Question

A compound formed by elements X and Y crystallizes in the cubic structure where Y atoms are at the corners of the cube and X atoms are at the alternate faces. What is the formula of the compound?

Answer 1

Step 1: Position of atoms

$X\to$ CCP lattice

$Y\to$ Alternate faces

Step 2: Contribution of atoms from corners and alternate faces

For $X$,

The contribution of the corner atom in the cube is 18\frac{1}{8}81​.

Number of $X-$ atoms per unit cell =18×8=1=\frac{1}{8}\times8=1=81​×8=1

For $Y$,

The contribution of the face-centered atom in the cube =12=\dfrac{1}{2}=21​.

Number of $Y-$ atoms per unit cell $=\frac{1}{2}\times 3=\frac{3}{2}$

Thus the formula is $X{Y}_{\frac{3}{2}}or{X}_2{Y}_3$ XY32XY_{\frac{3}{2}}Y$X{Y}_{\frac{3}{2}}or{X}_2{Y}_3$