Phonon-Phonon Interactions in Highly Anharmonic Systems

Citation

Ladygin, Vladimir Vladimirovich (2025) Phonon-Phonon Interactions in Highly Anharmonic Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/sjpe-v132. https://resolver.caltech.edu/CaltechTHESIS:05312025-030423243

Abstract

The phonon, a quantum of atomic vibrations, is a core ingredient in the description of materials’ behavior at both high and low temperatures. A harmonic theory of lattice dynamics treats phonons as independent, noninteracting normal modes with long lifetimes. The proper description of phenomena in solids requires the phonons to interact depending on temperature, or in other words, to act anharmonically. The phonon interaction in highly anharmonic crystals can result in intermodulation and an additional coherent scattering intensity at frequencies of the sums and differences of classical normal modes. At low temperatures, anharmonic interaction is triggered by nuclear quantum effects of zero-point motion, which can be observed as intermodulation and negative thermal expansion (NTE). In the thesis, I expand the general understanding of intermodulation phenomena using computational and experimental methods by adding missing parts expected in the theoretical intermodulation picture, such as phonon second harmonic generation and nuclear quantum intermodulation.

The phenomenon of second harmonic generation (SHG) was found for phonons in anharmonic NaBr by inelastic neutron scattering. The temperature dependence of this phonon SHG was measured from 300 K to 650 K. At 300 K the second harmonic (SH) is seen as a high-energy branch around 33 meV, nearly independent of Q. The temperature effective potential (TDEP) method and classical molecular dynamics (MD) simulation with machine learning interatomic potential were able to reproduce the SH, and showed that SHG occurs with the flat transverse optical (TO) phonon branch. A classical model of a nonlinear medium explains the intensity and lifetime of the SH, compared to those of the TO modes. Also successful was a quantum model based on the Heisenberg-Langevin equation for interacting phonons coupled to a thermal bath, which also predicts a spectral distribution of the SH. The measured temperature dependence of the intensity of the second harmonic showed that it follows the Planck distribution of a one-phonon quasiparticle, and not two TO phonons.

The anharmonic behavior of phonons and thermal expansion of hexagonal zinc were studied from 15 to 690 K by inelastic neutron scattering (INS) and ab initio simulations. Phonon spectra were measured for Q-points over the full Brillouin zone, giving the phonon density of states (DOS), and dispersions along high-symmetry directions. The dispersions were crisp at 15 K, but diffuse intensity was observed at energies above them. The dispersions broadened with temperature, T, and the diffuse intensity grew relatively stronger. This diffuse intensity appeared in all INS measurements and simulations, except for classical molecular dynamics at 15 K. The TDEP method was used to calculate the free energy and thermal expansion with the nuclear quantum effect from zero-point vibrational dynamics. For T < 100 K the nuclear quantum effect was essential for obtaining the negative thermal expansion, and path integral molecular dynamics (PIMD) was particularly effective for obtaining the negative thermal expansion in the basal plane. A Heisenberg-Langevin model for interacting phonons coupled to a thermal bath was able to reproduce the shape and intensity of the diffuse spectral features.

Thesis Files