Question

Distinguish between (i)Hexagonal and monoclinic unit cells (ii) Face-centred and end-centred unit cells.

Answer 1

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Answer :

(i) Hexagonal unit cell : In hexagonal unit cell, the axial distances or edge length is :

α = β ≠ c

α = β = 90°

γ = 90°

→ Monoclinic unit cell : In monoclinic unit cell, the axial distances or edge length is :

α ≠ b ≠ c

α = γ = 90°

β ≠ 90°

(ii) Face centered unit cell : In face centered unit cell,

α = b = c

α = β = γ = 90°

There are 8 lattice points on the corners of the cube, whereas 6 lattice points are on the centre of six faces.

→ End-centered unit cell : In this type of unit cell, 8 lattice points are present on the corners and 1 lattice point present at the centre of any two opposite faces of a cube.

Answer 2

Answer :

(i) In Hexagonal unit cell, edge lengths : a=b≠c and axial angles α=β=90° and γ=120°.

In Monoclinic unit cell, edge lengths : a≠b≠c and axial angles α=γ=90° and β≠90°.

(ii) Face centred unit cell's constituent particles are located at all the corners as well as centres of all faces. That is, total of 4 atoms, 8 lattice points at corner and 6 at the faces = 8×1/8+6×1/2=4.

End centred unit cell's constituent particles are located at all corners as well as centres of two opposite faces. That is, total of 2 atoms, 8 lattice points at corner and 2 at centres of two opposite faces = 8×1/8+2×1/2=2.

Extra Information :

• Unit cells make a crystal lattice.
• Different types of unit cells are :

1. Primitive cubic unit cell
2. Body-centered cubic unit cell
3. Face centered cubic unit cell
4. End centred conic unit cell
5. Cubic unit cell
6. Tetragonal unit cell
7. Orthorhombic unit cell
8. Hexagonal unit cell
9. Trigonal/Rhombohedral unit cell
10. Monoclinic unit cell
11. Triclinic unit cell