Searching the stable segregation configuration at the grain boundary by a Monte Carlo tree search

Non-stoichiometric structure localized at the grain boundary, namely, segregations of impurities, dopants, and vacancies, has an important effect on a broad variety of material properties. An understanding of this behavior is therefore indispensable for further material development. Although molecular dynamics simulation and a simulation combined with randomly swapping atoms and vacancies have usually been used to investigate the segregation structures, they require more than ten thousand structures and energy calculations to reach the stable configuration. Although several mathematical or informatics approaches, for example, genetic algorithm and Bayesian optimization, have been proposed to solve such combination optimization problems, they required some hyper parameters which crucially affect efficiency and huge computations to tune these parameters. Furthermore, a parallelization of the computation task is often impossible in molecular dynamics simulation and Bayesian optimization because their structures are related to each other before and after the time or simulation steps. Here, we develop a Monte Carlo tree search algorithm for grain boundary segregation and apply it to determine the stable segregation configuration of copper Σ5[001]/(210) and Σ37[001]/(750) with silver impurities. We achieved a determination of the stable configuration by searching only 1% of all possible configurations. Furthermore, we found that the search path and the number of playouts at the branch provide important insight to comprehend the background of the search. In the present case, the search path was identical to the sites with the spatially larger sites.