Past exam of the materials science course of the University of Cambridge / 2015 / Paper 1 / 1 / a / ii / Solution

Bond-centred inversion in diamond cubic gives one inversion centre at the midpoint of a nearest-neighbor bond:Mark its projected point $(1/8,1/8)$ and label its height $z/a=1/8$. Inversion about this point sends $\mathbf{r}$ to $(1/4,1/4,1/4)-\mathbf{r}$. It exchanges the two identical FCC sublattices and therefore preserves the crystal. An individual atom at the chosen origin is not an inversion centre.