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Single crystal neutron diffraction is combined with synchrotron x-rayscattering to identify the different superlattice phases present in$Cs_{0.8}Fe_{1.6}Se_2$. A combination of single crystal refinements and firstprinciples modelling are used to provide structural solutions for the$\sqrt{5}\times\sqrt{5}$ and $\sqrt{2}\times\sqrt{2}$ superlattice phases. The$\sqrt{5}\times\sqrt{5}$ superlattice structure is predominantly composed ofordered Fe vacancies and Fe distortions, whereas the $\sqrt{2}\times\sqrt{2}$superlattice is composed of ordered Cs vacancies. The Cs vacancies only orderwithin the plane, causing Bragg rods in reciprocal space. By mapping x-raydiffraction measurements with narrow spatial resolution over the surface of thesample, the structural domain pattern was determined, consistent with thenotion of a majority antiferromagnetic $\sqrt{5}\times\sqrt{5}$ phase and asuperconducting $\sqrt{2}\times\sqrt{2}$ phase.

Two-dimensional Cs-vacancy superstructure in iron-based superconductor $Cs_{0.8}Fe_{1.6}Se_2$