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Question

a unit cell consists of a cube in which there are A atoms at the corners and B atoms at the face centres and A atoms are missing from 2 corners in each unit cell. What is the simplest formula of the compound?

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Solution

A atoms are at the corners and B atoms are at the face centres. Therefore, the given compound has an fcc lattice structure.
If two A atoms are missing,
contribution from corner atoms = 6 x 1/8 = 3/4
Contribution of B atoms at face centres = 1/2 x 6 = 3
Formula of the compound = A3/4B3
Simplest formula = A3B12 = AB4

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