In recent years, observations of highly-ordered, hexagonal arrays of self-organized nanostructures on binary or impurity-laced targets under normal-incidence ion irradiation have excited interest in this phenomenon as a potential route to high-throughput, low-cost manufacture of nanoscale devices or nanostructured coatings. The currently-prominent explanation for these structures is a morphological instability driven by ion erosion discovered by Bradley and Shipman; however, recent parameter estimates via molecular dynamics simulations suggest that this erosive instability may not be active for the representative GaSb system in which hexagonal structures were first observed. Motivated by experimental and numerical evidence suggesting the possible importance of phase separation in ion-irradiated compounds, we here generalize the Bradley-Shipman theory to include the effect of ion-assisted phase separation. The resulting system admits a chemically-driven finite-wavelength instability that can explain the order of observed patterns even when the erosive Bradley-Shipman instability, and in a relevant simplifying limit, provides an intuitive instability criteria that agrees qualitatively with experimental observations on pattern wavelengths. Finally, we identify a characteristic experimental signature that distinguishes the chemical and morphological instabilities, and highlights the need for specific additional experimental data on the GaSb system.
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