The Atomistic Basis of Non-Equilibrium Thermal Processes in Materials

Brent Kraczek, Reese Jones, Frederic Legoll, Kranthi Mandadapu

Atomic-scale thermal processes are important in: heat management in electronic devices, both in heat dissipation and thermoelectric effects; friction and material damage mechanisms, including shearbanding; liquid instabilities and boundary effects; fracture; and laser-heating of materials. Atomic-scale modeling of these thermally-dominated, non-equilibrium processes in solids is essential for capturing material-specific behaviors and for tuning of continuum-scale material properties when length-scales of interest approach the atomic scale or the processes are difficult to investigate experimentally. Submissions to this MS should focus on development and/or use of methods described in the following paragraphs or similar methods.

A widely-used approach to compute non-equilibrium thermal processes and properties is the non-equilibrium molecular dynamics (NEMD) method which is essentially a direct approach where the system is driven out of equilibrium using boundary conditions. For example, thermal conductivity can be estimated using thermostats to hold the boundaries of the system at different temperatures while monitoring the heat flux. There are however many non-equilibrium settings where the best means to control the primary or flux variables is less apparent. A focus of this MS is to survey the latest methods in this area.

Another class of methods extracts thermal properties through linear response theory and the associated Green-Kubo relations. These formulae yield thermal conductivity as an integral of the equilibrium heat flux autocorrelation function under certain time-scale separation assumptions. Unlike direct methods, transport coefficients can be obtained from relatively small systems but can suffer from noise and convergence issues. These issues are especially problematic in insulators at low temperatures as the characteristic correlation times are very large and require very long simulation times.

An alternative linear response method is the homogeneous NEMD method, where a fictitious force is applied to the system to mimic the temperature gradient. This yields a linear relationship between the ensemble averaged heat flux and the external force with the constant of proportionality being the Green-Kubo formula for thermal conductivity. This method alleviates the problems related to the accuracy of correlation function and still yields values with system sizes on the order of the equilibrium method. However, this method requires simulations for various values of external field, like the NEMD method, to identify the linear response range. This MS aims to review methods based on linear response theory and identify the difficulties that arise in their application.

Lattice dynamics (LD) in the harmonic or quasiharmonic approximation is another widely employed method. Starting from linearizations of empirical or quantum potentials, these methods directly solve for the phonon modes of the system. Using these modes transport properties can then be calculated through the Boltzmann transport equation (BTE). Of current particular interest in this MS are the development of tools for improved calculation of phonon scattering in a variety of materials and defect types and the development of multiscale methods to capture atomic-scale properties at length- and time-scales for which full atomistic simulations are impractical.

A final topic of interest is the augmentation of the phononic processes naturally represented in molecular dynamics with the effects of electron-mediated heat transport. Examples include the use of the two temperature model to mimic the heat flow in metallic materials.