Homogeneous Non-Equilibrium Molecular Dynamics Methods for Calculating the Heat Transport Coefficient of Solids and Mixtures
This thesis presents a class of homogeneous non-equilibrium molecular dynamics (HNEMD) methods for obtaining the heat transport coefficient that relates the heat flux and temperature gradient in the linear irreversible regime. These methods are based on the linear response theory of statistical mechanics. The proposed HNEMD methods are parallelizable, and yield better statistical averages at lower overall computational cost than the existing direct and Green-Kubo methods.
The HNEMD method, as it was initially proposed, is applicable only to single-species systems with two-body interactions. In this thesis, the HNEMD method is extended to single species systems with many-body interactions, and is applied to silicon systems where three-body interactions are taken into account.
The HNEMD method developed for single-species systems is inadequate for obtaining the heat transport coefficient of multi-species systems. A further development of the HNEMD method, the Mixture-HNEMD (M-HNEMD) method, is presented for multi-species systems with many-body interactions. This M-HNEMD method satisfies all the requirements of linear response theory and is compatible with periodic boundary conditions. Applications of the M-HNEMD method to liquid argon-krypton systems with two-body interactions and to perfectly crystalline gallium-nitride systems with three-body interactions are presented, and the results are consistent with the results from the Green-Kubo method. This is the first HNEMD method which can be used for calculating the heat-transport coefficient of multi-species systems.
The expressions for stress tensor and heat-flux vector needed for the development of HNEMD method for single-species systems and of the M-HNEMD method for multi-species systems with many-body interactions require an extension of the statistical mechanical theory of transport processes proposed by Irving and Kirkwood. This extension forms an integral part of the thesis.