# What's the relationship between phonon spectrum and thermal conductivity

1. Aug 22, 2011

### wdliwei

I mean how can i analysis the thermal conductivity of two structures with their phonon spectrum.
thank you!

2. Aug 23, 2011

### shawl

It's hard to get the formula of thermal conductivity only by the spectrum.

Because:
The spectrum is analyzed when the material is under thermal equilibrium, which suggesting the temperature of the material is a fixed value, i.e. T0.

During the analysis of thermal conductivity, two different temperature is applied to two ends of the material.

That means different number of acoustic phonon will be produced at each end.

And therefore phonon at one end with high temperature will flow toward the other with low temperature.

In a conclusion, if you want to get the specific formula, you need to know the average velocity of the phonon in flowing.

3. Aug 24, 2011

### wdliwei

Thank you!Your reply is vividly,it did help me a lot about the physical meaning of phonon and the thermal conductivity.

May I ask you another question?

If I got spectra of two materials at the same temperature, how can I distinguish which material's thermal conduction is better (more efficient). The number of acoustic phonon, or some other parameters.

4. Aug 24, 2011

### shawl

To comparison for the thermal conductivity of two different materials, you need to know the respective velocity of phonon. Without the velocity, it is hard to do anything.

I dont know what phonon spectrum you have. Generally, the spectrum respresents the number of phonon (axis Y) at each energy (axis X). The energy is denoted by the frequency w.

Therefore, you may calculate the total number of phonon by integral the spectrum.

5. Sep 3, 2011

### wdliwei

I read some literature about the analytical model for the thermal conductivity of nanostructures, fount that there are two methods for us to get the thermal conductivity from the phonon properties:
1. phonon spectrum method;
2. wave vector method.
You can see the details in Patrice Chantrenne's paper :the analytical model for the thermal conductivity of nanostructures.

6. Sep 5, 2011

### shawl

Thank you! You really give me a lesson.

Noted the eq. 6 in the paper you given. The thermal conductivity to be calculated requires not only the group volecity v but also the relaxation time torr.

Please refer to "proposal for a single molecule field effect transistor for phonons" (Phys. Rev. B 81 (2010) 012302.) authored by Marcos G. Menezes.

Last edited: Sep 5, 2011