Question

In a face-centred cubic arrangement of atoms A and B, A are present at the corners and B at the face-centres. If A atoms are missing from 4 corners in each unit cell, what is the simplest formula of the compound?

Answer 1

In a face-centred cubic (FCC) arrangement A atoms are present at the 8 corners of the cube, and each corner atom is shared by 8 unit cells, contributing `1/8` atom per corner. Normally, this would result in 

`8 xx 1/8 = 1` atom of A per unit cell

However, since 4 corners are missing, the remaining A atoms are

`(8 - 4) xx 1/8 = 4/8 = 1/2`

B atoms are present at the 6 face centres, and each face-centred atom is shared by 2 unit cells, contributing `1/2` atom per face centre

`6 xx 1/2 = 3` atoms of B per unit cell

Now, the ratio of A to B is `1/2 : 3 = 1 : 6`

∴ The simplest formula of the compound is AB₆.