  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.
