Location of the liquid-vapor critical point in aluminum

Abstract

The precise location of the liquid-vapor critical point in aluminum has remained elusive for decades, with reported critical temperatures spanning nearly 4000 K. Here we resolve this long-standing uncertainty by combining deep potential molecular dynamics with large-scale simulations trained on high-fidelity electronic-structure data. We benchmark multiple exchange-correlation functionals against experimental liquid densities and identify PBEsol as providing the most consistent description. Using complementary approaches -- spinodal analysis of the equation of state and direct coexistence simulations with Gaussian mixture phase identification -- we converge on a critical temperature of 6531-6576 $^\circ$K, a critical density of $0.637$ g/cm$^{3}$, and a critical pressure of $1.6$ kbar. The precision of these values, with temperature uncertainties of $\sim$50 K, represents a marked improvement over previous estimates. Our framework establishes a transferable strategy for predicting critical phenomena in metals, with implications for laser ablation, shock compression, and planetary modeling under extreme conditions.