Grain-boundary thermodynamics with artificial-neural-network potential: Its ability to predict the atomic structures, energetics, and lattice vibrational properties for Al

An artificial neural network (ANN) potential for Al, trained with density-functional-theory (DFT) data, is constructed to accurately predict lattice vibrational properties and thermodynamics of grain boundaries (GBs) in Al. The ANN potential is demonstrated to accurately predict not only atomic structures and energetics of the GBs at 0 K but also partial phonon densities of states and vibrational entropies, even for GBs absent in the training data sets. In addition, their total potential energies and atomic forces by DFT at elevated temperatures up to 800 K can also be well reproduced by molecular dynamics with the ANN potential. In contrast, a modified embedded atom method (MEAM) potential shows larger errors in phonon frequencies and atomic forces for atoms at GBs, as well as in the bulk, than the ANN potential. The MEAM potential is thus likely to be inadequate to quantitatively predict thermodynamic properties of GBs, particularly at high temperature. The present ANN potential is also applied to systematically examine thermodynamic stability of asymmetric tilt GBs. It is predicted that for the \ensuremath{\Sigma}9 system, the GB free-energy profile as a function of inclination angle exhibits a cusp at elevated temperatures, due to its larger vibrational entropies of asymmetric tilt GBs than those of \ensuremath{\Sigma}9 symmetric tilt GBs.