Untangling high-temperature thermal expansion and lattice thermal conductivity behavior of vanadium using machine-learned molecular dynamics

Vanadium metal is extensively used in modern technology, especially in the alloy and steel industry; it exhibits anomalous thermal expansion behavior across the entire temperature regime. Here, we extensively investigate the phonon anharmonicity contributed by volume change (implicit anharmonicity) and thermal amplitude (explicit anharmonicity) and their impact on thermal expansion and thermal transport in vanadium up to 2000 K, close to the melting temperature. We compared the different methods to evaluate the phonon anharmonicity, namely, the quasiharmonic approximation (QHA), temperature-dependent effective potential (TDEP) method, and machine-learned force-field-based molecular dynamics (MLMD) simulations. At 300 K, QHA overestimates the thermal expansion coefficient by $\ensuremath{\sim}20%$, while TDEP provides an excellent description of the experimental data. This reveals a significant explicit anharmonicity at room temperature. At higher temperatures, the experimental thermal expansion coefficient continues to rise up to twice the QHA estimates, indicating significant anharmonicity. However, TDEP underestimates the experimental observations, as it only includes low orders of anharmonicity. MLMD, which includes all the anharmonic effects, successfully explains the anomalous expansion behavior over 500--2000 K. It is expected that the electronic entropy and the electron-phonon interaction would influence the thermal expansion, but their effect appears to be small. We used MLMD to calculate the spectral energy density of phonons up to 2000 K, which revealed small phonon shifts but large broadening. Above $\ensuremath{\sim}2000\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, MLMD captures the melting and reproduces the experimental volume increase on melting. We have also calculated the lattice thermal conductivity using the TDEP-based third-order-perturbation method and the MLMD-based Green-Kubo method, over 300--1500 K, which includes a higher order of anharmonicity. This brings out the important contribution from the four and higher orders of phonon anharmonicity to the lattice thermal conductivity.