  Ion Beam Sputtering (IBS) is a cost-effective technique able to produce
ordered nanopatterns on the surfaces of different materials. To date, most
theoretical studies of this process have focused on systems which become
amorphous under irradiation, e.g. semiconductors at room temperature. Thus, in
spite of the large amount of experimental work on metals, or more recently on
semiconductors at high temperatures, such experimental contexts have received
relatively little theoretical attention. These systems are characterized by
transport mechanisms, e.g. surface diffusion, which are anisotropic as a
reflection of the crystalline structure not being overruled by the irradiation.
Here, we generalize a previous continuum theory of IBS at normal incidence, in
order to account for anisotropic surface diffusion. We explore systematically
our generalized model in order to understand the role of anisotropy in the
space ordering properties of the resulting patterns. In particular, we derive a
height equation which predicts morphological transitions among hexagonal and
rectangular patterns as a function of system parameters and employ an angular
correlation function to assess these pattern symmetries. By suitably choosing
experimental conditions, it is found that one might be able to experimentally
control the type of order displayed by the patterns produced.

Mesoscale and Nanoscale Physics;Materials Science;Statistical Mechanics;Pattern Formation and Solitons