Question

The no of the tetrahedral void is always $8$ for any $fcc$ lattice? As the Zeff of $Fcc$ is $4$ which is unchanged always.

Answer 1

The cubic crystal system is one in which the unit cell is shaped like a cube. This is one of the most straightforward and simple crystal and mineral types.

Complete answer:
The cubic crystal system come in three different types:
Primitive cubic $\left( {cP} \right)$ or simple cubic
Body-centered cubic $\left( {cl} \right.$ or $\left. {bcc} \right)$
Face-centered cubic $\left( {cF} \right.$ or $\left. {fcc} \right)$ or cubic close-packed $\left( {ccp} \right)$
For a total of $8$ net tetrahedral voids, a face-centered cubic unit cell has $8$ tetrahedral voids located halfway between each corner and the unit cell's base. There are also $12$ octahedral voids at the midpoints of the unit cell's sides, as well as one octahedral hole in the cell's very middle, making a total of four net octahedral voids.
The hexagonal close-packed $\left( {hcp} \right)$ system is closely similar to the face-centered cubic system, with the main difference being the relative placements of their hexagonal layers. A hexagonal grid is the plane of a face-centered cubic structure.
If there are no atoms or ions in a close-packed structure $\left( {ccp} \right.$ or $\left. {fcc} \right)$ , the number of octahedral voids and tetrahedral voids would be $nn$ and $2n2n$ , respectively. The fcc structure has $8$ tetrahedral voids per unit cell, $Zeff = 4$ . Each small cube has one tetrahedral void at its own body center if the $fcc$ unit cell is divided into $8$ small cubes.
That is, the total number of tetrahedral void in a unit cell is $2 * Zeff = 8$ .

Note:
The face centered lattice is the same as the simple cubic lattice but with a lattice point in the middle of each of the cube's six faces. Each unit cell in the face-centered cubic lattice has four lattice points.