Distinct modes of oscillation in a 3D crystal lattice

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Homework Statement


Silicon crystalises in a cubic structure whose lattice is face-centred, with a basis [000],[1/4,1/4,1/4].
How many optic/acoustic modes are to be found in the phonon dispersion diagram for silicon. How many distinct branches would you expect along the [100] direction?

Homework Equations




The Attempt at a Solution


2 atoms in the primitive unit cell, therefore expect 3N degrees of freedom, so a total of 6 modes.
I also have it on good authority that you expect 3(N-1) optical modes and N acoustic modes, but I do not see why. So a total of 3 of each modes
For distinct modes, imagining looking at a lattice of atoms joined with springs down the x direction, I would imagine the modes that vibrate in the x-direction would be invisible, whereas the ones in y and z would be visible (so 1 acoustic and 1 optical invisible).
I think this because when looking at dipole radiation from an electron in a magnetic field the mode identified with linear motion in the direction of the B field (delta Mz = 0), you cannot see it when looking along the B field. I don't get this either.

None of this really makes sense to me! Many thanks for any help.
 

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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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