Accurate and flexible neural-network interatomic potential for mixed materials: TixZr1−xO2 from bulk to clusters and nanoparticles

Abstract

Many interesting systems, such as interfaces, surfaces, grain boundaries, and nanoparticles, contain so many atoms that quantum-mechanical atomistic simulations become inconvenient or outright impossible. It is therefore desirable to develop accurate and flexible general-purpose interatomic potentials to make it possible to explore the potential energy surface of such structures. In this work we generate a neural-network potential through charge equilibration technique (CENT) for ${\text{Ti}}_{x}{\text{Zr}}_{1\ensuremath{-}x}{\text{O}}_{2}$ with $0\ensuremath{\le}x\ensuremath{\le}1$. Optimized symmetry functions for multicomponent systems make it possible to train the potential on less than 10 000 diverse structures containing different cation ratios $x$, from pure ${\text{TiO}}_{2}$ to ${\text{ZrO}}_{2}$, in free and periodic boundary conditions in the framework of density functional theory. The combination of the CENT potential with the symmetry functions generates a flexible and reliable method to reproduce the complexity of the energy landscape of these mixed materials with different boundary conditions at zero pressure. The reliability and transferability of the potential are verified by calculating some properties of bulk and slab configurations. Moreover, in order to investigate the performance of potential for different crystal phases and cluster configurations which are not included in our training data set, we performed a crystal structure search by minima hopping method. Beside reproducing known results in agreement with DFT calculations, we discovered novel crystal structures for bulk ${\text{TiZr}}_{3}{\text{O}}_{8}$ and ${\text{TiZrO}}_{4}$, as well as for small clusters and ${\text{ZrO}}_{2}$ nanoparticles.