UNIT CELL AND LATTICE PARAMETERS

Unit cell

In Crystals the arrangement of particles is described with three dimensional geometrical parallelepiped structure. 
The unit cell is defined as the smallest size of parallelepiped structure with minimum number of atoms.

In a unit cell there are 6 faces and 8 corners. So 8 atoms are required to form a unit cell and all the 8 atoms are located at the 8 corners each.

Lattice

Lattice is defined as a three dimensional array of atoms.
It describes the size and shape of the unit cell.

Parameters of a unit cell

A unit cell is described by six parameters. These parameters are three dimensions  and the angles between them .
The Dimensions of unit cell  along three axes of a unit cell are represented by (a, b ,c) .
The angle between b and c is represented by α, between a and c by β and between a and b by γ.
we can identify the structure of crystal by knowing the parameters of unit cell.
Properties of unit cell :
1. Unit cell is the minimum structure.
2. We cannot divide the unit cell further.
3. It gives the properties of the crystal.
4. Unit cell is the fundamental size. It is microscopic. It cannot be found experimentally.

Coordination number

It is defined as he number of atoms which are the closely surrounded to a given atom in the lattice structure.
Coordination number represents characteristic of lattice. It gives an idea of closeness of atoms.

Example: 1. in a simple unit cell of cubic structure an atom located at a point on X- axis is very close by one neighborhood atom and also another atom on –ve X- axis. So there are 2 atoms very closely surrounding a given atom on X-axis.
Similarly there will be 2 atoms on Y-axis and 2 atoms on Z – axis.
Hence the coordination number in the case of simple cubic crystal is 6.

2. In the case of body centered crystal, an atom located at the center of the body of unit cell
Is closely surrounded by all the 8 atoms each located at the corner. Hence the coordination
number is 8

3. In the case of face centered cubic crystal an atom at any corner is closely surrounded by 4
atoms along each plane. There are 3 planes XY, YZ and ZX.
4. Hence the coordination number = 4*3 =12

Types of unit cells:

The unit cell is classified into 4 types.

1. Simple or Primitive Unit Cells: if the atoms are located only at the corner positions, it is known as Primitive (simple) Unit Cell. Example: NaCl , Ca, Li etc.

2. Body Centered cubic crystal: if an extra atom is at the center of the body, it is known as Body Centered Unit
cell. Example :CsCl, Iron , Cr

3. Face Centered cubic crystal: if an extra atom is located at the center of each face, it is known as Face Cantered Unit cell. Example : Zinc , Cd, Mg

4. Base Centered cubic crystal:  an extra atom is at the centre of base of unit cell, it is known as base Cantered Unit cell. It is almost equivalent to face cantered.

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