Computational Methods for Studying Phonon Dynamics

Abstract

In solids and molecules, atoms vibrate about their respective equilibrium positions at finite temperature. This thermal motion can be understood as a superposition of the structure’s normal modes, often termed phonons, which are collective motions of atoms vibrating at certain frequencies. These vibrational modes play important roles in a variety of material properties and physical phenomena such as chemical reactions, phase transitions, mass/ion diffusivity, thermal conductivity, electrical conductivity, and any property which is affected by atomic vibration. It is therefore important to study the dynamics and energy transfer processes of normal modes in a variety of systems, so that we may better understand and engineer a wide variety of phenomena. Traditional methods for studying molecular vibrations do not represent a complete framework for studying phonon transport in all solids, however, because of two problems.

Problem 1: Traditional interatomic potentials cannot accurately model phonon/vibrational properties.

Problem 2: The traditional physical picture of heat transfer by phonons is limited to crystalline solids.

We formulate five questions to investigate which will help solve these problems. First, we investigate Question 1: Why do traditional potentials fail for phonons? Answering this question is the first step in solving Problem 1. We then apply the knowledge gained here to answer Question 2: How to make fast & accurate potentials for phonons? While the answers to these first two questions present a major contribution to Problem 1, they do not provide a physical picture. To solve Problem 2, we begin with Question 3: How do modes interact? Here, we investigate a physical model that allows phonon interactions to be simulated. From there, we propose Question 4: How do modes transport heat? Here we seek an understanding of how modes transport heat in disordered solids. Finally, using the knowledge gained here, we investigate Question 5: What determines temperature-dependent thermal conductivity behavior in disordered solids? Traditional pictures of phonon transport based on kinetic theory have difficulties explaining the constant or even increasing thermal conductivity as a function of temperature for disordered solids, so explaining this phenomenon is the first step in realizing a new physical picture.