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

A model of the grain surface chemistry involving the accretion of atoms of two different elements, X and Y, and their reactions to form species X2, XY, and Y2 was examined for a wide range of choices for the values of its three free parameters – the accretion rate of X and Y, the desorption rate of X and the grain surface sweeping time of Y, all considered relative to the grain surface sweeping rate of X. Relative production rates of the diatomics were calculated with five methods involving, respectively, a high-order truncation of the master equation, a low-order truncation of the master equation, the standard deterministic rate equation approach, a modified rate equation approach and a set of approximations which are in some cases appropriate for accretion dominated chemistry. The accuracies of the relative production rates calculated with the different methods were assessed for the wide range of model parameters. The more accurate of the low-truncation master equation calculations and the standard deterministic rate equation approach gives results which are in most cases within ten or twenty per cent of the results given by the high-truncation master equation calculations. For many cases, the more accurate of the low order truncation and the standard deterministic rate equation approaches is indicated by a consideration of the average number of atoms of the two species on the grain's surface.