“…In order to understand the interface properties at the atomic scale, numerous theoretical studies have been carried out, focusing mostly on well defined, typically 10 highly ordered boundaries, which can be modelled easily with periodic boundary conditions and relatively small supercells [4,5,8,6,7,9,10,11,12]. More recently, the ionic transport has been addressed by calculating migration barriers of oxygen vacancies in Al 2 O 3 grain boundaries [13,14].…”