# Phonon

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Can someone explain to me (without loads of maths!) the phonon.

http://en.wikipedia.org/wiki/Phonon

but don't understand all of it.

They seem to be to do with vibration of atoms in a solid, possibly to do with wave-particle duality, you have a wave in a solid (caused by sound, or thermal energy?) and that's the wave, the phonon is the particle.

But I'm not really sure, if a photon is part of the EM spectrum making light, the a phonon is _________ what?

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Can someone explain to me (without loads of maths!) the phonon.

http://en.wikipedia.org/wiki/Phonon

but don't understand all of it.

They seem to be to do with vibration of atoms in a solid' date=' possibly to do with wave-particle duality, you have a wave in a solid (caused by sound, or thermal energy?) and that's the wave, the phonon is the particle.

But I'm not really sure, if a photon is part of the EM spectrum making light, the a phonon is _________ what?[/quote']

Phonon?. Now theres a word I never heard before.

I've browsed a couple of sites

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/phonon.html

http://www.encyclopedia.com/html/p1/phonon.asp

It sounds like phonons are a type of vibrational energy caused by the kinetic energy of atoms. The energy is quantised into packets called phonons. These could then explain stuff like resonance, harmonics and on to resistivity permeability, etc.

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An update from something I found in one of physics books, under the heading of thermal conduction in solids:

"Since electrons are the carriers in electrical conduction, it is considered that electrons transport energy through metals. Thus on heating a metal bar the free electrons gain thermal energy and distribute this energy by collision with the fixed positive metal ions in the solid lattice.

Poor conductors ... have no free electrons. The transport of thermal energy ... is mainly due to waves. They are produced by lattive vibrations due to the thermal motion of the atoms. The waves are scattered by atoms ... and so distribute thermal energy to the solid.

The energy and momentum of the waves can also be considered carried by particles (p.877)" <<p.877 talks about wave-particle duality "These particles are called phonons. Like the waves they represent, they travel with the speed of sound"

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- A phonon is a state of oscillation of the crystal´s atoms.

- As these states have definite momentum and energy and are quantized, they are usually threatened as particles and called quasi-particles (I´d think that´s because their existence is bound to a medium while similar particles like photons can exist without a medium).

- As phonons describe the relative motion of the atoms (where relative means that the crystal´s movement in space as a whole is not considered) they are also used for calculating thermal properties like the heat capacity (although the free electrons also have to be considered for metals).

- Phonons are not photons and not related to electromagetism.

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So is a phonon a particle with mass?

Seemingly it can be a carrier of sound or thermal energy.

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No, a phonon doesn´t really have mass. In fact, I wouldn´t even say they are massless - they just don´t have an attribute called mass (what would be the mass of a wave in water?).

Well, you could assign a mass to phonons like you apply the so-called "effective mass" to electrons in a crystal but this would be rather abstract (inverse of the 2nd derivative of the dispersion relation or something like that) and would not resemble the mass as you probably know it. I have not seen this being done so far. My guess would be that this is not nessecary because unlike electrons the number of phonons is not conserved.

When you heat up your crystal, for example, the number of phonons is increased and more of the higher energetic phonons states are occupied (or occupied by more phonons as phonons are bosonic particles so a state can be occupied by more than one phonon). That´s a difference to the free electrons of a crystal. When the crystal's temperature is increased the number of electrons of course stays the same. The electrons just move to higher energetic states. Both phonons and free electrons contribute to thermal energy. Excitation of the bound electrons is usually not considered.

About phonons being carriers of sound: Yes. Take a look at the "dispersion relation" in the wikipedia page. Sound waves have a long wavelenght in comparison with typical interatomic distances. This translates to very small wave-vectors k. The velocity of a wave packet is equal to (or porportional to, doesn´t really matter) the derivative of energy omega. As you can see, the curve in the plot is nearly a line for small k. So the slope of the line is the speed of sound in the crystal.

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okay, we are getting somewhere but I still dont fully understand the phonon.

Is it part of the wave?

Is it a product of the wave?

looking at this image:

where do phonons fit into that?

"A phonon is a state of oscillation of the crystal´s atoms" -- Atheist

Can you explain that in a bit more detail?

I mean, is a phonon a particle? If not, a wave? Or what actually is it?

Maybe one way of doing this is, if possible, how would explain a phonon to a baby? Just get the real basics like what it is, because I'm really not understanding it at all!

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I thought a lot and quite long about how to describe what and got lost in details so let´s try the short version:

- The movement equation for an atom in a crystal is a differential equation F = m*a, where the force F depends on the atoms´relative positions. The movement of the atoms (the solution of the diffEq) are oscillations.

- Differential equations have a vector space of functions as their solution. The particular solution for a given problem is a vector of this vector space that´s determined by boudary conditions.

- As in real valued vector spaces like R² or R³ you can describe elements of the vector space of functions as a linear combination of a valid set of base functions (base vectors): $\vec v = a_1 \vec e_1 + a_2 \vec e_2 + ...$

- The basevectors (basefunctions) you chose are the phonons. Any oscillation can be described by a linear combination of phonon states.

- Choosing the basefunctions is arbitrary in classical mechanics (though most people like to avoid headaches and chose the easiest one) but can become important in quantum mechanics (at least if you want to avoid serious headaches). The phonons are chosen to be states of definite energy and momentum.

- If you scatter neutrons (a common way to experimental get the phonon distribution in crystals) on a crystal and the scattered neutron has energy and momentum different from the original one you can say that the crystal simply went to another state. Alternatively you can say that a phonon was produced (or destroyed). In this alternative view you give the phonons an actual existence as a particle.

The same can be done with the electromagnetical field where it´s actually quite common to treat the basefunctions of the field as particles (photons, then).

-

Hope that helps.

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Okay, I kinda get that... a bit!

As a phonon is a boson it is classified as a particle, I think, because particles are bosons or fermions, a phonon is a boson making it a particle, i think, so is a phonon a particle?

when Atheist said:

"No, a phonon doesn´t really have mass. In fact, I wouldn´t even say they are massless - they just don´t have an attribute called mass (what would be the mass of a wave in water?)."

It makes it sound like it isn't a particle, then how can it be a boson?

and

I asked this before, but I think it'd be useful if you could tell me, where do phonons fit into this diagram:

?

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- Phonons are bosons in the sense that any (natural) number of them can be in the same state. Same is true for the euro-cents on my bank account (ok, they can be negatve). Not sure if I´d call them particles because of that.

- In the picture a wave is shown. The wave reusults from the displacement of the atoms off their rest position. As these exitations from the rest postions can be described by phonons (see last post about different bases of the movement equation´s solution) the wave can be described as a number of phonons being in the crystal.

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the wave can be described as a number of phonons being in the crystal.

OK, so is that wave a certain amount of phonons high? or is that wave made up of phonons?

Although normal modes are wave-like phenomena in classical mechanics, they acquire certain particle-like properties when the lattice is analysed using quantum mechanics (see wave-particle duality.) They are then known as phonons.

So you have the wave motion of the atoms and then because of QM's wave-particle duality, so if you 'looked' at the atoms with QM in mind there must be a particle side to the wave, these are phonons?

in that case what makes phonons? How do they appear?

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I think I'm beginning to understand phonons now, but can I just ask:

1) if photons are massless energy particles what does that make a phonon?

2) if electrons jumping energy levels makes photons what makes phonons? (or is it just vibrational energy e.g. heat or sound?)

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Didn´t understand question 1), sry.

For q 2):

As said phonons describe the crystal´s state (of oscillation). Assume a neutron is scattered by the crystal. An incoming neutron can interact with the crystal´s atoms and cause them to vibrate. The outgoing neutron can have a different momentum and energy than before. This difference is taken by the crystal (in form of the atom´s oscillating differently than before).

In the phonon picture the same process reads as the neutron interactin with the phonons and destroying some of them (taking over the related momentum and energy) and/or creating some (giving energy/momentum away). The most basic (and also most probable, I think) effects are either absorbing or creating one single phonon.

Same is true for other particles, of course. I choosed neutrons because they are actually most commonly used for measuring the dispersion relation E(p) of a crystal´s phonon spectrum.

Sidenote to araise further confusion: I´d like to note that saying the phonons describe the crystal´s vibrations is an analogy to classical mechanics. From the QM perspective they simply describe it´s state. The classical picture of oscillating atoms would demand the atoms to be at a certain position with a certain velocity which they cannot be in QM.

A similarity would be the harmonic oscillator. While in classical mechanics you´d have your particle bouncing aroung with a certain frequency, the energy-eigenfunctions of QM are not related to any movement at all (a superpoition of them is, though).

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They are not singular particles, merely abstract particles that quantise the vibrational energy created by temperature invariances.

There is some interesting research going on based around materials with low phonon transfer but high conductivity and/or vice versa. I can't remember the process exactly i'll hunt around for a link but the basic premise was that if successful they could utilise the temperature invariance to generate a current thus transforming everyday objects such as exhast pipes into potential batteries.

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