  We derive an Ising Hamiltonian for kinetic simulations involving interstitial
and vacancy defects in binary alloys. Our model, which we term `ABVI',
incorporates solute transport by both interstitial defects and vacancies into a
mathematically-consistent framework , and thus represents a generalization to
the widely-used ABV model for alloy evolution simulations. The Hamiltonian
captures the three possible interstitial configurations in a binary alloy: A-A,
A-B, and B-B, which makes it particularly useful for irradiation damage
simulations. All the constants of the Hamiltonian are expressed in terms of
bond energies that can be computed using first-principles calculations. We
implement our ABVI model in kinetic Monte Carlo simulations and perform a
verification exercise by comparing our results to published irradiation damage
simulations in simple binary systems with Frenkel pair defect production and
several microstructural scenarios, with matching agreement found.
