Figure contains the calculated phase diagram of the Al 0.5 In 0.5 P(001) surfaces structures considered here. Only 10 out of the more than 80 candidate structures considered in our work turn out to be energetically relevant. Schematic top views of these surfaces are compiled in Fig. . At hydrogen-deficient conditions (∆µ H ∼ -1 eV), P-dimer structures known from clean III-V(001) surfaces dominate the phase diagram. This concerns the c-4×4 structure for anion-rich surfaces, and the β2-2×4 surface for intermediate preparation conditions. The occurrence of [110] oriented P dimers in the P-rich c-4×4 structure and of oriented dimers in 2×4 surface reconstructions is in accord with MOVPE-grown AlInP surfaces in N 2 atmosphere . Hetero-dimer structures featuring either In-P or Al-P dimers in the topmost layer occur for cation-rich preparation conditions. They differ from the mixed-dimer structure known from InP(001) by the staggered arrangement of the second-layer cation dimers, due to the size mismatch between Al and In.