Thermal conductivity of glasses: first-principles theory and applications.

Abstract

Predicting the thermal conductivity of glasses from first principles has hitherto been a very complex problem. The established Allen-Feldman and Green-Kubo approaches employ approximations with limited validity-the former neglects anharmonicity, the latter misses the quantum Bose-Einstein statistics of vibrations-and require atomistic models that are very challenging for first-principles methods. Here, we present a protocol to determine from first principles the thermal conductivity <i>κ</i>(<i>T</i>) of glasses above the plateau (i.e., above the temperature-independent region appearing almost without exceptions in the <i>κ</i>(<i>T</i>) of all glasses at cryogenic temperatures). The protocol combines the Wigner formulation of thermal transport with convergence-acceleration techniques, and accounts comprehensively for the effects of structural disorder, anharmonicity, and Bose-Einstein statistics. We validate this approach in vitreous silica, showing that models containing less than 200 atoms can already reproduce <i>κ</i>(<i>T</i>) in the macroscopic limit. We discuss the effects of anharmonicity and the mechanisms determining the trend of <i>κ</i>(<i>T</i>) at high temperature, reproducing experiments at temperatures where radiative effects remain negligible.