  Hydrodynamic phonon transport phenomena, like second sound, have been
observed in liquid Helium more than 50 years ago. More recently second sound
has been observed in graphite at over 200 K using transient thermal grating
techniques. In this work we explore the signatures of second sound in ultrafast
electron diffuse scattering (UEDS) patterns. We use density functional theory
and solve the Boltzmann transport equation to determine time-resolved
non-equilibrium phonon populations and subsequently calculate one-phonon
structure factors and diffuse scattering patterns to simulate experimental data
covering the regimes of ballistic, diffusive, and hydrodynamic phonon
transport. For systems like graphite, UEDS is capable of extracting
time-dependent phonon occupancies across the entire Brillouin zone and
ultimately lead to a more fundamental understanding of the hydrodynamic phonon
transport regime.
