Past exam of the materials science course of the University of Cambridge / 2019 / Paper 1 / 1 / d / Solution

Taking Cu K$\alpha$ wavelength $\lambda =0.15418\mathrm{nm}$, Bragg's law gives $d=\lambda /(2\sin \theta )$. For cubic $111$, $a=\sqrt{3}{d}_{111}$ and the nearest Zn–S separation is $\sqrt{3}a/4=3d_{111}/4$. For ideal wurtzite structure, $c=2d_{002}$ and the nearest separation is $3c/8=3d_{002}/4$. ThereforeBoth have tetrahedral nearest-neighbour coordination number four, but different further-neighbour stacking and lattice relaxation can shift their equilibrium bond lengths. The hexagonal value assumes ideal $c/a=\sqrt{8/3}$ and $u=3/8$; a real distorted wurtzite structure can have unequal axial and inclined bonds. One measured $002$ spacing alone does not determine every bond length without that structural assumption.