Past exam of the condensed matter physics major option course of the University of Oxford / 2015 / 1 / b / Solution

Take the square projection cell $0\le x,y\le 1$ and label the heights rather than erasing them in projection. The Fe positions appear at the cell corners and at $(1/2,1/2)$, both with $z=0$. The Se projections are $(1/2,0)$ at height $+\eta$ and $(0,1/2)$ at height $-\eta$, together with their periodic copies on opposite edges. These are distinct height classes even though the observer looks down the $z$ axis.

The corner Fe sites together count as one atom per cell, the central Fe as one, and each edge-shared Se projection contributes half at each of two equivalent edges. The count is therefore two Fe and two Se per primitive tetragonal lattice cell. The Fe sublattice has its shorter nearest-neighbor directions along the projected cell diagonals. The distinction between those directions and the conventional tetragonal axes matters for the distortion in d.