The Limits of The Quasi-Harmonic Approximation: Anharmonicity in Germanium and the Entropy of Melting

Citation

Mudide, Shiva (2021) The Limits of The Quasi-Harmonic Approximation: Anharmonicity in Germanium and the Entropy of Melting. Senior thesis (Major), California Institute of Technology. doi:10.7907/9mn0-y471. https://resolver.caltech.edu/CaltechTHESIS:12012021-011312125

Abstract

Inelastic Neutron Scattering (INS) measurements were made at the Wide Angular-Range Chopper Spectrometer (ARCS) on Germanium at temperatures higher than what has been done before, from 296 K to 1203 K. Raw data was used to calculate the dynamic structure factor. Multi-phonon and multiple scattering events were accounted for and subtracted. These dynamic structure factors were then used to calculate single phonon density of states (DOS) for temperatures throughout the said temperature range. Thermal softening of the phonon modes was observed. The softening was quantitatively characterized with several Gruneisen parameters to better understand the effects phonon anharmonicity in Germanium. We find the quasi-harmonic approximation alone cannot explain the large phonon softening. The vibrational entropy contribution to the total entropy was also determined. We find that the vibrational entropy makes up almost all of the total entropy in Germanium, even at elevated temperatures.

We also conduct melting experiments to ensure containment of Si, Bi, and Pb in quartz ampules. These metals will be heated through their melting points at ARCS in the near future in order to determine the vibrational entropy contribution to the latent heat of melting. Furthermore, we write an algorithm based on the work of Sivia to determine the number of phonon modes there is the maximum evidence for in any given phonon DOS.

Thesis Files