We discuss in detail a model which makes definite predictions for the fractionation of isotopes in sputtered material. The fractionation patterns can be nonlinear, and the pattern for the particular set of isotopes depends on the chemical matrix within which those isotopes are contained. Calculations are presented for all nonmonoisotopic elements contained in the minerals perovskite, anorthite, ackermanite, enstatite, and troilite. All isotopes are fractionated at the level of approximately 4-6% per atomic mass unit. O is always positively fractionated (heavier isotopes sputtered preferentially), and heavier elements are generally negatively fractionated (lighter isotopes sputtered preferentially). The value of Δ(18O:16O) is always less by about 1.8% than a linear extrapolation based upon the calculated Δ(17O:16O) value would suggest. The phenomenon of both negative and positive fractionation patterns from a single target mineral can be used to make an experimental test of the proposed model.