Deep inside Neptune and Uranus, temperatures and pressures are extreme enough to produce superionic water—a phase in which oxygen ions crystallize while highly mobile hydrogen ions float through interstitial spaces. Information about superionic water’s phase behavior would help planetary scientists model and understand the ice giants’ evolution, structure, and unusual magnetic fields.

Theoretical and computational studies of superionic water’s structure and stability have supplemented scarce experimental data—the phase was observed for the first time in 2019. But those have yielded limited, and sometimes contradictory, results. Now Bingqing Cheng at the University of Cambridge and her collaborators have made predictions about superionic water’s lattice structure at planetary conditions by simulating the material using machine-learning potentials (MLPs) and an artificial neural-network architecture.

Molecular-dynamics simulations include all the forces acting on all the particles. Computationally expensive, the first-principles approach is limited in the size of systems that it can tackle. Simulations that use MLPs can be performed at lower computational costs, even when modeling large systems and including nuclear quantum effects; they’re trained on accurate calculated atomic interactions in smaller systems before being applied to larger ones. By employing MLPs, Cheng and coworkers simulated thousands of atoms over nanosecond timescales, a significant improvement over the tens of atoms and picosecond timescales in first-principles simulations.

The simulations produced pressure–temperature plots that indicated the phase transitions from insulating ice to superionic water with three different lattice structures- body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal close packed (hcp). In all the cases, the hydrogen diffusion coefficient increased rapidly but smoothly across an ice–superionic water transition, consistent with an interstitial formation model.

For the expected conditions inside Uranus and Neptune, the simulations predict that deep inside each planet is a liquid–superionic water interface where temperature and pressure reach around 3000 K and 100 GPa. Chemical potentials extracted from the data show that the bcc lattice is favored at lower temperatures and pressures than the fcc one, consistent with experimental x-ray diffraction measurements. A small predicted region of bcc–fcc coexistence suggests that a thin bcc layer could exist near the liquid–superionic water interface; otherwise, the planetary conditions lie squarely in the fcc stability region.

A complicating factor, however, is that the chemical potentials of the fcc and hcp lattices are nearly identical throughout the simulations’ explored range of planetary conditions (100–800 GPa and 2000–5500 K). Both close-packed lattices are denser than a bcc lattice. The simulations suggest that over much of the explored phase space, the two close-packed lattices coexist in a layered structure. From that structure, the researchers created a diffraction pattern that can be compared with future experimental data to confirm their prediction. (B. Cheng et al., Nat. Phys., 2021, doi-10.1038/s41567-021-01334-9.)