The phonon dispersion relation (PDR), i.e., the dependence of phonon frequency ω on its wavevector q, ω(q), was measured traditionally by inelastic neutron scattering (INS) or inelastic X-ray scattering (IXS).

How do you calculate phonon energy?

Similar to photons, the phonon energy is related to the frequency of the sound waves E = hf and the phonon momentum is related to the wavelength of the sound waves p = h/λ. Sound waves with wavelengths much longer than the lattice constant of a crystal, are described by the wave equation.

How are phonon dispersion curves measured?

In principle, the complete phonon dispersion relations can be measured by coherent inelastic neutron scattering, or by inelastic X-ray scattering, provided the phonon peaks are well resolved, and their intensities are sufficient.