Grain boundary segregation of Y and Hf dopants in α-Al₂O₃: A Monte Carlo simulation with artificial-neural-network potential and density-functional-theory calculation

Artificial-neural-network (ANN) interatomic potentials for Al–Y–O and Al–Hf–O systems are constructed using density-function-theory (DFT) data and combined with Monte Carlo (MC) simulations in order to predict Y and Hf segregation behavior at the ∑7(4510)/[0001] grain boundary (GB) in α-Al2O3. The ANN potentials are demonstrated to accurately predict preferential substitutional sites of not only an isolated but also multiple dopant ions. This enables us to circumvent DFT calculations for MC trial moves, thereby greatly reducing computational cost. There is a tendency that both Y and Hf ions substitute for 6-fold Al ions with elongated Al–O bonds at the GB and have coordination numbers greater than 6 after structural relaxation. This may suggest that even at the GB, Y and Hf ions prefer atomic environments in Y- and Hf-containing oxides with 7- and 8-fold coordination. Furthermore, effects of dopant species and concentrations on band-gap reduction at the GB are elucidated by analyzing partial density of states for the dopant-segregated GBs. The ANN-MC method with DFT analysis will pave the way for systematically determining atomic and electronic structures of GBs involving dopants, as demonstrated in this work.