Assignments on crystallography

date: 10.11.2014

Theoritical Questions:

I 1. Define the following terms: (i) space lattice (ii) basis (iii) crystal structure (iv) unit cell (v) primitive cell (vi) non-primitive cell.

2. Explain how the combination of lattice with a basis forms the crystal structure? 3. What are Miller indices? Explain with examples. What are their utilities? 4. Sketch the Miller planes: (100), (010), (001), (110), (101), (011), (111). 5. Show that in a cubic crystal of side a, the inter-planar spacing between consecutive parallel planes of Miller indices

(hkl) is 2 2 2hkl

adh k l

.

6. Give comparative study of (i) atomic positions (ii) effective number of atoms in a unit cell (iii) co-ordination number (iv) atomic radius in terms of lattice constant (v) packing fraction (vi) void space of SC, BCC, FCC crystal.

7. Derive a relation between lattice constant and density of the material of a cubic crystal. 8. How many crystal structures are there in 3-dimensions? Mention their lattice parameters. 9. Mention how many Bravais lattices are corresponding to each crystal system.

Numericals:

1 A crystal has FCC structure and its atomic radius is 0.175 nm. What is the volume of the unit cell?

2 The molecular weight of KBr (FCC) is 119.01 gm-mole-1 and its density is 2.75 gm-cm-3. Calculate the lattice constant of

this crystal. 3 If the lattice constant for a BCC crystal is 3.57 A and the density of the material of the crystal is 8575 kg-m-3, find its atomic

mass. 4 A crystal plane cuts at 3a, 4b and 2c along the crystallographic axes. Find Miller indices.

5 A crystal has lattice constants of 1 A, 2 A and 3 A. A plane (321) cuts an intercept of 1 A along x-axis. Find the intercepts along other axes.