Question

Which of the following relation is true for cubical voids?
Where, $R$ is radius of sphere
$r$ is radius of octahedral void
$a$ is edge length of unit cell

• A. $2[R+r]=\sqrt{2}a$
• B. $3[R+r]=\sqrt{2}a$
• C. $[R+r]=a$
• D. $2[R+r]=\sqrt{3}a$

Answer 1

The correct option is D $2[R+r]=\sqrt{3}a$

Cubical voids are formed in the cubical arrangement between 8 closely formed spheres which occupy all the corners of a cube.
The cubical void is in contact with all the 8 spheres in the corner of the unit cell. Thus, the coordination number of cubical void is 8.
Since, these voids are in contact with spheres along the body diagonals of the cube.

$\sqrt{3}a=2[R+r]2\sqrt{3}R=2[R+r](\because a=2R)\frac{r}{R}=0.732$
Thus, option (a) is correct.