Temperature effect on the phonon dispersion stability of zirconium by machine learning driven atomistic simulations

Abstract

It is well known that conventional harmonic lattice dynamics cannot be applied to dynamically unstable crystals at 0 K, such as high temperature body centered cubic (BCC) phase of crystalline Zr. Predicting phonon spectra at finite temperature requires the calculation of force constants to the third, fourth and even higher orders, however, it remains challenging to determine to which order the Taylor expansion of the potential energy surface for different materials should be cut off.Molecular dynamics, on the other hand, intrinsically includes arbitrary orders of phonon anharmonicity, however, its accuracy is severely limited by the empirical potential field used.Recently, machine learning algorithms emerge as a promising tool to build accurate potentials for molecular dynamics simulation. In this work, we approach the problem of predicting phonon dispersion at finite temperature by performing molecular dynamics simulations with machine learning-driven potential fields. We developed Gaussian approximation potential models for both the hexagonal closed-packed (HCP) phase and the body centered cubic (BCC) phase of Zirconium crystals. The developed potential field is first validated with static properties including energyvolume relationship, elastic constants and phonon dispersions at 0 K. Molecular dynamics

Gaussian Process Regression for Materials and Molecules

“… 314 The prediction of thermal properties for crystals in the GAP framework was exemplified for zirconium. 315 Two separate studies discussed the thermal properties of crystalline, diamond-type silicon. 196 , 316 A separate potential was fitted to describe the thermal conductivity in silicene.…”

Predicting interfacial thermal resistance by machine learning

“…Xin Qian et al developed Gaussian approximation potential models for analyzing the phonon dispersion stability. 5 Shenghong Ju et al designed the Si/Ge interfacial structure for controlling heat conduction through atomistic Green's function and Bayesian optimization. 6 Masaki Yamawaki et al used Bayesian optimization for multifunctional structural design of graphene nanoribbons for thermoelectric materials.…”

Effect of Nonequilibrium Transient Electronic Structures on Lattice Stability in Metals: Density Functional Theory Calculations

“…Phonon dispersion with quasi-harmonic approximation might not be persuasive, especially for cases far away from equilibrium. Focusing on the crystal instability and phonon hardening [46,51,65,[69][70][71] cases, we plotted the potential energy surface (PES) of Al and Cu in the normal coordinates for the transverse acoustic (TA) and longitudinal acoustic (LA) modes at the high-symmetry point L( 12 , 1 2 , 1 2 ) in the first Brillouin zone to include anharmonicity effect. The scaling factor Q 1 of the lowest TA mode and the scaling factor Q 2 of the LA mode are applied in the calculation, and the PES is a function of scaled coordinates E = E(Q 1 , Q 2 ); we do not show the second-lowest TA mode because it is degenerate with the lowest TA mode.…”

“…During this period, the lattice temperature is lower than the electron temperature. By calculating phonon dispersion, we can understand lattice stability and predict the macroscopic thermal properties, which are dependent on the microscopic description of ionic vibrational dynamics [46]. The calculation is usually performed using density functional perturbation theory (DFPT) [47] or finite displacement method [48].…”

“…In addition, electronic structures, potential energy surface (PES), and formation enthalpies, etc. are also helpful tools to study lattice stability [46,49,50]. In addition to the nonequilibrium between ions and electrons, the electronic subsystem also moves away from equilibrium because of the excitation process.…”