Structure and Thermal Transport in Disordered Materials: Molecular Dynamics Simulation and Analysis with the Wavelet Transform

The disordered atomic structure of alloys and glasses hinders the development of theoretical models of thermal transport through them, as many of the assumptions used for crystals, which are ordered, are no longer valid. The vibration of atoms carries most of the heat in semiconductors and insulators, whether they be disordered materials or crystalline. Yet because the normal modes of vibration are inherently non-localized, broadband, and interact with each other in complex ways, directly observing their behavior in either experiments or simulations poses a major challenge. Attempting to answer questions like, “how does the phonon population interact with or change near an interface?” adds further complexity. Classical molecular dynamics simulation offers a means to study alloys and glasses by explicitly modeling the disordered arrangement of atoms within “virtual experiments.” Furthermore, molecular dynamics simulations implicitly contain everything there is to know about the vibrational transport through them, and so the challenge becomes one of developing post-processing techniques capable of extracting the desired information on thermal transport.

In this work, I develop the wavelet transform as a tool to analyze molecular dynamics simulations to extract the localized—with respect to both location and time—dynamics of vibrational heat carriers in bulk crystals, interfacial systems, and glasses. Three types of simulations developed with the wavelet transform in mind may yield the following: 1) visualization of phonon wave-packets undergoing anharmonic decay and scattering with an interface, 2) steady-state phonon populations versus position during non-equilibrium thermal transport across an interface in a 1-D chain, and 3) ballistic-diffusive transport of vibrational energy in response to localized heating and transient decay of thermal energy in a glass. Using the newly developed simulation and analysis technique for glasses, I demonstrate its efficacy for calculating the frequency-dependent vibrational diffusivity of amorphous silicon and silica. The results for amorphous silicon agree with the Allen-Feldman theory but the method has two advantages: it scales more efficiently with the number of atoms, requiring only O(N) instead of O(N^3) computation time; and the bond force constants are not required. Lastly, using molecular dynamics simulation, I decouple the short-range order from the long-range order in a model of SiGe alloy and find that the short-range order accounts for the entire change of the thermal conductivity upon ordering.