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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.