Question

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

Answer 1

CCP:

• Cubic closed packing or CCP is an arrangement of the crystal lattice in which the third layer is not aligned with the first two layers.

• If the first layer is A, the second layer B, and the third layer is C then their arrangement is ABCABC this arrangement is present in CCP crystal lattice.
• CCP is also known as face-centered packing.
• The structure of CCP lattice is:

• There are six faces of the cube each containing half of the atom. That means one atom is shared between two adjacent faces of two unit cells.
• Eight corners of the cube each contain $\frac{1}{8}$ of part of the atom. So, one atom is shared between eight adjacent unit cells.
• So, six faces of a unit cell share each half of the atom which means the total atoms on the facial side are $6\times \frac{1}{2}=3$atoms.
• Eight corners of the unit cell share each $\frac{1}{8}$ of atom which means the total atoms on the corner are $8\times \frac{1}{8}=1$ atom.
• The total number of atoms present in ccp structure is $$\begin{gathered} Totalnumberofatoms=atomspresentonfacetheofcube+atomspresentintnecornerofthecube \\ Totalnumberofatoms=3+1 \\ Totalnumberofatoms=4 \end{gathered}$$

Hence, the total number of atoms present in the ccp structure is 4.