What's the relationship between phonon spectrum and thermal conductivity

In summary: There, it is proposed a single molecule field effect transistor for phonons. By measuring the electrical current through the transistor when a laser beam is shone on it, one can determine the phonon wave vector. From this, one can calculate the thermal conductivity of the material.
  • #1
wdliwei
5
0
I mean how can i analysis the thermal conductivity of two structures with their phonon spectrum.
thank you!
 
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  • #2
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
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
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 don't 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
shawl said:
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 don't 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.

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
wdliwei said:
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.

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:

What is a phonon spectrum and how does it relate to thermal conductivity?

A phonon spectrum is a representation of the vibrational modes or wavelengths of a material. It is related to thermal conductivity because the movement of phonons, or energy-carrying particles, contributes to the transfer of heat in a material. The frequency and velocity of phonons determine how well a material can conduct heat.

Can the phonon spectrum be manipulated to control thermal conductivity?

Yes, the phonon spectrum can be modified through various methods such as changing the crystal structure, altering the composition of the material, or introducing defects. These modifications can alter the phonon scattering and affect the thermal conductivity of the material.

How does the phonon spectrum differ between different materials?

The phonon spectrum can vary greatly between materials depending on factors such as crystal structure, composition, and temperature. Materials with larger atoms or more complex crystal structures tend to have lower thermal conductivities due to increased phonon scattering.

Is there a relationship between phonon spectrum and temperature?

Yes, the phonon spectrum is affected by temperature. As temperature increases, the phonon spectrum shifts to higher frequencies and velocities, resulting in increased thermal conductivity. This is because higher temperatures lead to more phonon scattering and thus more efficient heat transfer.

How does the phonon spectrum impact the thermal conductivity of a material?

The phonon spectrum plays a crucial role in determining the thermal conductivity of a material. A material with a wider range of phonon frequencies and velocities will have a higher thermal conductivity as there are more pathways for heat transfer. Conversely, a material with a narrow phonon spectrum will have a lower thermal conductivity due to fewer phonon scattering mechanisms.

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