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In an FCC lattice with identical atoms at corners, which of the following statements about tetrahedral voids is/are correct?

1. A tetrahedral void is formed by one corner atom and three face-centred atoms.
2. Two tetrahedral voids lie on a single body diagonal of the FCC unit cell.
3. The number of tetrahedral voids equals the number of atoms in the lattice.
4. The volume of a tetrahedral void is half the volume of an octahedral void.

Correct answer: A tetrahedral void is formed by one corner atom and three face-centred atoms.

Solution

Each tetrahedral void in an FCC structure is surrounded by 4 atoms: 1 corner and 3 face-centred atoms (or equivalently 1 face-centred and 3 corner atoms). Two such voids sit on each body diagonal. Statement A and B are correct; C is wrong (T.V. = 2 * atoms); D is wrong (r_T/r_O = 0.225/0.414, so volume ratio is far from 1/2).

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