Equivalence of the equilibrium and the nonequilibrium molecular dynamics methods for thermal conductivity calculations: From bulk to nanowire silicon

Abstract

Molecular dynamics simulations play an important role in studying heat transport in complex materials. The lattice thermal conductivity can be computed either using the Green-Kubo formula in equilibrium MD (EMD) simulations or using Fourier's law in nonequilibrium MD (NEMD) simulations. These two methods have not been systematically compared for materials with different dimensions and inconsistencies between them have been occasionally reported in the literature. Here we give an in-depth comparison of them in terms of heat transport in three allotropes of Si: three dimensional bulk silicon, two-dimensional silicene, and quasi-one-dimensional silicon nanowire. By multiplying the correlation time in the Green-Kubo formula with an appropriate effective group velocity, we can express the running thermal conductivity in the EMD method as a function of an effective length and directly compare it with the length-dependent thermal conductivity in the NEMD method. We find that the two methods quantitatively agree with each other for all the systems studied, firmly establishing their equivalence in computing thermal conductivity. arXiv:1805.00269v1 [physics.comp-ph] 1 May 2018

Finite-size effect of the thermal conductivity in one dimensional chain

“…where α 1 =1/κ 0 , and β 1 =2λ 1 /κ 0 . In this case 1/κ dependent on 1/L linearly and the slope is β 1 , which is consistent with MD simulations [29] and experimental results [23]. While in the case of L = l(ω) , the thermal conductivity can be approximated as…”

“…The calculation shows that 1/κ dependent on 1/L linearly under the condition of L l w  ( )and/or L l w  ( ), the relation has been identified and extrapolated to general cases [28,29,[39][40][41][42][43][44][45][46]. However, in our study, the slops (as well as the intercepts) of the two limit cases are not equal, with ).…”

“…At time t, the existing probability of a ω phonon that exists at zero time satisfies [56] where t w ( )is the lifetime of the ω phonons. The mean free path relate to the lifetime as follows [17,29,38]…”

“…However, Sellan et al [17] reported that the relation is hold only if the size of the sample is larger than a critical length, and they expanded 1/κ with Taylor's series of 1/L. Nevertheless, recent studies show [28,29] that neither the linear dependence nor the Taylor's expansion (up to the second power) can be extrapolated to all the scenarios. The problem is still not fully appreciated and more investigations are needed.…”

“…Qualitatively, it is easy to see that the rapid nonlinear temperature drops [22,29,30,46] in boundary layers are chief reasons for the decrease of thermal conductivities with decreasing system size. As a result, a smaller temperature gradient in the middle regions, a smaller heat current, and a smaller thermal conductivity than ideal cases emergence.…”