Hydrodynamic finite-size scaling of the thermal conductivity in glasses

Abstract

In the past few years, the theory of thermal transport in amorphous solids has been substantially extended beyond the Allen-Feldman model. The resulting formulation, based on the Green-Kubo linear response or the Wigner-transport equation, bridges this model for glasses with the traditional Boltzmann kinetic approach for crystals. The computational effort required by these methods usually scales as the cube of the number of atoms, thus severely limiting the size range of computationally affordable glass models. Leveraging hydrodynamic arguments, we show how this issue can be overcome through a simple formula to extrapolate a reliable estimate of the bulk thermal conductivity of glasses from finite models of moderate size. We showcase our findings for realistic models of paradigmatic glassy materials.

Temperature-invariant heat conductivity from compensating crystalline and glassy transport: from the Steinbach meteorite to furnace bricks

“…15 , which is in agreement with the larger '5184(G)' model discussed in the same reference). We also note that our theoretical predictions for the conductivity of vitreous silica are in agreement with the result obtained by a recent, independent work 51 . The analysis of the geometric disorder in Fig.…”

“…This is a fundamental difference compared to other, common types of disorder that break translational symmetry (e.g. compositionally disordered alloys 9,23,50 or amorphous solids 15,47,51 ), which do not allow to rigorously define a phonon band structure. In the context of Ref.…”

Thermal transport of glasses via machine learning driven simulations

“…The QHGK approximation works on crystals and glasses alike, reducing to the result of the Boltzmann Transport Equation in the former case, and-at the expense of neglecting anharmonic effects-to the Allen-Feldman (AF) model of harmonic disordered solids in the latter (Isaeva et al, 2019;Barbalinardo et al, 2020;Fiorentino and Baroni, 2023). Neglecting anharmonic effects is no trivial matter-it remarkably transforms the finite bulk thermal conductivity of a glass into an infinite quantity, thereby emphasizing the AF calculations' qualitative accuracy driven solely by size effects (Fiorentino et al, 2023a;Fiorentino et al, 2023b).…”

“…If compared with crystals, glasses present an additional complexity in numerical computations due to their inherent aperiodic nature (Fiorentino et al, 2023b). The customary application of periodic boundary conditions (PBC) to finite simulation cells, from which quantities in Eq.…”

Machine learning boosted ab initio study of the thermal conductivity of Janus PtSTe van der Waals heterostructures

“…Even with the significant acceleration afforded by the machine-learning calculation of energies and forces, ordinary BTE-based methods have limited scalability with the number of atoms in the unit cell. This has been alleviated recently by several generalizations of the formalism [16][17][18] to encompass diffusive thermal transport mediated by the coupling of non-propagating vibrational modes. These generalizations have created quantitative frameworks and calculation workflows that include diffusons (introduced by Allen and Feldmann [19]) as heat carriers in addition to phonons, and are applicable to com-plex unit cells as well as disordered systems.…”