Acoustic and optical branches in phonons dispersion curves

[chikou24i]

What is the physical meaning of acoustic and optical branches in phonons dispersion curves ?

 

[DrDu]

Acoustic branches correspond to sound waves, i.e. all molecules or units making up the solid move in phase.
Hence, the frequency goes to 0 with k to 0 as this limit corresponds to a pure translation of the solid.
In the optical branches, the atoms inside the molecules or within the elementary cell move out of phase. Even for long wavelength, the frequency remains finite. This corresponds to the vibrations as also observed in IR or Raman spectroscopy on single molecules.

 

[chikou24i]

Thank you DrDu.