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A model of the grain surface chemistry involving the accretion of atoms oftwo different elements, X and Y, and their reactions to form species X_2, XY,and Y_2 was examined for a wide range of choices for the values of its threefree parameters - the accretion rate of X and Y, the desorption rate of X andthe grain surface sweeping time of Y, all considered relative to the grainsurface sweeping rate of X. Relative production rates of the diatomics werecalculated with five methods involving, respectively, a high-order truncationof the master equation, a low-order truncation of the master equation, thestandard deterministic rate equation approach, a modified rate equationapproach and a set of approximations which are in some cases appropriate foraccretion dominated chemistry. The accuracies of the relative production ratescalculated with the different methods were assessed for the wide range of modelparameters. The more accurate of the low-truncation master equationcalculations and the standard deterministic rate equation approach givesresults which are in most cases within ten or twenty per cent of the resultsgiven by the high-truncation master equation calculations. For many cases, themore accurate of the low order truncation and the standard deterministic rateequation approaches is indicated by a consideration of the average number ofatoms of the two species on the grain's surface.

Diffusive grain-surface chemistry involving the atoms and diatomic molecules of two elements