# optical and acoustic modes

by aaaa202
Tags: acoustic, modes, optical
 P: 864 Basically phonons in crystals can either be acoustic or optical according to my book. But then it stresses that a necessary condition for this to hold is that the crystal has more than atom per primitive basis. The optical modes are then when neighbouring atoms oscillate out of phase (i.e. no motion of the center of mass) and the acoustical mode is the exact opposite. But I don't understand why it is so crucial that the crystal has two or more atoms per primitive basis. Can't optical and acoustical modes happen between neighbouring atoms regardless of this?
 Thanks P: 959 If there is only one atom per unit cell, how many degrees of freedom are available? The unit cell is the repeating unit of a crystal; you should be able to define everything that occurs in the crystal in terms of the unit cell - this is especially convenient if you move to the reciprocal space.
 P: 864 I don't understand what you are hinting at :( I know the unit cell is the smallest repetitive unit. But what does have to do with the degrees of freedom? Maybe you can point to a drawing which shows what you are hinting at. I am thinking if there is two atoms per unit cell they can oscillate relative to each other, which is a degree of freedom which is not there if there is only one atom per unit cell? But then why can't an atom just move relative to another atom in the neighbouring unit cell?
P: 524

## optical and acoustic modes

It can. You still can have an acoustic mode, but not the optic one(s).
 P: 864 why cant u have an optic mode, i.e. neighbouring atoms oscillating in opposite phase wrt each other?
Thanks
P: 959
 Quote by aaaa202 I know the unit cell is the smallest repetitive unit. But what does have to do with the degrees of freedom?
A perfect crystal contains a vast number of unit cells - think Avogadro's number for its gram molecular weight - and when you apply an impulse to the crystal, the rigidity of the system makes it felt everywhere.

If one unit cell responds with a particular motion, why should its immediate neighbors respond in some other way? Being identical means that they should have the same response ... they are physically the same.

The the degrees of freedom of the unit cell tell you what responses are possible.

This should be clear from a careful reading of an introductory text like Kittel.
PF Patron