Total number of voids in cubic close packed lattice

In a cubic close packed (CCP) lattice, there are two types of voids: octahedral voids and tetrahedral voids. The total number of voids in a CCP lattice can be calculated as follows:

Octahedral Voids
- An octahedral void is located at the center of a tetrahedron formed by six atoms.
- Each atom in the CCP lattice is surrounded by 12 nearest neighbors, which form an octahedron around it.
- Therefore, the number of octahedral voids in a CCP lattice is equal to the number of atoms in the lattice.

Tetrahedral Voids
- A tetrahedral void is located at the center of a tetrahedron formed by four atoms.
- Each tetrahedral void is shared by four neighboring octahedral voids.
- Therefore, the number of tetrahedral voids in a CCP lattice is twice the number of octahedral voids.

Total Number of Voids
- The total number of voids in a CCP lattice is equal to the sum of octahedral and tetrahedral voids.
- Therefore, the total number of voids in a CCP lattice can be expressed as:

Total number of voids = Number of octahedral voids + Number of tetrahedral voids
= Number of atoms in the lattice + 2(Number of atoms in the lattice)
= 3(Number of atoms in the lattice)

Conclusion
- In a cubic close packed lattice, there are a total of three voids for every atom in the lattice.
- This information is useful in understanding the properties of materials that have a CCP lattice structure, such as metals like copper, silver, and gold.