  During the ion bombardment of targets containing multiple component species,
highly-ordered arrays of nanostructures are sometimes observed. Models
incorporating coupled partial differential equations, describing both
morphological and chemical evolution, seem to offer the most promise of
explaining these observations. However, these models contain many unknown
parameters, which must satisfy specific conditions in order to explain observed
behavior. The lack of knowledge of these parameters is therefore an important
barrier to the comparison of theory with experiment. Here, by adapting the
recent theory of "crater functions" to the case of binary materials, we develop
a generic framework in which many of the parameters of such models can be
estimated using the results of molecular dynamics simulations.
  As a demonstration, we apply our framework to the recent theory of Bradley
and Shipman, for the case of Ar-irradiated GaSb, in which ordered patterns were
first observed. In contrast to the requirements therein that sputtered atoms
form the dominant component of the collision cascade, and that preferential
redistribution play an important stabilizing role, we find instead that the
redistributed atoms dominate the collision cascade, and that preferential
redistribution appears negligible. Hence, the actual estimated parameters for
this system do not seem to satisfy the requirements imposed by current theory,
motivating the consideration of other potential pattern-forming mechanisms.
