Atomic Level Green-Kubo Stress Correlation Function for a Model Crystal: An Insight into Molecular Dynamics Results on a Model Liquid

In order to get insight into the connection between the vibrational dynamics and the atomic level Green-Kubo stress correlation function in liquids we consider this connection in a model crystal instead. Of course, vibrational dynamics in liquids and crystals are quite different and it is not expected that the results obtained on a model crystal should be valid for liquids. However, these considerations provide a benchmark to which the results of the previous molecular dynamics simulations can be compared. Thus, assuming that vibrations are plane waves, we derive analytical expressions for the atomic level stress correlation functions in the classical limit and analyze them. These results provide, in particular, a recipe for analysis of the atomic level stress correlation functions in Fourier space and extraction of the wavevector and frequency dependent information. We also evaluate the energies of the atomic level stresses. Obtained energies are significantly smaller than the energies that were obtained in MD simulations of liquids previously. This result suggests that the average energies of the atomic level stresses in liquids and glasses are largely determined by the structural disorder. We discuss this result in the context of equipartition of the atomic level stress energies. Analysis of the previously published data suggests that it is possible to speak about configurational and vibrational contributions to the average energies of the atomic level stresses in a glass state. However, this separation in a liquid state is problematic. We also consider peak broadening in the pair distribution function with increase of distance. We find that peak broadening (by ~40%) occurs due to the transverse vibrational modes, while contribution from the longitudinal modes does not change with distance. Finally, we introduce and consider atomic level transverse current correlation function.