Phonon Anharmonicity at the Limits of Perturbation Theory

Abstract

Phonons, as the building blocks of solid-state physics, have been studied for almost one hundred years. The harmonic model is helpful when introducing the concepts and offering a basic physics picture of atomic vibrations. However, there are many properties that cannot be explained by the harmonic model or its extension to the quasiharmonic approximation (QHA), which ignores the pure temperature dependence of phonon frequencies. The rapid development of materials science requests a deep understanding of the phonon behaviors at elevated temperatures, where phonon-phonon interactions, as a main source of phonon anharmonicity, account for a number of abnormal phonon behaviors and the thermodynamical properties of many materials. In this thesis, I present the phonon anharmonicity in metals of Pd and Pt, the metallic compound FeGe2, and the polar material NaBr to show the limitation of the harmonic or QH model and the importance of taking anharmonic effects into consideration. Inelastic neutron scattering (INS) was used to measure the phonon density of states (DOS) in fcc Pd and Pt metal at temperatures from 7 K to 1576 K. Both phonon-phonon interactions and electron-phonon interactions were calculated by methods based on density functional theory (DFT) and were consistent with the measured shifts and broadenings of phonons with temperature. Contributions to the entropy from phonons and electrons were assessed and summed to obtain excellent agreement with prior calorimetric data. The QH entropy is positive for both phonons and electrons but larger for phonons. The anharmonic phonon entropy is negative in Pt, but in Pd it changes from positive to negative with increasing temperature. Phonon dispersions in a single crystal of FeGe2 with the C16 structure at 300, 500, and 635 K were measured by INS. Phonon DOS were also measured on polycrystalline FeGe2 from 325 to 1050 K, and the Fe partial DOS was obtained from polycrystalline 57FeGe2 at 300 K using nuclear resonant inelastic X-ray scattering (NRIXS). The dominant feature in the temperature dependence of the phonon spectrum is thermal broadening of high-energy modes. The energy shifts of the low- and high-energy parts of the spectrum were almost the same. DFT calculations performed with the QHA gave results in moderate agreement with the experimental thermal energy shifts, although the isobaric Gruneisen parameter calculated from the quasiharmonic model was smaller than that from measurements. The thermal broadening of the phonon spectrum and dispersions, especially at high energies, indicates a cubic anharmonicity to second order that should also induce phonon shifts. There are cancellations of different anharmonic contributions to energy shifts, giving average phonon shifts in moderate agreement to calculations with the QHA. The different parts of the large phonon contribution to the entropy are separated for FeGe2, showing modest but interpretable anharmonic contributions. All phonons in a single crystal of NaBr were measured by INS at temperatures of 10, 300 and 700 K. Even at 300 K the phonons, especially the longitudinal optical (LO) phonons, showed large shifts in frequencies, and showed large broadenings in energy owing to anharmonicity. The QHA was an unqualified failure for predicting the temperature dependence of phonon frequencies, even at 300K, and it predicted a thermal expansion that was in error by a factor of four. Ab initio computations that included both anharmonicity and quasiharmonicity successfully predicted both the temperature dependence of phonons and the large thermal expansion of NaBr. The frequencies of LO phonon modes decrease significantly with temperature owing to the real part of the phonon self-energy from explicit anharmonicity. The origin of the large cubic anharmonicity was identified with nearest-neighbor Na-Br bonds. Anharmonicity is not a small correction to the QHA predictions of thermal expansion and thermal phonon shifts, but anharmonicity dominates the behavior. New spectral features were found in phonon dispersions of NaBr at 300 K. Ab initio calculations based on anharmonic perturbation theory also showed these spectral features as many-body effects. Their physical origin is better elucidated with a Langevin model, similar that in recent work in optomechanics. The transverse optic (TO) part of the new features originates from phonon intermodulation between the transverse acoustic (TA) and TO phonons. The LO spectral features originate from three-phonon coupling between the TA modes and the TO lattice modes.