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The superconducting and magnetic properties of phase-separatedA$_x$Fe$_{2-y}$Se$_2$ compounds are known to depend on post-growth heattreatments and cooling profiles. This paper focusses on the evolution ofmicrostructure on annealing, and how this influences the superconductingproperties of Rb$_x$Fe$_2-y$Se$_2$ crystals. We find that the minority phase inthe as-grown crystal has increased unit cell anisotropy (c/a ratio), reduced Rbcontent and increased Fe content compared to the matrix. The microstructure israther complex, with two-phase mesoscopic plate-shaped features aligned along{113} habit planes. The minority phase are strongly facetted on the {113}planes, which we have shown to be driven by minimising the volume strain energyintroduced as a result of the phase transformation. Annealing at 488K resultsin coarsening of the mesoscopic plate-shaped features and the formation of athird distinct phase. The subtle differences in structure and chemistry of theminority phase(s) in the crystals are thought to be responsible for changes inthe superconducting transition temperature. In addition, scanning photoemissionmicroscopy has clearly shown that the electronic structure of the minorityphase has a higher occupied density of states of the low binding energy Fe3dorbitals, characteristic of crystals that exhibit superconductivity. Thisdemonstrates a clear correlation between the Fe-vacancy-free phase with highc/a ratio and the electronic structure characteristics of the superconductingphase.

High resolution characterisation of microstructural evolution in Rb$_{x}$Fe$_{2-y}$Se$_{2}$ crystals on annealing