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

In summary, the conversation discusses the dispersion curve of a 1D lattice with diatomic basic and the existence of optical and acoustic branch of phonon in a crystal. The speaker also asks about the band gap between these branches and requests a recommendation for a book on crystal physics. The responder suggests the book "Brillouin: Wave propagation in periodic structures" and explains that the acoustic band is formed when atoms of the bases move in the same direction, while the optical band is formed when they move in opposite directions due to their alternating charges.
  • #1
ghegde
1
0
Hi there,
I am trying to understand the dispersion curve(as shown below) of a 1D lattice with diatomic basic.
640px-Diatomic_phonons.png

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
 
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  • #2
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 [Broken]
 
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1. What is a dispersion curve?

A dispersion curve is a graphical representation of the relationship between the frequency of a wave and its corresponding wavelength. It shows how the wave propagates through a medium and can provide valuable information about the properties of the medium.

2. How does a 1D lattice with diatomic basic affect the dispersion curve?

A 1D lattice with diatomic basic refers to a 1-dimensional chain of particles, where each particle is made up of two different types of atoms. This type of lattice can affect the dispersion curve by introducing additional periodicity and complexity in the medium, resulting in multiple branches in the dispersion curve.

3. What factors influence the dispersion curve of a 1D lattice with diatomic basic?

The dispersion curve of a 1D lattice with diatomic basic is influenced by several factors, including the mass and spacing of the atoms in the lattice, the strength of the bonds between the atoms, and the type of lattice structure.

4. How can understanding the dispersion curve of a 1D lattice with diatomic basic be useful?

Understanding the dispersion curve of a 1D lattice with diatomic basic can be useful in various fields, such as materials science and engineering. It can provide insights into the behavior of waves and the properties of the medium, which can be used to design and optimize materials for specific applications.

5. Are there any experimental methods for studying the dispersion curve of a 1D lattice with diatomic basic?

Yes, there are several experimental techniques for studying the dispersion curve of a 1D lattice with diatomic basic, including inelastic neutron scattering, X-ray diffraction, and Brillouin scattering. These methods allow for the measurement of the dispersion curve and can provide valuable information about the properties of the lattice.

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