Calculating thermal conductivity in a transient conduction regime: theory and implementation

We present a molecular dynamics method addressed to the calculation of the lattice thermal conductivity during the transient regime of approach to equilibrium from an initial condition of nonuniform temperature profile. We thoroughly assess the basics, the robustness, and the accuracy of the method, in particular by showing that its results are basically independent of most of the arbitrary simulation parameters. In addition, the method here presented is computationally light, thus paving the way for the investigation of large systems. This feature is fully exploited to investigate the thermal transport properties of disordered and nanostructured silicon samples, providing a clear atomistic picture on the ability of grain boundaries and lattice disorder to affect thermal conductivity by improved scattering of vibrational modes with long mean free path.