Ab initio grand canonical Monte Carlo calculation of grain boundary composition and structure

The prediction of grain boundary structure has gained great attention in materials science because grain boundaries have a significant effect on material properties. However, the prediction of grain boundaries by multi-elemental systems has been difficult so far because the number of atoms and compositions are determined by a delicate energy balance between elements, which requires high calculation accuracy. Here, we have developed the ab initio grand canonical Monte Carlo (ai-GCMC) theory to grain boundaries, combining density functional theory and grand canonical Monte Carlo to overcome this problem, and apply this methodology to predict Ti segregation patterns in Ti-doped Σ13[1210](1014) α-Al2O3 grain boundaries. That is, we generated tons of Ti-segregated Al2O3 grain boundaries with DFT accuracy by GCMC and compare their free energy to determine the thermodynamically stable structure. Our prediction successfully corresponds with the experimentally observed structure, while providing precise chemical compositions. This dataset includes those Al2O3 grain boundaries generated by ab initio GCMC.

Methods
All energy evaluations of grain boundaries were conducted using VASP software.