What is the formula of a compound in which the element Y forms ccp lattice and atoms of X occupy 1/3^rd of tetrahedral voids?

X₂Y₃ is the formula of a compound in which the element Y forms ccp lattice and atoms of X occupy 1/3^rd of tetrahedral voids. Usually the anions occupy the lattice (as they are bigger in size) while cations occupy the voids as they are smaller in size. In ccp(cubic close packing) or hcp(hexagonal close packing) if there are N number of lattice points there will be 2N number of tetrahedral voids.

In this compound Y is anion as it occupies lattice, while X is the cation as it is in the voids.

Let us assume there are N number of element Y.

Then there will be 2N number of tetrahedral voids.

But only 1/3 of tetrahedral voids are occupied. Therefore no. of atoms of

N

X:Y= 2/3:1=2:3

This tells us that for every 2 atoms of X there are 3 atoms of Y hence the formula X₂Y₃.