How many number of atoms are present in each unit cell in ccp structure?

Definition of Unit Cell

The smallest recurring unit of the crystal lattice is the unit cell, the building block of a crystal is called the unit cell.

Cubic Closed Packing

In cubic close packing, the spheres of the third layer are not aligned with those of either the first or the second layer. So if we consider the first layer as ‘A’ and second layer as ‘B’, then the third layer as ‘C’. The specific pattern of layers can be written as ABCABC. This type of crystal structure is called a cubic close-packed (ccp) or face-centred cubic (fcc) structure.

Face Centred Cubic

A face-centred cubic unit cell comprises of atoms placed at all the corners and at the centre of all the faces of the cube. The atom present at the centre of the face is shared between 2 adjacent unit cells and only half of each atom belongs to an individual cell.

Cubic closed packing (CCP) is an alternative name given to face centred cubic (FCC). They both have the closest possible packing of atoms. The layers of plane sheets of atoms are arranged in a slightly different manner.

In ccp structure or fcc structure, the number of atoms per unit cell is calculated as follows

Thus, in a face-centred cubic unit cell (fcc) or cubic closed packing (ccp), we have:

8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom
6 face-centred atoms × 1/2 atom per unit cell = 3 atoms
Therefore, the total number of atoms in a unit cell = 4 atoms.

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