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An account is presented of our studies of the order-disorder phase transitions in KN3, RbN3, and CsN3. These are based on parameter-free interionic potentials based on the Gordon-Kim modified electron-gas formalism extended to molecular ions. We performed static structural relaxations and supercell molecular dynamics and predicted with reasonable accuracy the temperatures for the onset of the transitions. In particular, we address the question of how the N3- ions reorient to yield the transitions. We found the existence of NaCl-type high-temperature phases in disordered KN3 and RbN3 and argue that this restructuring is preempted by melting in these two systems.