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.
Thermal Conductivity in Glassess: Fluid Dynamics Extrapolation
The theory of thermal transport in crystalline and disordered solids has witnessed a major advancement in the past few years. However, the numerical simulation of heat transport in glasses remains a formidable task, because it requires the use of large finite models for the bulk systems, comprising up to several thousand atoms. The spurious crystalline order introduced by the use of periodic boundary conditions in the simulation of finite glass models results in unphysical long-wavelength features in their transport properties. These issues call for a method able to efficiently and accurately extrapolate to infinite size the value of the thermal conductivity of aperiodic solids, without the need to artificially introduce nonphysical normal modes, which may lead to a gross overestimate of the final result. In this work, Alfredo Fiorentino et al. from Scuola Internazionale Superiore di Studi Avanzati, Italy, reported a method, which they dubbed hydrodynamic extrapolation, able to lift these problems through a combination of two ingredients that can be inexpensively computed from finite models of moderate size: one is the quasi-harmonic Green-Kubo (QHGK) approximation contribution of diffuson and locons, and the other being an effective low-frequency model for propagons. They developed an effective model for the low-frequency excitations in amorphous solids that allows one to accurately compute the bulk limit of the thermal conductivity from glass models of moderate size. Their method stands on a combination of the QHGK with various ideas that have been floating around in the literature and naturally accounts for the interplay of anharmonicity and disorder in determining the transport properties of glasses. The resulting protocol gets around the need for mock crystalline models for the glass, which introduce spurious modes whose group velocities bear little physical meaning. They have tested their model on three paradigmatic glassy materials, aSiC, aSiO2, and aSi, which display different convergence properties to the bulk limit. Their work underscores their findings for realistic models of paradigmatic glassy materials.
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