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 patternforming mechanisms.

In recent years, many papers have been devoted to the regularity of doubly nonlinear singular evolution equations. Many of the proofs are unnecessarily complicated, rely on superfluous assumptions or follow an inappropriate approximation procedure. This makes the theory unclear and quite chaotic to a nonspecialist. The aim of this paper is to fix all the misprints, to follow correct procedures, to exhibit, possibly, the shortest and most elegant proofs and to give a complete and self-contained overview of the theory.

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