Direct calculation of modal contributions to thermal conductivity via Green–Kubo modal analysis

Abstract

We derived a new method for direct calculation of the modal contributions to thermal conductivity, which is termed Green-Kubo modal analysis (GKMA). The GKMA method combines the lattice dynamics formalism with the Green-Kubo formula for thermal conductivity, such that the thermal conductivity becomes a direct summation of modal contributions, where one need not define the phonon velocity. As a result, the GKMA method can be applied to any material/group of atoms, where the atoms vibrate around stable equilibrium positions, which includes non-stoichiometric compounds, random alloys, amorphous materials and even rigid molecules. By using molecular dynamics simulations to obtain the time history of each mode's contribution to the heat current, one naturally includes anharmonicity to full order and can obtain insight into the interactions between different modes through the cross-correlations. As an example, we applied the GMKA method to crystalline and amorphous silicon. The modal contributions at each frequency result from the analysis and thereby allow one to apply a quantum correction to the mode heat capacity to determine the temperature dependence of thermal conductivity. The predicted temperature dependent thermal conductivity for amorphous silicon shows the best agreement with experiments to date. The GKMA method provides new insight into the nature of phonon transport, as it casts the problem in terms of mode-mode correlation instead of scattering, and provides a general unified formalism that can be used to understand phonon-phonon interactions in essentially any class of materials or structures where the atoms vibrate around stable equilibrium sites.

Thermal conductivity decomposition in two-dimensional materials: Application to graphene

“…Usually, quantum corrections as applied in MD simulations only account for the quantum specific heat of the phonons, but not the quantum effects in the dynamics. This is also the case for some recently proposed mode-by-mode quantum correction methods in both EMD [34,35] and NEMD [61] simulations. Applying quantum corrections in this way only makes the results deviate more from lattice dynamics calculations.…”

“…However, when used in their traditional form, little insight can be gained regarding the underlying transport * brucenju@gmail.com mechanisms. There have been intensive efforts in developing MD-based methods for studying spectrally decomposed properties [25][26][27][28][29][30][31][32][33][34][35], but most of them are targeted for general materials. One exception is the method by Gill-Comeau and Lewis [34], where the total thermal conductivity is decomposed into a single-particle component and a collective one, the latter being crucial to materials in which the nonresistive normal (non-umklapp) scattering is important, which is the case for graphene [10,14,15].…”

Rethinking phonons: The issue of disorder

“…[1][2][3] Each step in vibrational mode energy is then thought of as a quasi-particle termed a phonon, and the theory describing their transport is known as the phonon gas model (PGM). [1][2][3][4][5][6][7][8][9] The PGM was largely born out of the types of vibrations that would exist in an infinitely large, pure, homogeneous crystal (IPHC). In such a system, one can solve the equations of motion in the harmonic limit and find that all solutions correspond to plane wave modulated vibrations, as a result of the periodicity.…”

“…The detailed formulation is given in previous work by Lv and Henry, 4 but in the end the heat flux associated with each mode is calculated by substituting the modal velocity into heat flux operator,…”

Rayleigh waves, surface disorder, and phonon localization in nanostructures

“…At higher frequencies, the participation ratios differ little between free and fixed BCs. While it is hard to definitively prove a connection between localization and conductivity, it is widely believed that localized modes contribute less to the conductivity than delocalized modes [35,[94][95][96].…”