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  4. How many octahedral and tetrahedral holes are present per unit cell in a face centred cubic arrangement of atoms?

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Q. How many octahedral and tetrahedral holes are present per unit cell in a face centred cubic arrangement of atoms?

NTA AbhyasNTA Abhyas 2022

Solution:

4 octahedral and 8 tetrahedral holes are present per unit cell in a face-centred cubic.
Tetrahedral voids:
Number $=8$
Tetrahedron $=8voids.$
There is one tetrahedral void in each edge.
One edge is shared by $4$ lattices in FCC.
Total edges $=12$
Total no. of voids from edges = $\frac{1}{4}\times 12=3$
The octahedral void at the every centre of FCC lattice $=1$
Total $=4$
Therefore, Octahedral $=4$ Tetrahedral $=8$ .