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

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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.