Abstract
We study analytically the effect of the chemical disorder produced by displacement cascades in a stoichiometric $L{1}_{2}$ alloy under irradiation. A continuum kinetic model is proposed to describe the coupled evolution under irradiation of the specific area covered by antiphase boundaries and of the volume fraction of the domains belonging to the four translation variants of the $L{1}_{2}$ structure. Combining this description with existing mean-field results for the order-disorder transition under irradiation, we construct a steady-state dynamical phase diagram, where the control parameters are the cascade size and the irradiation-induced disordering rate. Three stable steady states are predicted: long-range ordered, disordered, and a state of patterning of order. This analytical phase diagram is in good agreement with the one constructed from kinetic Monte Carlo simulations. The present analytical model indicates that patterning of chemical order should be a general phenomenon in irradiated ordered structures, provided that the cascade size is large enough for the annealing of disordered zones to form additional antiphase domains.
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