玻璃的导热率：流体动力学外推

晶体和非晶固体的热传导理论近年来取得了重大进展。然而，在玻璃中进行热传导的数值模拟仍然是一项艰巨的任务，因为它需要对大型系统使用大型有限模型，包括多达数千个原子。在对有限玻璃模型进行模拟时，由于周期性边界条件引入了人工晶体序，导致了其传输性质中出现了非物理的长波特征。

为处理这些问题，人们需要一种能够有效且准确地对非周期性固体的热导率值进行无限尺寸外推的方法，而不需要人为引入非物理的正态模式（这可能会严重高估最终的结果）。

来自意大利国际高级研究学院的 Alfredo Fiorentino 等，展示了一种他们称为“流体动力学外推”的方法，该方法能够通过两种成分的组合来解决这些问题。这两个成分可以从中等大小的有限模型中计算得出：一个是扩散子和局部子的准谐波 Green-Kubo 近似（ QHGK ）贡献，另一个是传播子的有效低频模型。

他们开发了一种适用于非晶固体低频激发的有效模型，能够从有限大小的玻璃模型中准确计算出热导率的极限。该方法结合了 QHGK 与文献中已经存在的一些各种想法，很好地解释了非晶固体输运性质中的非谐性和无序性的相互作用。同时，作者在该方法中引入了随机模型，由于其群速度几乎没有物理意义，从而摆脱了对玻璃模拟晶体模型的需要。他们的外推技术的唯一要求是有限的样本，其大小范围可以从数百个原子到数千个原子，具体取决于材料的特性。

Fig. 4 Size scaling of the thermal conductivity for three glassy materials at different temperatures.

作者们在三种具有不同块体极限的典型玻璃材料（ aSiC 、 aSiO ₂ 和 aSi ）上测试了模型，并展示了对典型玻璃材料实际模型的发现。 作者的这一工作为准确预测非晶玻璃中热导率数值提供了重要的推动力。本文近期发布于 npj Computational Materials 9 : 157 (2023)。

Fig. 5 Thermal conductivity of aSi as a function of temperature.

Editorial Summary

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, aSiO ₂ , and aSi, which display different convergence properties to the bulk limit. Their work underscores their findings for realistic models of paradigmatic glassy materials. This article was recently published in npj Computational Materials 9 : 157 (2023).

原文Abstract及其翻译

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.

摘要 在过去的几年中，非晶固体中的热输运理论已经大大超出了 Allen-Feldman 模型的范围。基于 Green-Kubo 线性响应或维格纳传输方程产生的公式，将玻璃模型与晶体的传统玻尔兹曼动力学方法联系起来。这些方法所需的计算工作量通常按原子数的三次方进行缩放，从而严重限制了计算上可承受的玻璃模型尺寸范围。利用流体动力学论证，我们展示了如何通过一个简单的公式来克服这个问题，从中等尺寸的有限模型中推断出玻璃体积导热系数的可靠估计。我们展示了对典型的非晶材料的发现。