Primitive unit cell:-

  • The unit cell in which the constituent particles are present only at the corners are called “simple unit cells” or “primitive unit cells”.

Face centred:-

  • When particles are present not only at the corners, but also at the centre of each face of unit cell, it is called face centred unit cell.

End centred:-

  • When in addition to the particles at the corner, there are also the particles at the centre of any of two opposite faces it is called end centred unit cell.

Body centred:-

  • When in addition to the particles present at the corner one particle is also present at the centre of unit cell it is called body centred unit cell.

Bravais Lattices:-

  • The fourteen lattices corresponding to seven crystal systems are known as the bravais lattices.
  • We generally represents the unit cells by three dimensional arrangement of spheres.

Coordination Number:-

  • The coordination number of any constituent particle in a given unit cell is the no. of particles touching that particle.

CALCULATION OF NUMBER OF PARTICLES PER UNIT CELL OF A CUBIC CRYSTAL SYSTEM:-

1. Calculation of contribution of atom present at different lattice sites.

  1. An atom at the corner is shared by eight unit cells so its contribution is = 1x(1/8)=1/8
  2. An atom on the face is shared between two unit cells so its contribution is =1x(1/2)=1/2
  3. An atom present at centre of unit cell is not shared by any unit cell so it contribution is = 1
  4. An atom present at the edge is shared by four unit cells so its contribution is =1x(1/4)=1/4

2. Calculation of number of atoms per unit cell:-

  1. Simple [primitive] unit cell:- It has only Eight atom present at corner each have contribution 1/8 so 8 x 1/8 = 1 atom.
  2. In body centred unit cell (BCC):- 1. 8 atom on corner = 1/8 x 8 = 1 atom
    1 atom at the centre = 1 x 1 = 1
    So total no. of atoms = 1 + 1 = 2 atoms.

3. In face centred unit cell [FCC]:-

  1. Contribution by atoms at corner = 1/8 x 8 = 1
    Contribution by atoms at faces = 1/3 x 6 = 3
    So total atoms = 3 + 1 = 4 atoms.
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