Discovery of zirconium dioxides for the design of better oxygen-ion conductors using efficient algorithms beyond data mining

It is important to find crystal structures with low formation (E(v)) and migration-barrier (E(m)) energies for oxygen vacancies for the development of fast oxygen-ion conductors. To identify crystal structures with lower E(v) and E(m) than those of ground-state ZrO(2), we first reoptimize the crystal structures of various oxides reported in the database, and then directly construct them using an evolutionary algorithm. For efficient searching, we employ the linearized ridge regression model for E(v) using descriptors obtained from density functional theory calculations of the unit cells and apply the predicted E(v) as a fitness value in the evolutionary algorithm. We also find a correlation between the E(v) and E(m) for the crystal structures of ZrO(2). On the basis of this correlation, we confirm that the newly constructed crystal structures, as well as certain reoptimized structures from the database, that possess low E(v) also have E(m) lower than that of ground-state ZrO(2). Our successful strategy consisting of a combination of the evolutionary algorithm, first-principles calculations, and machine-learning techniques may be applicable to other oxide systems in finding crystal structures with low E(v) and E(m).