Archimedean solidlike superconducting framework in phase-separatedK0.8Fe1.6+xSe2(0≤x≤0.15)

The superconducting (SC) phase in phase-separated (PS) ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6+x}\mathrm{S}{\mathrm{e}}_{2}\phantom{\rule{0.16em}{0ex}}(0\ensuremath{\le}x\ensuremath{\le}0.15)$ materials is found to crystallize on Archimedean solidlike frameworks, and this structural feature originates from a spinodal phase separation (SPS) at around ${T}_{s}\ensuremath{\approx}540\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, depending slightly on the Fe concentration, as revealed by in situ heating TEM observations and shown in a phase diagram. Two stable phases in ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6+x}\mathrm{S}{\mathrm{e}}_{2}$ are demonstrated to be the SC ${\mathrm{K}}_{0.5}\mathrm{F}{\mathrm{e}}_{2}\mathrm{S}{\mathrm{e}}_{2}$ and antiferromagnetic (AFM) ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6}\mathrm{S}{\mathrm{e}}_{2}$. The spinodal waves go along the systematic $[113]$ direction and result in notable lamellar structure as illustrated by strain-field theoretical simulations. The three-dimensional SC framework is constructed with hollow truncated octahedron similar to that discussed for Archimedean solids. Based on this structural model, we can efficiently calculate the volume fraction of the SC phase in this type of PS SC material.