Thermal conductivity tensor of $\beta$-HMX as a function of pressure and temperature from equilibrium molecular dynamics simulations

We apply the Green-Kubo (G-K) approach to obtain the thermal conductivity tensor of $\beta$-1,3,5,7-tetranitro-1,3,5,7-tetrazocane ($\beta$-HMX) as a function of pressure and temperature from equilibrium molecular dynamics (MD) simulations. Direct application of the G-K formula exhibits slow convergence of the integrated thermal conductivity values even for long (120 ns) accumulated simulation times. To partially mitigate this slow convergence, we apply a recently implemented numerical procedure [Int. J. Heat Mass Trans. 188, 122647 (2022)] that involves physically justified filtering of the MD-calculated G-K heat current and fitting the integrated time-dependent thermal conductivity to a physically motivated double-exponential function. The thermal conductivity tensor was determined for pressures 1 atm $\leq P \leq$ 30 GPa and temperatures 300 K $\leq T \leq$ 900 K. The thermal conductivity ${\kappa}^{\alpha \beta} (T,P)$ increases with increasing pressure, by approximately an order of magnitude over the interval considered, and decreases with increasing temperature. The MD predictions are compared to experimental and other theoretically determined values for the thermal conductivity of ${\beta}$-HMX. A simple, semi-empirical fitting form is proposed that captures the behavior of $\kappa^{\alpha \alpha} (T,P)$ over the pressure and temperature intervals studied.