Question

In a ccp structure, a cube is formed by joining the centres of all the tetrahedral voids to generate a new cube. Then, the new cube would contain:

• A. 1 full tetrahedral void, 1 full octahedral void
• B. 1 full tetrahedral void only
• C. 8 full tetrahedral voids and 1 full octahedral void
• D. 1 full octahedral void only

Answer 1

The correct option is A 1 full tetrahedral void, 1 full octahedral void

In ccp, there are two tetrahedral voids on the every body diagonal of fcc. Thus, totally 8 tetrahedral voids present inside the unit cell.
Also, there is one octahedral in centre of cube which gives full contribution to the unit cell and 12 edge centred octahedral voids which contributes $\frac{1}{4}$ to the unit.
Thus, the total number of octahedral voids in ccp is 4.

Here, the centres of all tetrahedral voids are joined to generate a new cube as shown in figure. Thus, all centres of tetrahedral voids are in the corners of the new cube.
Hence, now each tetrahedral voids contibutes $\frac{1}{8}$ portion to the new cube
Thus,
$\text{Total no. of tetrahedral voids in new cube}=\frac{1}{8}\times 8=1$

The octahedral voids present in edge centre of outer cube does not contributes to inner cube. Only the octahedral void at centre contributes to the new cube.
$\therefore$
$\text{No. of octahedral voids in new cube}=1$

Thus, option (a) is correct.