Two-fluid nature of phonon heat conduction in a monatomic lattice

The thermal resistance of a crystal lattice with a monatomic unit cell due to three-phonon scattering processes is investigated in detail theoretically. A general expression for the lattice thermal conductivity is derived from a combined analysis based on: (i) the Boltzmann equation and (ii) data on the heat current autocorrelation function obtained via molecular dynamics simulations in conjunction with the Green–Kubo formalism. It is argued that the phonon gas in a monatomic lattice conducts heat as if it consisted of two distinct parts (two ‘thermal fluids’), so that the lattice thermal conductivity can be decomposed into contributions from these two parts. The origin of the behaviour of the phonon gas, which is explored in the present work, is due to an intrinsic interplay between Umklapp and normal three-phonon scattering processes. New insight into the nature of the lattice thermal conductivity is demonstrated and the results of the present work are in agreement with previous studies in this area.