Body-centred Cubic Unit Cell-

## Definition of  Unit Cell

“The smallest repeating unit of the crystal lattice is the unit cell.It is the building block of a crystal.”

The unit cells which are all identical & arranged in such a way that they fill space without overlapping.

“The 3D arrangement of atoms, molecules or ions inside a crystal is called  a crystal lattice.”

It is made up of so many unit cells.

A unit cell can either be primitive cubic, body-centred cubic (BCC) or face-centred cubic (FCC).

## Types of Unit Cell

Many unit cells together make a crystal lattice. Constituent particles like atoms, molecules are also present. Each lattice point is occupied by one such particle.

1. Primitive or simple  Cubic Unit Cell
2. Body centred Cubic Unit Cell
3. Face centred cubic unit cell

## Primitive Cubic Unit Cell

In the simple cubic unit cell, the atoms are present only at the corners. Every atom at the corner is shared among 8 adjacent unit cells. There are 4 unit cells in the same layer and 4 in the upper (or lower) layer. Therefore, 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. This structure is known as an open structure.

1. The atoms in the primitive cubic unit cell are present only at the corners
2. Every atom at the corner is shared among eight adjacent unit cells
3. Four unit cells are present in the same layer
4. Four unit cell in the upper/lower layer
5. Each small sphere in the following figure represents the centre of a particle which occupies that particular position and not its size
6. In each cubic unit cell, there are 8 atoms at the corners. Therefore, the total number of atoms in one unit cell is 8 × 1/8 = 1 atom.

## Body-centred Cubic Unit Cell (BCC)

A BCC unit cell has atoms at each corner of the cube and an atom at the centre of the structure. The atom at the body centre completely belongs to the unit cell in which it is present.

In BCC unit cell every corner has atoms.

There is one atom present at the centre of the structure.

According to this structure atom at the body centre completely belongs to the unit cell in which it is present.

### Number of Atoms in BCC Cell:

Hence, in a BCC cell, we have:

• 8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom
• 1 body centre atom = 1 × 1 = 1 atom

Therefore, the total number of atoms present per unit cell = 2 atoms.

## Face-centred Cubic Unit Cell (FCC)-

source: excellup.com

An FCC unit cell contains atoms at all the corners of the crystal lattice and at the centre of all the faces of the cube. The atom present at the face-centred is shared between 2 adjacent unit cells and only 1/2 of each atom belongs to an individual cell.

1- In FCC unit cell atoms are present in all the corners of the crystal lattice

2-  There is an atom present at the centre of each face of the cube

3- This face-centre atom is shared between two adjacent unit cells

### 4-Number of Atoms in FCC Cell

a) 8 corners × 1/8 per corner atom = 8 × 1 / 8 = 1 atom
b) 6 face-centred atoms × 1/2 atom per unit cell = 3 atoms

Hence, the total number of atoms in a unit cell = 1 + 3 = 4 atoms

Therefore, the total number of atoms in a unit cell = 4 atoms.