The role of phase separation and the effect of Fe-vacancy ordering in the emergence of superconductivity in alkali metal doped iron selenides ${\mathrm{A}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2$ (A = K, Rb, Cs) is explored. High energy x-ray diffraction and Monte Carlo simulation were used to investigate the crystal structure of quenched superconducting (SC) and as-grown nonsuperconducting (NSC) ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2$ single crystals. The coexistence of superlattice structures with the in-plane $\sqrt{2}\times \sqrt{2}$ K-vacancy ordering and the $\sqrt{5}\times \sqrt{5}$ Fe-vacancy ordering were observed in both the SC and NSC crystals alongside the I4/mmm Fe-vacancy-free phase. Moreover, in the SC crystals, an Fe-vacancy-disordered phase is additionally proposed to be present. Monte Carlo simulations suggest that it appears at the boundary between the I4/mmm vacancy-free phase and the I4/m vacancy-ordered phases ($\sqrt{5}\times \sqrt{5}$). The vacancy-disordered phase is nonmagnetic and is most likely the host of superconductivity.

• Received 17 May 2017
• Revised 25 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.184502