Fig. 3. Characteristic features of acoustic and optical phonons in a solid and the Debye model. Reused with permission from Brews ohare (CC by-sa 3.0) diatomic phonons and optical & acoustic vibrations. (a) Linear diatomic solid with “a” being the lattice parameter; acoustic and optical phonons assimilated as in-phase and out-of-phase movements. (b) Acoustic and optical branches (dispersion relations) as a function of wavenumber k in a linear diatomic solid. (c) Transverse vibrations in a 3D solid; the atomic separation d imposes a minimum wavelength, and thus, a maximum frequency, ωD (Debye frequency). (d) Density of phonons ρ available at each frequency as given in the Debye model; ωD can be translated in terms of the Debye temperature, ΘD.
