Abstract
Powers and coefficients of polynomials describing the concentration dependent probabilities of small clusters of impurities are presented. For singles, pairs, and triples of impurities randomly distributed in simple cubic, body-centered-cubic, or face-centered-cubic host lattices, all interaction ranges between first next neighbor (1NN) and 8NN interaction are considered (singles and pairs up to 16 NN). The change of the probability functions with increasing interaction range is described. It is noted that an additional consideration of clusters with more impurities than a triple does not essentially improve the statistical error in the case of long-range interaction. For the three lattices, empty shells and inequivalent lattice vectors are given.
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