Phonon Dispersion: Definition & Explanation

[mosqui]

I understand that the relationship between the phonon frequency and its wavenumber is the phonon dispersion. But is there a much more indepth definition of phonon dispersion and if i was asked to explain in a few lines (and in english not mathematical equations) what the phonon dispersion relation is, how would i go about it?

 

[M Quack]

It is the phonon energy (or frequency) as function of the wave vector (i.e. wavelength and direction of propagation) . For each wave vector there are several "branches" of phonons, i.e. modes with different energies. One distinguishes between "acoustic" phonons with E=0 at k=0 and optical phonons with E>0 at k=0.

 

[mosqui]

Thank you