Phase-separation control of K$_x$Fe$_{2-y}$Se$_2$ superconductor through rapid-quenching process

K$_x$Fe$_{2-y}$Se$_2$ exhibits an iron-vacancy ordering at $T_{rm s} {sim}270{deg}$C and separates into two phases: a minor superconducting (iron-vacancy-disordered) phase and a major non-superconducting (iron-vacancy-ordered) phase. The microstructural and superconducting properties of this intermixture can be tuned by an appropriate control of the quenching process through $T_{rm s}$. A faster quenching rate leads to a finer microstructure and a suppression of formation of the non-superconducting phase by up to 50%. Nevertheless, such a faster cooling rate does induce a monotonic reduction in the superconducting transition temperature (from 30.7 K down to 26.0 K) and, simultaneously, a decrease in the iron content within the superconducting phase such that the compositional ratio changed from K$_{0.35}$Fe$_{1.83}$Se$_2$ to K$_{0.58}$Fe$_{1.71}$Se$_2$.