Which of the following statements is/are correct about tetrahedral voids in an fcc unit cell?

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Number of tetrahedral voids is twice the number of atoms in the fcc unit cell

Number of tetrahedral voids per atom in fcc unit cell is 2

All of these

Number of tetrahedral voids per unit cell is 8

answer is D.

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Detailed Solution

Tetrahedral interstices : We have seen that in hexagonal close packing (hcp) and cubic close packing (ccp), each sphere of second layer touches with three spheres of first layer. Thus, they leave a small space in between which is known as tetrahedral site or interstices or the vacant space between 4 touching spheres is called as tetrahedral void. Since a sphere touches three spheres in the below layer and three spheres in the above layer, there are two tetrahedral sites associated with one sphere. It may by noted that a tetrahedral site does not mean that the site is tetrahedral in geometry but it means that this site is surrounded by four spheres and the centres of these four spheres lie at the apices of a regular tetrahedron.
In FCC, one corner and its face centres form a tetrahedral void,
In FCC, two tetrahedral voids are obtained along one cube diagonal. So, in FCC, 8 tetrahedral voids are present.
In FCC, total number of atoms =4.
In FCC, total number of tetrahedral voids =8.
So, we can say that in 3D close packing, 2 tetrahedral voids are attached with one atom.