Heat conduction of inhomogeneous solid material: phonon analysis and application to thin films

我们发展了一种新的晶格振动数值分析技术，以研究固体中振动的寿命和平均自由程，以研究非金属固体的导热系数。这项技术利用小波变换来分析通过分子动力学模拟获得的原子位置的时间序列或空间数据。将原子数据分解成不同的小波层，计算每一层的自相关函数。根据自相关函数的衰减，估算每一级在时间分析情况下的振动寿命，或在空间分析情况下的平均自由程。与通常的傅里叶变换技术相比，该技术具有以下优点：(1)寿命和平均自由程的概念更加清晰，(2)寿命或平均自由程的模式依赖关系更容易估计。我们将这一技术应用于不同温度下的简单面心立方晶体、晶体混合物和非晶态体系，发现估算的导热系数与非平衡分子动力学模拟的直接估算相当吻合。因此，基于小波变换的晶格振动分析方法对于表征具有微纳尺度结构的固体材料的热学性质是非常有用的。

We have developed a novel numerical technique of lattice vibration analysis in order to study the lifetime and the mean free path of vibration in solids for the purpose of investigating thermal conductivity of non-metallic solids. This technique utilizes a wavelet transformation to analyze time-sequential or spatial data of atomic positions obtained with molecular dynamics simulations. The atomic data are decomposed into different wavelet levels, and the autocorrelation function at each level is calculated. From the damping of the autocorrelation functions, the vibration lifetime in case of temporal analysis, or the mean free path in case of spatial analysis is evaluated for each level. In comparison with the usual Fourier transformation technique, the technique developed in this research has advantages that (I) the concepts of 'lifetime' and 'mean free path' are clearer, and (ii) mode-dependence of the lifetime or the mean free path is estimated more easily. We have applied this technique to a simple FCC crystal at various temperatures, crystal mixtures, and amorphous systems, and found that the estimated thermal conductivity is in fair agreement with direct estimation of non-equilibrium molecular dynamics simulations. Thus, we conclude that the lattice vibration analysis with the wavelet transformation technique is useful to characterize the thermal properties of solid materials with micro/nano-scale structure.