# Unit cell and its classification

A unit cell is the smallest part of the complete space lattice which on repetition again and again in all the possible directions results in the formation of crystal lattice or space lattice.In other words it is is said to be the smallest repeating unit of the space lattice.

This term is used to visually simplify the crystalline patterns solids arrange themselves in. When the unit cell repeats itself, the network is called a lattice.

### Contribution of a lattice point at a particular position:

location             Contribution
Body center       1
Face center        1/2
Edge center       1/4
Corner               1/8

### Classification of unit cell:

This classification is based on the location of the lattice points(atoms) within the unit cell.Therefore it is divided into which may two types.

### 1st classification of the unit cell:

#### 1.Primitive unit cell

In this type, the lattice points are present only at corners(8 corners).

Therefore every atom at the corner is shared among 8 adjacent unit cells. There are 4 in the same layer and 4 in the upper (or lower) layer. As a result a particular unit cell has the only 1/8th of an atom.

Each small sphere in the following figure represents the centre of a particle that occupies that particular position and not its size. So this structure is known as an open structure.

For example SCC(Simple Cubic)
To clarify from the diagram given above, there are 8 atoms at the corners.So the total number of atoms in one unit cell is
Coordination number(Z)=8*1/8=1

#### 2.Non-Primitive unit cell

In this type, the lattice points are present not only at corners but also at some other specific position. For example,
(a)BCC(Body center cubic)

In this type atoms are present at each corner of the cube and  at the centre of the structure.

The diagram shown above is an open structure .According to this structure, the atom which is present  at the centre of the  body wholly belongs to the unit cell in which it is present.So in BCC cell we have
Coordination number(Z)=Lattice point at corner+Lattice point at the body

=(8 corners × 1/8 per corner atom )+1 body centre atom=2
(b)FCC(Face center cubic)

In this type the lattice points are present at all the corners of the crystal lattice and at the centre of all the faces of the cube.Therefore the lattice points(atoms) present at the face-centered is shared between 2 adjacent unit cells and only 1/2 of each atom belongs to an individual cell.So in FCC we have
Coordination number(Z)=Lattice point at all corner+lattice point at each face

=(8 corners × 1/8 per corner atom)+(6 face-centered atoms × 1/2 atom per unit cell)
=(8*1/8)+(6*1/2)
=1+3=4
Where the coordination number(Z)is the total number of particles or atoms or lattice points per unit cell.

### 2nd classification of the unit cell:

On the basis of axial length in x,y, z-direction, and interfacial angles, unit cells can be classified into 7 types which are called seven crystal system or seven crystal habits and these are Cubic, Tetragonal, Orthorhombic(Rhombic), Monoclinic, Triclinic, Hexagonal, Rhombohedral.

For a brief understanding of the above seven crystals, follow the link below: