Neural-network-backed effective harmonic potential study of the ambient pressure phases of hafnia

Abstract

Phonon-based approaches and molecular dynamics are widely established methods for gaining access to a temperature-dependent description of material properties. However, when a compound's phase space is vast, density-functional-theory-backed studies quickly reach prohibitive levels of computational expense. Here, we explore the complex phase structure of HfO2 using effective harmonic potentials based on a neural-network force field (NNFF) as a surrogate model. We detail the data acquisition and training strategy that enable the NNFF to provide almost ab-initio accuracy at a significantly reduced cost and present a recipe for automation. We demonstrate how the NNFF can generalize beyond its training data and that it is transferable between several phases of hafnia. We find that the thermal expansion coefficient of the low-symmetry phases agrees well with experimental results, and we determine the P¯43m phase to be the favorable (stoichiometric) cubic phase over the established Fm¯3m. In contrast, the experimental lattice constants of the cubic phases are substantially larger than what is calculated for the corresponding stoichiometric phases. Furthermore, we show that the stoichiometric cubic phases are unlikely to be thermodynamically stable compared to the tetragonal and monoclinic phases and hypothesize that they exist only in defect-stabilized forms.