Relaxons Heat Up Thermal Transport

Abstract

T hermal transport—the flow of energy in the form of heat—is ubiquitous in engineered and natural sys-tems. Managing it efficiently is critical for increasing the performance and lifetime of electronic circuitry, energy-conversion devices, and living organisms. In metals, heat is mainly carried by free electrons, whereas in electri-cally insulating solids, it is transported by atomic vibrations. Andrea Cepellotti and Nicola Marzari from the Swiss Fed-eral Institute of Technology in Lausanne, Switzerland, now propose [1] a theoretical framework for thermal transport in crystalline electrical insulators that applies consistently to a range of two-and three-dimensional materials. In electrically insulating, or dielectric, crystals, all atoms are at regular positions in a periodic lattice. To model thermal transport in these materials, it is convenient to change the coordinate frame from the localized positions of the individual atoms to a set of delocalized plane waves. The frequencies and other properties of these plane waves, which are called phonon modes, can be obtained from lattice dynamics calculations. In a quantum physics formulation, the phonon modes are harmonic oscillators whose energies are quantized and carried by particles—phonons—that are described by Bose-Einstein statistics. For decades, phonons have formed the basis of our under-standing of thermal transport in dielectric crystals. In these materials, thermal conductivity—which dictates how much heat will flow through an object when it is exposed to a tem-perature difference—results from two processes: intrinsic scattering between phonons due to atomic vibrations at fi-nite temperature, and disruptions to the periodic lattice such as interfaces and point defects. The most common model of phonon scattering is the relaxation time approximation (RTA), which simplifies the solution of the complicated Boltzmann transport equation for thermal conductivity. Un-der the RTA, the phonons are imagined as particles of a gas described using kinetic theory. The population of a phonon mode perturbed from thermal equilibrium by scattering is assumed to decay, or relax, exponentially back to that of an equilibrium population comprising all other phonon modes.