Cellular automata simulation of the ordering process in Ni–Al–Ti (Cr, Co) ternary alloys

The disorder–order transformation of three-dimensional Ni–Al–X (X = Ti, Cr, Co) ternary alloys is simulated on the atomic scale by a cellular automata (CA) method. The interaction of atom pairs and the total energy of the system are calculated using Lennard–Jones potential. The variables to be optimized in yielding a minimized energy were found to include the atomic positions, the (long- and short-range) ordering parameters, the volume fraction of the γ′ (L12) phase, and the configuration energy dependence on the number of CA steps. The results are consistent with the ordering kinetics and the atomic arrangement found by a cluster variation method (CVM).