The Boltzmann transport equation is used to describe a beam of ions of atomic species 1 (1-atoms) bombarding a target modelled as an amorphous mixture of 2-atoms and 3-atoms. In a manner familiar in nuclear reactor theory, the method of characteristics is used to integrate the resulting transport equations. An exact expression for the migration flux J3 of 3-atoms is obtained in closed form. This expression can be evaluated in terms of a power series in a distance parameter s. For the case of slowly varying density N3 of 3-atoms, Fick's law, relating J3 to the gradient of N3, is derived from this expression; it is given by the lowest order term of the power series. J3 is shown to be proportional to the bombarding flux. Concomittantly, a closed expression for the mixing parameter in Fick 's law is obtained, which allows a calculation of this quantity for realistic interatomic potentials. A model Kinchin-Pease displacement cascade is proposed, which is expected to allow a reasonable first approximation calculation of the mixing parameter in Fick's law. It is deduced that the mixing parameter will depend sensitively on the lattice displacement energy. This dependence constitutes a physical mechanism for chemical effect in cascade mixing, as well as for fluence and temperature dependence of cascade mixing.