Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Xiulin Ruan

Committee Chair

Xiulin Ruan

Committee Member 1

Xianfan Xu

Committee Member 2

Yong P. Chen


The prediction of spectral phonon relaxation time, mean-free-path, and thermal conductivity can provide significant insights into the thermal conductivity of bulk and nanomaterials, which are important for thermal management and thermoelectric applications. We perform frequency-domain normal mode analysis (NMA) on pure bulk argon and pure bulk germanium. Spectral phonon properties, including the phonon dispersion, relaxation time, mean free path, and thermal conductivity of argon and germanium at different temperatures have been calculated. We find the dependence of phonon relaxation time τ on frequency ω and temperature T vary from ~ω-1.3 to ~ω-1.8 and ~T-0.8 to ~T-1.8 for argon, and from ~ω-0.6 to ~ω-2.8 and ~T-0.4 to ~T-2.5 for germanium. The predicted thermal conductivities are in reasonable agreement with those obtained from the Green-Kubo method.

We show, using both analytical derivations and numerical simulations, that the eigenvectors are necessary in time-domain NMA but unnecessary in frequency-domain NMA. The function of eigenvectors in frequency-domain NMA is to distinguish each phonon branch. Furthermore, it is found in solids not only the phonon frequency but also the phonon eigenvector can shift from harmonic lattice profile at finite temperature, due to thermal expansion and anharmonicity of interatomic potential. The anharmonicity of phonon eigenvector, different with that of frequency, only exists in the materials which

contain at least two types of atoms and two different interatomic forces. Introducing anharmonic eigenvectors makes it easier to distinguish phonon branches in frequency-domain NMA although does not influence the results. For time-domain NMA, anharmonic eigenvectors make the results more accurate than harmonic eigenvectors.

In addition, the phonon spectral relaxation time of defective silicon is calculated from frequency-domain NMA based on molecular dynamics. We show that the thermal conductivity k predicted from this approach is in excellent agreement with the Green-Kubo method. We find that the Matthiessen's rule that combines the intrinsic phonon scattering and defect scattering to yield total phonon scattering rate is not accurate in defective silicon. The defect scattering rate itself is small but causes large increase in the total scattering rate, due to the strong interplay between these phonon-phonon and phonon-impurity scatterings. This finding successfully explains why a small concentration of defects causes large reduction in k. The Mattheissen's rule is found to over-predict k of Ge-doped and mass-doped silicon bulks by a factor of 2~3, and C-doped and vacancy-doped silicon bulks by a factor of 3~8 at 300 K. Furthermore, the phonon scattering caused by the changing the interatomic bonds, often ignored, is found to be not negligible. Our results provide new physical insight into thermal transport in defective materials as well as other perturbed systems, and offer important guidance in nanoscale thermal predictions and applications.