Understanding Phonon Dispersion Relation

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Discussion Overview

The discussion centers around the phonon dispersion relation in solid state physics, specifically the significance of angular frequency (\omega) in relation to phonons and their role in energy transfer within materials. Participants explore the measurement of phonon dispersions and the implications for understanding thermal properties.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Abby expresses confusion about the importance of angular frequency (\omega) in the context of phonon dispersion relations.
  • One participant explains that phonon dispersions can be measured using inelastic neutron diffraction, where neutrons interact with phonons, affecting their energy and momentum.
  • Abby seeks clarification on how a sample can emit phonons and questions whether phonons are quantized.
  • Another participant confirms that phonons are quantized and describes them as quanta of vibrational mechanical energy.
  • A later reply emphasizes the significance of understanding phonons in terms of energy transfer, linking angular frequency to the energy capacity of phonons and its relevance to calculating material properties like heat capacity and thermal conductivity.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the significance of phonons and their quantization. While some points are clarified, there remains uncertainty about the broader implications and details of phonon behavior.

Contextual Notes

The discussion touches on complex concepts such as energy transfer, measurement techniques, and the relationship between phonons and material properties, which may involve assumptions about prior knowledge in solid state physics.

Abigale
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Hi Guys,

I am learning some solid state physics.

I see a lot of pictures with Phonon Dispersion Relation, with
\omega (\vec{k}) on the y-axis and \Gamma, X, M, \Gamma, R on the x-axis.

I don't understand, why the angular frequenzy \omega (\vec{k}) is important.
Or why is this information important?


THX
Abby
 
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Phonon dispersions can be measured by inelastic neutron diffraction. Neutrons are fired at a sample and they absorb or emit a phonon, changing their energy by the angular frequency and their momentum by the k value for the phonon.
 
OK, thx.
But I need to talk a little bit more about it for full comprehension ^^


"Phonon dispersions can be measured by inelastic neutron diffraction. Neutrons are fired at a sample and they absorb or emit a phonon",
this means the crystal absorbs a phonon ( so just kinetic energy ) by a neutron.

But how can the sample emit the phonon?

Are these Phonons quantized?
 
yes,the phonos are quantised.They are quanta of vibrational mechanical energy.
 
Abigale said:
I don't understand, why the angular frequenzy \omega (\vec{k}) is important.
Or why is this information important?

I think you are getting lost in the details. Let me give you a bigger picture to always keep in mind.
The reason we care to understand phonons is because they carry and transfer energy. And knowing how and in what capacity they carry energy allows us to calculate the heat capacity and thermal conductivity of any material, which are very important for engineers and applied physicists.

The angular frequency of the phonon is what determines HOW much energy it can carry. The higher its vibration frequency, the more energy it can carry. The dispersion relation allows you to know how many photons there are and how much energy each of them carries. E = \hbar \omega

You will see this eventually when you get to thermal properties and start calculating density of states.
 

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