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This Demonstration models the phonon dispersion relation within the Brillouin zone of a crystal. The top of the graphic shows the dispersion relation, while the bottom shows an animation of the collective vibration of the atoms in the crystal. You can observe the effects of both the acoustic and optical modes of phonons on the group velocity of the atoms in a crystal. Near the edge of the Brillouin zone, the group velocity approaches zero.

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      EUN,LOM,LRE4,work-cmr-id:262482,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/PhononDispersionRelationInBrillouinZone/,ilox,learning resource exchange,LRE metadata application profile,LRE

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