Bravais Space Lattice

Bravais Space Lattice:

Bravais showed that there are 14 ways of arranging points in space lattice called the Bravais lattice. In case of a cubic system, there are 3 Bravais lattice.

Those are 1) Simple Cubic or Primitive Cubic

2) Face Centered Cubic (fcc)

3) Body Centered Cubic (bcc)

1.Simple Cubic:

There is one lattice point at each of eight corners of the unit cell. The share of each lattice point to the cubic lattice = 1/8.

Number of lattice points in unit cell = 1/8 x 8 = 1

i.e. there is only one lattice point per unit cell.

2. Face Centred Cubic:

There is one lattice point at each of the eight corners and one lattice point at the centers of each of the six faces of the cubic cell.

Total number of corners lattice points in unit cell 8 x (1/8) = 1

Total number of face centered lattice points in unit cell = 6 x ½ = 3.

Total number of lattice points concerned with unit cell = 1+3=4.

3. Body Centered Cubic:

There is one lattice point at each of the eight corners and one lattice point at the center of each cell.

Total number of corner lattice points per unit cell 8 x (1/8) = 1.

Total number of body centered lattice points per unit cell = 1.

Total number of lattice points concerned with unit cell = 1 + 1 = 2.