Past exam of the materials science course of the University of Cambridge / 2022 / Paper 1 / 1 / b / Solution

Reduce the supplied fractional coordinates modulo one. The rutile structure has Ti at $(0,0)$ with height $z=0$ and at $(1/2,1/2)$ with height $z=1/2$. The oxygen projections are $(0.30,0.30),(0.70,0.70)$ at $z=0$, and $(0.80,0.20),(0.20,0.80)$ at $z=1/2$. Include equivalent corner sites to show the boundary of a complete unit cell; the cell edges are $a$ along $[100]$ and $[010]$.