Optical Phonons in Single Atom Crystals: Unraveling the Mystery

[BeauGeste]

I thought optical phonons only existed in crystals with two or more types of atoms in a unit cell. But I keep reading references of optical phonons in single atom crystals, like silicon.
What's the deal here?

 

[Dr Transport]

The crystal symmetry, O_h doesn't eliminate the possibility of optical transitions in Si, but the deformation potentials and dipole mements in silicon are very small yeilding quite small transition intensities.

 

[Joe-b716]

<111> direction in silicon has two different spacings between atoms and thus two spring constants. The eigenvalue equation sets up the same as if there were two different masses.

 

[genneth]

Remember that the total number of phonon modes is equal to the number of atoms. The number of distinct wave-vectors possible is equal to the number of lattice sites. There are therefore a number of different modes at each wavevector equal to the number of atoms per lattice site.

Even in mono-atomic structures, you can have a non-trivial lattice (not a simple cubic) and so have more than one atom per lattice point.

 

[DrDu]

To put it differently, silicium cristallizes in the diamond lattice. A primitive cell of the diamond lattice contains two atoms. Compare this to some simpler monoatomic lattice, e.g. I_2 (Iodine).