Discussion
If there are p atoms in the primitive cell, the phonon dispersion relation will have :
Answer: B
There are 3p - 3 optical phonon branches.
With p atoms in the primitive cell, each atom can move in three directions, so there are 3p normal modes for every wave vector, that is 3p branches in all. Three of them are acoustic branches (one longitudinal and two transverse), in which the whole cell moves together and the frequency goes to zero at long wavelengths. The remaining branches are optical:
\[ 3p - 3 \]
A monatomic lattice (p = 1) therefore has no optical branches, and a diatomic one such as NaCl has three. '3' counts the acoustic branches, '3p' all of them, and '3p - 1' has no basis.
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