Adatom migration, capture and decay among competing nuclei on a substrate

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Abstract
The capture and decay of randomly migrating and desorbing monomer among competing nuclei is considered by extending Halpern's probability of arrival treatment. The method is applied to several specific arrays of nuclei and the results are compared with those for more approximate treatments. For an almost random array with a deficiency of near neighbours, such as occurs naturally in nucleation on a substrate, the uniform depletion model is shown to be a good approximation. The results also support the use of constant capture numbers for critical and supercritical nuclei.