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The search for new superconducting materials has been spurred on by thediscovery of iron-based superconductors whose structure and composition isqualitatively different from the cuprates. The study of one such material,K$_x$Fe$_{2-y}$Se$_2$ with a critical temperature of 32 K, is made moredifficult by the fact that it separates into two phases: a dominantantiferromagnetic insulating phase with a K$_2$Fe$_4$Se$_5$ structure, and aminority superconducting phase whose precise structure is as yet unclear. Herewe perform electrical and magnetization measurements, scanning electronmicroscopy and microanalysis, X-ray diffraction, and scanning tunnellingmicroscopy on K$_x$Fe$_{2-y}$Se$_2$ crystals prepared under different quenchingprocesses to better understand the relationship between its microstructure andits superconducting phase. We identify a 3D network of superconductingfilaments within this material and present evidence to suggest that thesuperconducting phase consists of a single Fe vacancy for every eight Fe-sitesarranged in a $\sqrt{10}\times\sqrt{8}$ parallelogram structure.

Influence of microstructure on superconductivity in K$_x$Fe$_{2-y}$Se$_2$ and evidence for a new parent phase K$_2$Fe$_7$Se$_8$