Question

The total number of tetrahedral voids in face centered unit cell is _________
A: 6
B: 8
C: 10
D: 12

Answer 1

Hint :A unit cell refers to the smallest representation of the whole crystal. The cubic crystal system in crystallography refers to the crystal system in which the unit cell acquires the shape of a cube which is the most common or the simplest shape in case of minerals or crystals. The three main types of crystals include Primitive cubic (i.e. cP), Body-centered cubic (i.e. bcc) and Face-centered cubic (i.e. fcc).

Complete Step By Step Answer:
The fcc (i.e. face-centered cubic) lattice possesses a coordination number of 12 and comprises 4 atoms per unit cell. The maximum packing density exists when the atoms possess a radius equal to one quarter of the diagonal of one of the faces of the unit cell.
In fcc, tetrahedral voids are located on the body diagonals. The void surrounded by the four spheres positioned at the corners of regular tetrahedra is known as a tetrahedral void. When the sphere of the second layer is above the void of the first layer, it leads to the formation of a tetrahedral void.
In fcc, two tetrahedral voids are present on each body diagonal at a distance of $ \left( {1/4} \right)th $ from every corner. Thus, the total number of tetrahedral voids is equal to the product of the number of tetrahedral voids in one body diagonal and total number of body diagonals.
 $ total{\text{ }}number{\text{ }}of{\text{ }}tetrahedral{\text{ }}voids = 2 \times 4 = 8 $
Hence, the total number of tetrahedral voids in the face centered unit cell is 8.
Thus, Option B is correct.

Note :
FCC crystal structure exhibits more ductility (deforms more readily) in comparison to BCC crystal structure. Actually, bcc lattice, though cubic, is not closely packed and thus, forms strong metals. On the other hand, fcc lattice is both cubic as well as closely packed and thus, forms more ductile materials.