Finite-temperature properties of NbO 2 ${\text{NbO}}_{2}$ from a deep-learning interatomic potential

Using first-principles-based machine-learning potential, molecular dynamics (MD) simulations are performed to investigate the micro-mechanism in phase transition of ${\text{NbO}}_2$. Treating the DFT results of the low- and intermediate-temperature phases of ${\text{NbO}}_2$ as training data in the deep-learning model, we successfully constructed an interatomic potential capable of accurately reproducing the phase transitions from low-temperature (pressure) to high-temperature (pressure) regimes. Notably, our simulations predict a high-pressure monoclinic phase (>14 GPa) without treating its information in the training set, consistent with previous experimental findings, demonstrating the reliability of the constructed interatomic potential. We identified the Nb-dimers as the key structural motif governing the phase transitions. At low temperatures, the displacements of the Nb-dimers drive the transition between the $I{4}_1/a$ ($\alpha$-${\text{NbO}}_2$) and $I{4}_1$ ($\beta$-${\text{NbO}}_2$) phases, while at high temperatures, Nb ions are prone to being equally distributed and the disappearance of Nb-dimers leads to the stabilization of a high-symmetry $P{4}_2/mnm$ phase. These findings elucidate the structural and dynamical mechanisms underlying the structural properties of ${\text{NbO}}_2$ and highlight the utility of combining DFT and deep potential MD methods for studying complex phase transitions in transition metal oxides.