Origin of the second peak in the mechanical loss function of amorphous silica

Abstract

The thermal noise in amorphous oxides is the limiting factor for gravitational wave detectors and other high-precision optical devices. Through the fluctuation-dissipation theorem, the thermal noise is directly connected to the internal friction (${Q}^{\ensuremath{-}1}$). Computational calculations of ${Q}^{\ensuremath{-}1}$ that use a two-level system (TLS) model have previously been performed for several coating materials, facilitating the search for coatings with lower thermal noise. However, they are based on a historical approximation made within the TLS model that treats the TLS distribution as uncorrelated, which has limited the predictive power of the model. In this paper, we demonstrate that this approximation limits the physical description of amorphous oxides using the TLS model and a fully correlated distribution must be used to calculate high-temperature behavior. Not only does using a correlated distribution improve the theoretical standing of the TLS model, calculations of ${Q}^{\ensuremath{-}1}$ using a fully correlated distribution reproduce and uncover the physical mechanisms of a second peak observed in measurements of ion-beam sputtered amorphous silica. We also explore the details of the thermal activation of TLSs and analyze the atomic transitions that contribute to ${Q}^{\ensuremath{-}1}$ in amorphous silica.