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

Hint: 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.