Neural network models simulate how lead titanate loses its electrical polarisation on heating

The work

Technical · from the record

Two neural-network models were fitted to SCAN density functional theory data for lead titanate: one representing the potential energy surface and one representing the local and total dipole moments. Molecular dynamics driven by these models reproduced the measured tetragonality, lattice constants, enthalpy, specific heat and polarization across the ferroelectric to paraelectric transition, with a transition temperature of 821 K about 60 K above the experimental value. The simulations showed that the average local dipole magnitude falls only slightly across the transition, from 2.1 eÅ to 1.7 eÅ, so the transition is dominated by orientational disordering, and that the system changes phase through nanoscale fluctuations distributed through the sample rather than by nucleation of a growing domain. Simulated far-infrared spectra reproduced the Raman-measured mode frequencies and showed a zero-frequency Debye relaxation feature coexisting with the soft mode near the transition temperature.

How AI was used

Static SCAN density functional theory calculations on 3x3x3 PbTiO3 supercells supplied energies, Hellmann-Feynman forces, virial tensors and, via maximally localized Wannier centroids, local and total dipole labels. A deep potential energy model and a deep dipole polarization model, both with a 6 Å spherical cutoff on the atomic environment, were trained on these labels using an active learning protocol automated with DP-GEN, with LAMMPS as the molecular dynamics engine and DeePMD-kit for training; 4432 of 5032 collected data points trained the energy model and 600 were held out, while the dipole model was trained on a reduced set of 1835 labelled points with a separate 61-point test set. A linear model with static Born charges as trainable parameters was fitted to the same dipole data for comparison. The trained models then drove all-atom NPT molecular dynamics with a 0.5 fs time step, under an added artificial hydrostatic pressure chosen to match the experimental room-temperature tetragonality, to obtain lattice constants, enthalpy, specific heat, spontaneous polarization and dielectric susceptibility for supercells of 9, 12 and 15 cells per side. Non-equilibrium trajectories started from equilibrated configurations and run at temperatures just across the transition, including a 512x16x16 supercell containing a twin domain, were used to follow local dipole configurations in real time. Far-infrared absorption spectra and total-dipole power spectra were obtained from the Fourier transforms of dipole autocorrelation functions along these trajectories, and the dipole model was also implemented as a collective variable in PLUMED for metadynamics free-energy calculations.