Help needed to understand dispersion curve of a 1D lattice with diatomic basic

[ghegde]

Hi there,
I am trying to understand the dispersion curve(as shown below) of a 1D lattice with diatomic basic.

Here are my questions
1) Can both optical and acoustic branch of phonon can simultaneously exist in crystal?
2)Why there is a band gap between optical and acoustic phonon branch ?

Also please suggest a good book to better understand the crystal physics if your are aware of any.

Thanks in advance for your help,
Ganesh

 

[ehild]

There is a good classics about the topics: Brillouin: Wave propagation in periodic structures.
In case of a chain of two different atom, both atoms of the bases can move in the same direction: that makes the acoustic band. If the different atoms of the bases move in opposite direction, you get the optical band.
The diatomic chain usually consist of atoms of alternating charge. The restoring force is higher when the opposite ions move in opposite directions, than in the case, when they move in the same direction. Try to read http://www.lcst-cn.org/Solid%20State%20Physics/Ch43.html