Question

How many of the following statement(s) is/are incorrect regarding tetrahedral voids in fcc lattice?
a) Each body diagonals contains 2 tetrahedral voids
b) Each tetrahedral void contributes $\frac{1}{4^{th}}$ part to a unit cell
c) One tetrahedral void is present at the body centre of unit cell
d) Each face diagonals contains 2 tetrahedral voids

• A. $4$
• B. $2$
• C. $3$
• D. $1$

Answer 1

The correct option is C $3$

In cubic close packing, each unit cell has 8 tetrahedral voids.
Each body diagonals in a unit cell contains 2 tetrahedral voids.
Since, each fcc unit cell has 4 body diagonals, the number of tetrahedral voids in fcc is 8.

Each tetrahedral void is surrounded by 4 atoms as shown in figure
In this figure, a cube is divided into 8 minicubes. Thus, one tetrahedral void is present at the centre of each minicube.
Hence, it will have 8 tetrahedral voids in a unit cell.
Thus, statement (a) is correct.
Tetrahedral voids are found only in the body diagonals.
So, statement (c) and (d) are incorrect.

Each tetrahedral void is present entirely inside the unit cell. Thus, each tetrahedral void contributes fully to the unit cell and not shared with other unit cell.
Hence, statement (b) is also incorrect.