Title: Superconductivity at the vacancy disorder boundary in K$_x$Fe$_{2-y}$Se$_2$,
Abstract: The role of phase separation in the emergence of superconductivity in alkali
metal doped iron selenides A$_{x}$Fe$_{2-y}$Se$_{2}$ (A = K, Rb, Cs) is
revisited. High energy X-ray diffraction and Monte Carlo simulation were used
to investigate the crystal structure of quenched superconducting (SC) and
as-grown non-superconducting (NSC) K$_{x}$Fe$_{2-y}$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 SC and NSC crystals along side the
\textit{I4/mmm} Fe-vacancy free phase. Moreover, in the SC crystal an
Fe-vacancy disordered phase is additionally present. It appears at the boundary
between the \textit{I4/mmm} vacancy free phase and the \textit{I4/m} vacancy
ordered phase ($\sqrt{5}\times\sqrt{5}$). The vacancy disordered phase is most
likely the host of superconductivity.