Phonon dispersion relation : meaning of mode crossings

In summary, the conversation discusses the meaning of crossed phonon branches in a phonon dispersion relation and the differences in the number of branches in different directions. It is suggested that crossing branches indicate a lack of coupling and that the number of branches may vary depending on the direction. A reference to a figure in the book "Solid State Physics" by Ashcrof & Mermin is also mentioned.
  • #1
dmit11
2
0
Hello all,


What does it mean when two phonon branches get crossed in phonon dispersion relation ? Also, in certain high symmetry direction, one can find only one transverse branch and other direction two separate branches, what do these response mean?

(Ref. Solid state physics by Ashcrof & Mermin, Fig 22.13: Typical dispersion curves in monoatomic Bravais lattice. FCC (lead))

Thank you!
 
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  • #2
Hi!

I would say that if two branches cross each other they are uncoupled, since if there were some coupling between them they would mix and avoid crossing.

Regarding the number of branches in different directions it might be that in some directions the two branches are degenerate and then you only see one single line in the plot, while in other directions both branches show up.

However I do not have Ashcrof & Mermin to see if this is what you are asking for...
 

1. What is a phonon dispersion relation?

A phonon dispersion relation is a graph that shows the relationship between the frequency and wavevector of phonons, which are quantized lattice vibrations in a solid material. It is a useful tool for understanding the vibrational properties of materials and is often used in the field of condensed matter physics.

2. What does "mode crossings" refer to in a phonon dispersion relation?

In a phonon dispersion relation, "mode crossings" refer to points where the lines representing different phonon modes intersect. This can occur when two modes have the same frequency at a certain wavevector, or when two modes have the same wavevector at a certain frequency.

3. What is the significance of mode crossings in a phonon dispersion relation?

Mode crossings in a phonon dispersion relation can provide important information about the vibrational properties of a material. They can indicate the presence of degenerate modes, where multiple phonon modes have the same frequency or wavevector, and can also reveal the presence of energy gaps or bandgaps in the material.

4. How do mode crossings affect the thermal and mechanical properties of a material?

The presence of mode crossings in a phonon dispersion relation can affect the thermal and mechanical properties of a material. In materials with degenerate modes, the thermal conductivity may be reduced due to scattering between these modes. Additionally, mode crossings can affect the material's stiffness and elasticity, leading to changes in its mechanical properties.

5. Can mode crossings be manipulated or controlled in materials?

Yes, mode crossings can be manipulated or controlled in materials through various methods such as applying external fields, changing the material's composition, or introducing defects. This can be useful for tailoring the thermal and mechanical properties of materials for specific applications.

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