Assignment 2

(1)

1] In the stereographic projection given below, if an operation of a pole is depicted for the (422) point group, how many points will actually be reflected on the projection.

a) 04

b) 08

c) 16 d) 12

Solution to Q1]

A [422] polar plot has been shown below

2] The plot depicts a stereographic projection with certain symmetry elements. Identify all the possible symmetry elements present. Mark the most appropriate choice as answer.

i] A 3-fold rotation ii] A mirror perpendicular to the z-axis

iii] A 3-fold rotation and mirror

perpendicular to it

iv] A 6-fold rotation v] A perpendicular mirror to the y-axis vi] A parallel mirror to x-axis

(2)

a) Only iii

b) i and v c) iv and ii d) Only vi

3] How many atom positions are depicted on the [001] projection for an Aluminium crystal unit cell.

a) 09

b) 08 c) 05 d) 08

Solution to Q3]

A [001] projection for an Aluminium crystal unit cell has been shown below This plot has 3/m symmetry

(3)

4] If a motif is placed on an arbitrary general point as shown, how many such motifs are required to form a motif cluster that will depict the fully symmetry of point group 3m. How many such motif clusters are required to represent P3m1 point group for the lattice shown?

a) 06, 04

b) 04, 05 c) 12, 04 d) 06, 05 Solution to Q4]

The motif cluster and the arrangement of cluster in the lattice are shown:

5] What type of Bravais lattice does the hexagonal closed pack structure belong to?

a) A primitive hexagonal lattice

b) A non-primitive hexagonal lattice c) Trigonal Lattice

d) None of the above

(4)

6) If the diameter of the circle is 18cm then what will be the linear distance from center N of Pole

‘R’ shown below on polar projection having coordinates 30º on latitude on northern hemisphere and 60º on longitude from East, E ?

a) 5.2 cm b) 2.4 cm

c) 2.6 cm

d) Data insufficient

Solution:

If r is the radius of the primitive, latitude making an angle  with north pole is represented by a circle around the centre with radius rtan(/2)

Here, r = 18/2 = 9 cm, θ = 30º

So, the distance, d = 9* tan(30º/2) = 2.4 cm.

7) Is honeycomb lattice structure shown below

periodic?

90

180

270

W N E

0

. R

(5)

a) Yes, it always periodic.

b) No.

c) Depends upon the motif d) None of the above

8) Why is it that when you look in the mirror left and right directions appear flipped, but not the up and down?

a) Because of object’s mirror axis b) Because of viewer’s mirror axis

c) Because of mirror only, it is not related to viewer and object d) It is not true always.

Z

Y

X Explanation: For periodicity,

Environment of each lattice point should be same but here case is not so