Neural network trained on quantum calculations maps how gallium melts and freezes

The work

Technical · from the record

The authors trained a deep neural-network interatomic potential for gallium on density functional theory energies and forces computed for configurations drawn from enhanced-sampling simulations that spanned liquid, solid and coexisting arrangements. Running that potential, they computed the liquid–α-Ga–β-Ga–Ga-II phase diagram between 240 and 340 K and 0 and 2.6 GPa, the structure of liquid gallium, and the nucleation of α-Ga and β-Ga. The calculated liquid-α-II triple point is 280.9 K and 1.58 GPa against an experimental value of 276.2 K and 1.19 GPa, and the computed melting temperature of α-Ga is 309.5 ± 6 K against an experimental 302.9 K. From seeded molecular dynamics and classical nucleation theory they report that the nucleation barriers of the two crystal phases cross at 174 ± 3 K, with β-Ga having the lower barrier above that temperature.

How AI was used

A deep neural-network potential (DeePMD) was fitted to reproduce ab initio energies and forces for gallium so that long molecular dynamics runs could be performed at a cost far below first-principles dynamics. Training configurations were collected by first running metadynamics of α-Ga nucleation with a classical empirical potential, then recomputing energies and forces for the extracted configurations with DFT (LDA functional, CP2K Quickstep, 600 Ry cutoff, 144 or 160 atoms per cell), and training a network of five hidden layers with 240, 120, 60, 30 and 10 neurons using the ADAM optimizer with a learning rate decaying from 1e-3 to 1e-5 on a total of 28,000 configurations. The procedure was iterated: an intermediate potential was used to run isothermal–isobaric nucleation simulations of α-Ga, β-Ga and Ga-II, and then multithermal–multibaric simulations, whose configurations were relabelled with DFT and used to retrain, yielding a potential intended for 150–340 K and 1 bar to 2.6 GPa. The resulting potential then supplied the forces for all subsequent simulations: variationally enhanced sampling multithermal–multibaric runs driven by SOAP-based per-atom crystallinity collective variables to obtain liquid–solid free energy differences and coexistence lines, well-tempered metadynamics nucleation runs in 144-, 2400- and 2560-atom systems, and seeding runs started from five extracted nuclei per phase to locate critical nucleus sizes. Barriers, interfacial free energies and rates were then obtained from classical nucleation theory expressions applied to those simulation outputs.