A formalism for calculating the modal contributions to thermal interface conductance
Abstract
A formalism termed the interface conductance modal analysis (ICMA) method is presented, which allows for calculations of the modal contributions to thermal interface conductance within the context of molecular dynamics (MD) simulations, which inherently include anharmonicity to full order. The eigen modes of vibration in this study are calculated from harmonic lattice dynamics (LD) calculations, however the generality of ICMA formalism also allows for incorporation of anharmonic LD results into the calculations. ICMA can be implemented in both equilibrium MD (EMD) and non-equilibrium MD (NEMD) simulations and both methods show qualitative agreement as validated through study of a simple system of Lennard-Jones solids. The formalism itself is based on a modal decomposition of the heat flow across an interface, which is then substituted into expressions for the conductance either based on EMD or NEMD. As a MD based method, it not only includes anharmonicity, but also naturally includes the atomic level details of the interface quality. The ICMA method now enables more in-depth study of various effects such as temperature, anharmonicity, interdiffusion, roughness, imperfections, dislocations, stress, changes in crystal structure through a single unified model, as it can essentially treat any material or object where the atoms vibrate around equilibrium sites (e.g., ordered or disordered solids and molecules). This formalism therefore serves as an important step forward toward better understanding of heat flow at interfaces.