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

The Weiss zone law gives $u+w=0$ and $u-v=0$, so a common direction is $[11\bar{1}]$. Its physical vector is $(a,a,-c)$, while $[100]$ is parallel to $(a,0,0)$. Their dot product therefore givesTaking a Euclidean angle directly between the index triples would incorrectly treat the tetragonal axes as equal in length. Reversing the chosen common direction gives the supplementary oriented angle.