Phonon chirality has attracted intensive attention since it breaks the traditional cognition that phonons are linear propagating bosons. This new quasiparticle property has been extensively studied theoretically and experimentally. However, characterization of the phonon chirality throughout the full Brillouin zone is still not possible due to the lack of available experimental tools. In this work, phonon dispersion and chirality of tungsten carbide were investigated by millielectronvolt energy-resolution inelastic X-ray scattering. The atomistic calculation indicates that in-plane longitudinal and transverse acoustic phonons near K and K$^prime$ points are circularly polarized due to the broken inversion symmetry. Anomalous inelastic X-ray scattering by these circularly polarized phonons was observed and attributed to their chirality. Our results show that inelastic X-ray scattering can be utilized to characterize phonon chirality in materials and suggest that a revision to the phonon scattering function is necessary.
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