  Despite their fundamental role in determining material properties, detailed
momentum-dependent information on the strength of electron-phonon and
phonon-phonon coupling (EPC and PPC, respectively) across the entire Brillouin
zone (BZ) has proved difficult to obtain. Here we demonstrate that ultrafast
electron diffuse scattering (UEDS) directly provides such information. By
exploiting symmetry-based selection rules and time-resolution, scattering from
different phonon branches can be distinguished even without energy resolution.
Using graphite as a model system, we show that UEDS patterns map the relative
EPC and PPC strength through their profound sensitivity to photoinduced changes
in phonon populations. We measure strong EPC to the $K$-point transverse
optical phonon of $A_1'$ symmetry ($K-A_1'$) and along the entire longitudinal
optical branch between $\Gamma-K$, not only to the $\Gamma-E_{2g}$ phonon as
previously emphasized. We also determine that the subsequent phonon relaxation
pathway involves three stages; decay via several identifiable channels to
transverse acoustic (TA) and longitudinal acoustic (LA) phonons (1-2 ps),
intraband thermalization of the non-equilibrium TA/LA phonon populations (30-40
ps) and interband relaxation of the LA/TA modes (115 ps). Combining UEDS with
ultrafast angle-resolved photoelectron spectroscopy will yield a complete
picture of the dynamics within and between electron and phonon subsystems,
helping to unravel complex phases in which the intertwined nature of these
systems have a strong influence on emergent properties.
