Back

1D Phonon Dispersion (Monatomic and Diatomic)

What you are seeing: the dispersion relation ω(k)\omega(k) for a 1D chain. Monatomic: a single acoustic branch. Diatomic (unequal masses): acoustic + optical branches with a gap at the zone boundary.

Figure 1. Phonon dispersion.
m11.00
m22.00
K1.80

WHAT TO TRY

  • Make the two masses equal: the gap closes and the optical branch folds into a single acoustic branch, the monatomic chain recovered as a special case.
  • Split the masses apart: a forbidden frequency gap opens between the acoustic and optical branches, where no travelling phonon exists, the lattice analogue of an electronic band gap.
  • At the zone boundary the two atoms move oppositely on the optical branch and together on the acoustic one, with the group velocity vanishing, a standing wave carrying no energy.