Analysis of Thermal Conductivity Expressions of Binary Systems near Melting Point using Equilibrium Molecular Dynamics Simulation

Abstract

In the field of nuclear engineering, one of the key parameter that governs the temperature of a component device of dielectric materials is the lattice thermal conductivity (TC). However, in the severe conditions of nuclear power plant (NPP) such as high radiation dose, high temperature and pressure, it is quite difficult task to measure or estimate the accurate value of TC of materials composing the devices of NPP during the operation. Therefore, approaches based on the theoretical calculation and simulations has been widely utilized for the estimation of TC under various circumstances. Among those approaches, the Green-Kubo relations have been considered as a trustworthy method for evaluation of the TC of condensed matters in equilibrium molecular dynamics (MD) calculation. In previous studies adopting the Green-Kubo relations, however, there exist mainly three different expressions of TC, each of which considers a different microscopic phenomenon as the substance of thermal conduction. In the present study, focusing on binary systems, we investigate the theoretical background of the three TC expressions and differences among calculated TC values. First of all, by deriving the TC expressions from the entropy production equation, we specified the assumptions and conditions employed in each TC expression. This procedure revealed the expression of the least approximation. In addition, three important material properties that affect the differences among the TC expressions are obtained: the Maxwell-Stefan (MS) diffusion coefficient, the partial specific enthalpy, and the reduced heat of transport. MD simulations of Li2O and TiO2 systems over a wide temperature range including crystal, amorphous and liquid phases show that when the MS diffusion coefficient exceeds around 10-7 cm2/s, one TC expression exhibits an abnormal value with up to 120% and 60% error compared to the least-approximate TC expression in Li2O and TiO2, respectively. Finally, simple method to predict the occurrence of the error based on the self-diffusion coefficient is suggested. This method contains the discussion about the possible advantages and disadvantages of the three TC expressions and about the conditions where a significant error may appear.