The Monte Carlo simulation of ordering kinetics in Ni-base superalloys

The Monte Carlo method was applied to the simulation of temporal evolutions of atomic arrangement in Ni-base superalloys. The ordering kinetics was controlled by direct exchange of a randomly selected single atom with one of its neighbouring atoms. The formation of γ′ phase γ′/γ equilibrium and substitutional behaviours of alloying elements were predicted by the model. The reductions of total energy normalized by initial energy by ordering are about 3% for superalloys CMSX-4 and about 2% for TMS63. The formation and coarsening rates of γ′ phase in CMSX-4 are higher than those in TMS63. The size distribution profiles for CMSX-4 and TMS63 approach time-invariant profiles. The variations of calculated phase composition of γ′ and γ phases of CMSX-4 and TMS63 with time are not significant. The enrichment of Al, Ti and Ta in γ′ phase and Co and γ phase is observed. Cr is partitioning into both γ′ and γ phases. This qualitatively agrees with the phase analysis of Ni-Al-Ti ternary alloys by cluster variation method. The variations of calculated concentration of alloying element in Ni and Al sublattices of γ′ phase in CMSX-4 and TMS63 with time are not significant. The preferential substitutions of Ti, Mo and Ta in Al sublattice and Co in Ni sublattice are predicted. Cr is entering into both Ni and Al sublattices. The tendency of site occupation predicted by the simulation is consistent with the classification given by Enomoto and Harada. The Monte Carlo simulation results on site occupancies of alloying elements of CMSX-4 and TMS63 are in good agreement with those observed by atom probe FIM analysis and then calculated by the cluster variation method except for Ni concentration in the Al sublattice.