MSE615: Structure and Characterization of Materials | IITK | Quiz 1 Solutions

MSE 615: Quiz-I

Date: August 21, 2025

Time: 20 minutes

Total Score: 45 Points

Question 1

Consider two point groups 23 and 32. Both the point groups have 3-fold rotational symmetry element.

(a) Is there any difference between the 3-fold symmetry existing in these two point groups?

(b) Which crystal systems do these two point groups belong to? Give the reasoning.

Question 2

The point group 6/m belongs to the hexagonal crystal system and it has 6-fold rotational symmetry and reflection symmetry.

Why can’t we write the point group as 6m instead of 6/m?

In other words, what special message is conveyed by expressing the point group as 6/m?

Question 3

In each of the following 1-D lattices, identify the motif and label the lattice points.

Also identify the symmetry elements present in the lattices.

(a) Identify motif, lattice points and symmetry elements for the given lattice.

(b) Identify motif, lattice points and symmetry elements for the given lattice.

Question 4

From each of the space groups listed below answer the following questions.

(a) Identify the Bravais lattice and 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) Specify if there is any redundant symmetry element for each point group.

(e) If there are any screw axis or glide plane present in these space groups, mention them along with the translation amount along the axis or direction.

The space groups are:

(i) R3̅c

(ii) P6̅

(iii) C2322

(iv) P43212