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An aluminum pot on the stove melts at 660 degrees Celsius — everyone knows that. But what happens if you heat aluminum a hundred times hotter? The liquid starts to boil, and here's the puzzle: at what exact temperature does that happen? Answers in scientific papers have varied by nearly 4000 degrees, as if arguing whether water boils at 50 or 350 degrees.

A group of researchers decided to put an end to the discrepancy. They built a computer model in which a neural network, trained on precise quantum calculations, tracks the motion of millions of aluminum atoms. Such a model is like an experienced pastry chef who can tell from the look of the dough when it will turn into a fluffy sponge cake. First, they tested several recipes (in science, these are called density functionals) and chose the one that best reproduces the known density of liquid aluminum.

Then they "heated" the aluminum in simulations in two ways. The first was to watch at what temperature the liquid loses stability and begins to spontaneously break apart into droplets and bubbles. The second was to place liquid and vapor in the same virtual box and see at what temperature the boundary between them disappears. Both paths led to the same result: a critical temperature of 6531–6576 kelvins (about 6260–6300 °C), a density of 0.637 grams per cubic centimeter, four times lighter than water, and a pressure of 1.6 kilobars, like at a depth of 16 kilometers underground.

Now that the critical point is known to within 50 degrees, engineers can more accurately calculate laser cutting and welding of metals, and planetary scientists can model how metals behave in the interiors of distant worlds, where pressure and temperature reach extreme values.

Original abstract

as written by the authors arXiv:2604.10561

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.