Comparison and validation of the lattice thermal conductivity formulas used in equilibrium molecular dynamics simulations for binary systems

摘要

The Green-Kubo relations have been widely utilized in equilibrium molecular dynamics (MD) simulations to evaluate the lattice thermal conductivity (TC) of condensed matter. In previous studies, however, three different formulas have been used to calculate the TC. In the present study, focusing on binary systems, we investigate differences among the three TC formulas to evaluate the appropriateness of each formula and estimate possible errors. First, by using theoretical means, the differences are explicitly expressed in terms of material properties such as the Maxwell-Stefan (MS) diffusion coefficient, the partial specific enthalpy, and the reduced heat of transport. Subsequently, MD simulations are conducted to quantify the differences over wide temperature ranges in Li2O and TiO2 model systems including crystal, amorphous and liquid phases. The results show that although the three TC formulas give virtually identical results at low temperatures, one TC formula may cause significant errors at high temperatures when the MS diffusion coefficient reaches approximately 10(-6)-10 (7) cm(2)/s. These large diffusion coefficients usually occur in liquid phases, often occur in amorphous and super-ionic crystal phases, and may occur in defective systems. Finally, a simple equation to roughly estimate the error in this TC formula is derived.