Monte Carlo Simulation for Formation of Ti and N Atoms Nanoclusters in BCC-Fe

Abstract

The effective cluster interactions (ECIs) in the Fe-Ti-N system were evaluated using the cluster expansion method. The ECIs were estimated under two different conditions. One condition was to evaluate the ECIs based on configurational energies of ordered structures in which each volume was fully relaxed. Another one was to obtain the ECIs from the energies of the structures with each volume was fixed to that of pure Fe. Then, these interactions were utilized in the free energy calculation and Monte Carlo (MC) simulation. Two-phase separation tendency between Fe and TiN was observed in the free energy calculation and the clustering behavior of Ti and N in the Fe bcc matrix was confirmed by the MC simulation. Thus, the result strongly suggests that the i-s clustering is caused by two-phase separation.

According to the MC simulation based on the interaction energies obtained by the condition of fixed volume to pure Fe, layered shaped i-s clusters appears. On the other hand, the MC simulation based on the interaction energies in which volumes were relaxed shows sphere shaped i-s clusters. Thus, elastic constraint from Fe lattice strongly influences the shape of i-s nanoclusters in the very first stage of annealing. Furthermore, energies were compared in structure models with different coordination of N atoms around Ti atoms. The result shows that the clusters of Ti:N = 1:1 preferably form when the tetragonal distortion of the matrix is small. However, when the tetragonal distortion is large, the clusters of Ti:N = 1:3 become stable.