Ab Initio Simulation of Heat Transport in Silica Glass

The simulation of heat transport and the estimation of thermal conductivity in glasses is of crucial importance for many technological applications, ranging from thermal insulation to semiconductor fabrication, and for the interpretation of laser damage of optical glasses. In particular, vitreous silica (a-SiO2) is one the most used and investigated materials, and serves as the basis of multicomponent silica glasses, which are usually characterised by a complex chemistry. Classical force fields have demonstrated to reproduce quite well all the structural properties of a-SiO2, but lacks a proper description of its vibrational spectrum, that instead requires first-principles simulations. The methods usually adopted to study heat transport in crystalline solids, such as the Boltzmann transport equation, cannot be applied to glasses, were the disorder makes the phonon picture break down. Instead, the Green-Kubo (GK) theory of linear response can be straightforwardly applied to obtain the thermal conductivity from the fluctuations of the heat current at equilibrium. Nonetheless, until very recently, the GK was not deemed compatible with quantum simulation techniques based on density functional theory because the concepts of energy density and current are not well defined at the atomic scale. Besides, the study of transport coefficients using the GK theory is known to require very long molecular dynamics (MD) simulations, thus making ab initio techniques unaffordable. We discuss how it is possible to overcome these two hurdles thanks to a paradigm shift based on the concept of gauge invariance of transport coefficients, and by using a novel data analysis technique based on the so-called cepstral analysis of stationary time series. These theoretical and methodological advances make the quantum simulation of heat transport in liquids and amorphous solids possible, using equilibrium ab initio molecular dynamics. By means of classical MD simulations we study the dependence of the thermal conductivity on the sample size and the quenching protocol adopted, and we show that relatively short trajectories are needed to obtain an accuracy of the order of 10% on the thermal conductivity. One sample of a-SiO2 is finally simulated with Car-Parrinello MD at four different temperatures. The resulting thermal conductivities show fairly good agreement with experimental data, and a substantial improvement with respect to classical MD results.