Posted by Steve Simon on June 11, 2015, 10:53 pm, in reply to "Distinct phonon branches"
The trick (which is certainly not obvious) is to ask whether vibrations in two directions will be equivalent to each other. For a diamond crystal (which is fcc witha basis), the crystal is essential identical to the crystal rotated by 90 degrees around the [100] axis. (Strictly it is equivalent to the rotation plus a translation). As a result a transverse vibration mode where the atoms move in the [010] direction and the wave moves in the [100] direction is exactly equivalent to a transverse mode where atoms move in the [001] direction and the wave moves in the [100] direction. This means the for both the acoustic and the optical branches, the two transverse modes will have the same frequency.
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