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”.
- 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.
- 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.
- 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.
- 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.
- 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.
- An atom at the corner is shared by eight unit cells so its contribution is = 1x(1/8)=1/8
- An atom on the face is shared between two unit cells so its contribution is =1x(1/2)=1/2
- An atom present at centre of unit cell is not shared by any unit cell so it contribution is = 1
- 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:-
- Simple [primitive] unit cell:- It has only Eight atom present at corner each have contribution 1/8 so 8 x 1/8 = 1 atom.
- 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]:-
- 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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