  The many surface reconstructions of (110)-oriented lanthanum--strontium
manganite (La$_{0.8}$Sr$_{0.2}$MnO$_3$, LSMO) were followed as a function of
the oxygen chemical potential ($\mu_\text{O}$) and the surface cation
composition. Decreasing $\mu_\text{O}$ causes Mn to migrate across the surface,
enforcing phase separation into A-site-rich areas and a variety of
composition-related, structurally diverse B-site-rich reconstructions. The
composition of these phase-separated structures was quantified with scanning
tunneling microscopy (STM), and these results were used to build a 2D phase
diagram of the LSMO(110) equilibrium surface structures.
