  Suppressed three-phonon scattering processes have been considered to be the
direct cause of materials exhibiting significant higher-order four-phonon
interactions. However, after calculating the phonon-phonon interactions of 128
Half-Heusler materials by high-throughput, we find that the acoustic phonon
bandwidth dominates the three-phonon and four-phonon scattering channels and
keeps them roughly in a co-increasing or decreasing behavior. The $aao$ and
$aaa$ three-phonon scattering channels in Half-Heusler materials are weakly
affected by the acoustic-optical gap and acoustic bunched features respectively
only when acoustic phonon bandwidths are close. Finally, we found that
Half-Heusler materials with smaller acoustic bandwidths tend to have a more
pronounced four-phonon effect, although three-phonon scattering may not be
significantly suppressed at this time.
