cell lattice vectors and all the symmetry elements present in the
structures of a. Graphene and b. 2D-Boron Nitride
2. Make a fair guess on the point group with the bits and pieces of information given below:
a. The point group does not have any higher order symmetry element like 3-fold, 4-fold or 6
fold rotation. There is a mirror plane present in this point group. The point group is
centrosymmetric
b. There is more than one 2-fold rotation element present in this point group and the mirror
plane is absent. The point group is non-centrosymmetric.
3. What is the point group of water (H​2​O). Justify your answer with a suitable diagram depicting
the symmetry elements. Can you identify another molecule with similar point group symmetry?
Draw the stereographic projection of the point group.
4. Determine whether the point group or the space group for the following materials contain a
center of symmetry or not.
a. Diamond Si
b. Wurtzite ZnO
c. Sphalerite GaAs
d. CsCl
e. Graphene
f. Graphite
g. CaF​2
5. Why do materials with non-centrosymmetric space groups possess piezoelectric properties?
Find at least two different compositions that are known to possess piezoelectric properties due
to their non-centrosymmetric space groups.
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