MSE615: Structure and Characterization of Materials | IITK | Quiz 2 Solutions PDF
MSE 615: Quiz-II
Date: August 29, 2025
Time: 50 minutes
Total Score: 70 Points
Question 1: Fill in the blanks
(a) Lattice is a 3D translationally periodic arrangement of __________.
(b) Among the different types of 2D space lattices, the only non-primitive lattice type is __________ lattice.
(c) __________ is a combined symmetry element found in 3D point groups, but absent in 2D point groups.
(d) ‘n’ glide is a glide along the half of a __________ diagonal.
(e) ‘d’ glide is associated with translation of __________ the unit cell.
(f) The corresponding point group of P2₁/c space group is __________.
(g) 2̅ is equivalent to __________ symmetry.
(h) In P4₃/m space group, the screw axis is associated with __________ translation along __________ direction.
(i) The number of 2D point groups is __________ and the number of 2D plane groups is __________.
Question 2
The definition of point group says it needs to be "Self-consistent." What do you mean by it?
Question 3
Prove mathematically that the possible crystallographic rotational symmetries are 1, 2, 3, 4, and 6-fold.
Question 4
Consider the following 2D crystals.
Label lattice points and identify the motif.
Write the symmetry of the lattice.
Write the symmetry of the motif.
Identify the symmetry of the crystal using the standard symmetry notation.
Determine which crystal class (2D lattice type) the crystals belong to.
Question 5
From each of the space groups listed below:
(i) F4₁32
(ii) P6₂22
(iii) F4̅3n
(iv) I2₁/a 3̅
(a) Identify the corresponding point group.
(b) For each point group, mention the axis or plane on which each symmetry element operates.
(c) Draw the stereographic projections for each point group showing the symmetry equivalent points and the location of the crystal physics axes Z₁, Z₂, and Z₃.
(d) If any screw axis or glide plane is present in the space groups, mention the translation amount along the axis or direction.
MSE615: Structure and Characterization of Materials | IITK | Quiz 1 Solutions PDF