The earlier-developed master equation approach and kinetic cluster methods are applied to study kinetics of L1_0 type orderings in alloys, including the formation of twinned structures characteristic of cubic-tetragonal-type phase transitions. A microscopical model of interatomic deformational interactions is suggested which generalizes a similar model of Khachaturyan for dilute alloys to the physically interesting case of concentrated alloys. The model is used to simulate A1->L1_0 transformations after a quench of an alloy from the disordered A1 phase to the single-phase L1_0 state for a number of alloy models with different chemical interactions, temperatures, concentrations, and tetragonal distortions. We find a number of peculiar features in both transient microstructures and transformation kinetics, many of them agreeng well with experimental data. The simulations also demonstrate a phenomenon of an interaction-dependent alignment of antiphase boundaries in nearly-equilibrium twinned bands which seems to be observed in some experiments.
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