Uncertainty quantification of thermal conductivities from equilibrium molecular dynamics simulations

Abstract

Equilibrium molecular dynamics (EMD) simulations along with the Green-Kubo formula have been widely used to calculate lattice thermal conductivities. Previous studies, however, focused primarily on the calculated thermal conductivities, with the uncertainty of the thermal conductivities remaining poorly understood. In this paper, we study the quantification of the uncertainty by using solid argon, silicon, and germanium as model material systems, and examine the origin of the observed uncertainty. We find that the uncertainty increases with the upper limit of the correlation time, tcorre, UL, and decreases with the total simulation time, t total , whereas the velocity initialization seed, simulation domain size, temperature, and type of material have minimal effects. The relative uncertainties of the thermal conductivities, σ kx /kx,ave, for solid argon, silicon, and germanium under different simulation conditions all follow a similar trend, which can be fit with a "universal" squareroot relation, as σ kx /kx,ave = 2(t total /tcorre, UL) −0.5 . We have also conducted statistical analysis of the EMD-predicted thermal conductivities and derived a formula that correlates the relative error bound (Q), confidence level (P ), tcorre, UL, t total , and number of independent simulations (N ). We recommend choosing tcorre, UL to be 5-10 times the effective phonon relaxation time, τ eff , and choosing t total and N based on the desired relative error bound and confidence level. This study provides new insights into understanding the uncertainty of EMD-predicted thermal conductivities. It also provides a guideline for running EMD simulations to achieve a desired relative error bound with a desired confidence level and for reporting EMD-predicted thermal conductivities. arXiv:1612.05107v2 [cond-mat.mtrl-sci]

Development of interatomic potentials for the complex binary compound Sb2Te3 and the prediction of thermal conductivity

“…To minimize statistical fluctuations, we perform runs for 10 independent ensembles at every temperature. The uncertainty associated with calculation of thermal conductivity from equilibrium MD simulations has recently been quantified by Wang et al 39 who correlated the standard deviation σ κ of the predicted thermal conductivity about the average κ ave , with the total simulation time t total , HCACF correlation time length t corr and number of independent runs N as…”

A molecular dynamics study of the thermal transport in silicon/germanium nanostructures: From cross-plane to in-plane

“…For each condition, three independent simulations are performed and the average results and their standard deviations are reported. It has been shown that NEMD simulations have much smaller uncertainties than EMD simulations [28]. Whereas the temperature profiles of C1 and C9 exhibit a large temperature jump at the Si/Ge interface and at regions close to the thermal reservoirs, respectively, the temperature profile of C5 is smooth over the entire simulation domain.…”

The lower limit of thermal conductivity in multicomponent solutions of rare gas solids

“…As a consequence the RGS are ideal objects for comparing experimental data with theory. A large number of experimental [1][2][3][4][5][6][7][8][9] and theoretical [10][11][12][13][14][15][16][17][18][19] studies have been devoted to examination of their thermal conductivity. Initially, a theoretical analysis of the thermal conductivity of dielectric crystals was carried out using the Boltzmann transport equation for phonons [20].…”

“…In recent years ab initio calculations of the thermal properties of disordered systems based on the Green Cubo approach using molecular (MMD) or lattice dynamics methods have developed extensively [25][26][27]. This method makes it possible to calculate as well the thermal conductivity of ordered solids, in particular, the thermal conductivity of crystalline argon [14][15][16][17][18][19]. Using MMD and the Green-Kubo method, it was shown that the thermal conductivity of a Lennard-Jones fcc crystal of argon is described by two time constants associated with the attenuation of the autocorrelation function of the heat flow.…”