The experimental investigations of "order-order" kinetics in Ni_{3} Al-based L1_{2}-ordered intermetallic compounds revealed the relaxation curves composed of two parallel processes considerably differing in relaxation rates. A simple Ising-type model based on a vacancy mechanism of atomic jumps was used to carry the Monte Carlo simulations of long-range-order relaxations in a binary A_{3}B system with L1_{2}-type superstructure. The simulated relaxation curves fitted weighted sums of two exponentials with significantly different relaxation times. It was found out that the fast relaxation process is controlled by the dynamics of the minority B-atom jumps.
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