  We modify the theory of nanoscale patterns produced by ion bombardment with
concurrent impurity deposition to take into account the effect that the
near-surface impurities have on the collision cascades. As the impurity
concentration is increased, the resulting theory successively yields a flat
surface, a rippled surface with its wavevector along the projected direction of
ion incidence, and a rippled surface with its wavevector rotated by 90 degrees.
Exactly the same morphological transitions were observed in recent experiments
in which silicon was bombarded with an argon ion beam and gold was co-deposited
[B.~Moon et al. arXiv:1601.02534 (2016)].
