Question

In a face centered lattice of X and Y, X atoms are present at the corners while Y atoms are at face centers. What would be the simplest formula of the compound if one of the X atoms is missing from a corner in each unit cell?

Answer 1

Each of the 8 corner atoms of a cube is shared by 8 such cubes so that each corner atom contribution to one cube will be \(\dfrac{1}{8}\).
After the removal of 1 corner X atoms,
\(\text{No. of X atom per unit cell }=7\times\dfrac{1}{8}=\dfrac{7}{8}\)

Each atom at the face centre is shared by two unit cell so that each face centred atom contributes half of it to each cube.
\(\text{No. of Y atom per unit cell }=6\times\dfrac{1}{2}=3\)

So, the number of atoms present or the formula of the compound is
\(X_\frac{7}{8}Y_3\) or \(X_7 Y_{24}\)