  The superconducting and magnetic properties of phase-separated
A$_x$Fe$_{2-y}$Se$_2$ compounds are known to depend on post-growth heat
treatments and cooling profiles. This paper focusses on the evolution of
microstructure on annealing, and how this influences the superconducting
properties of Rb$_x$Fe$_2-y$Se$_2$ crystals. We find that the minority phase in
the as-grown crystal has increased unit cell anisotropy (c/a ratio), reduced Rb
content and increased Fe content compared to the matrix. The microstructure is
rather 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 energy
introduced as a result of the phase transformation. Annealing at 488K results
in coarsening of the mesoscopic plate-shaped features and the formation of a
third distinct phase. The subtle differences in structure and chemistry of the
minority phase(s) in the crystals are thought to be responsible for changes in
the superconducting transition temperature. In addition, scanning photoemission
microscopy has clearly shown that the electronic structure of the minority
phase has a higher occupied density of states of the low binding energy Fe3d
orbitals, characteristic of crystals that exhibit superconductivity. This
demonstrates a clear correlation between the Fe-vacancy-free phase with high
c/a ratio and the electronic structure characteristics of the superconducting
phase.
