# Dispersion Relation

by Abigale
Tags: phonon, phonon dispersion, quantum mechanics, solid state physics, statistical mechanic
 P: 44 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
 P: 179 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.
 P: 44 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?
P: 2

## Dispersion Relation

yes,the phonos are quantised.They are quanta of vibrational mechanical energy.
P: 34
 Quote by Abigale 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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