phonons!
Tobin Fricke
concept of phonons. My current understanding is that a phonon is simply a
normal mode of oscillation of a lattice, and that all possible modes of
vibration are decomposed into these distinct modes via the discrete
fourier transform (with the atoms in the lattice acting as sampling
points).
In this interpretation, a phonon only has 'location' in reciprocal space
-- its corresponding wave vector. But then I encounter statements that
don't seem to correspond to this understanding of what a phonon is, such
as: "Shiren described an experiment in which a beam of longitudinal
phonons of frequency 9.20 GHz interacts in an MgO crystal with a parallel
beam of longitudinal phonons at 9.18 GHz. The interaction of the two
beams produced a third beam of longitudinal phonons at 18.38 GHz." What
is a beam of phonons, and how would one be produced? What does it mean
for a phonon to have a physical location?
Anyone care to help clear up the notion of a phonon?
I wrote up my current understanding in a bit more detail at
http://www.livejournal.com/users/nibot_lab/7245.html if anyone cares to
look, but perhaps just an explanation of how a phonon is considered to
have position and velocity might be enough. I suspect that phonon
velocity might be tied to the group velocity of a collection of normal
modes... or I might be way off base.
thanks,
Tobin Fricke
Rene Tschaggelar
> Reading Kittel's Solid State Physics book, I'm trying to understand the
> concept of phonons. My current understanding is that a phonon is simply a
> normal mode of oscillation of a lattice, and that all possible modes of
> vibration are decomposed into these distinct modes via the discrete
> fourier transform (with the atoms in the lattice acting as sampling
> points).
>
> In this interpretation, a phonon only has 'location' in reciprocal space
> -- its corresponding wave vector. But then I encounter statements that
> don't seem to correspond to this understanding of what a phonon is, such
> as: "Shiren described an experiment in which a beam of longitudinal
> phonons of frequency 9.20 GHz interacts in an MgO crystal with a parallel
> beam of longitudinal phonons at 9.18 GHz. The interaction of the two
> beams produced a third beam of longitudinal phonons at 18.38 GHz." What
> is a beam of phonons, and how would one be produced? What does it mean
> for a phonon to have a physical location?
>
> Anyone care to help clear up the notion of a phonon?
You're right so far. Just make the next step now.
A phonon is a sound wave. In this experiment they were able to
mix two sound waves.
As to the production of it, I'd be interested myself.
Perhaps by coupling microwave into the cristal ?
Rene
--
Ing.Buero R.Tschaggelar - http://www.ibrtses.com
& commercial newsgroups - http://www.talkto.net
Joseph.D.Warner
Tobin Fricke wrote:
> Reading Kittel's Solid State Physics book, I'm trying to understand the
> concept of phonons. My current understanding is that a phonon is simply a
> normal mode of oscillation of a lattice, and that all possible modes of
> vibration are decomposed into these distinct modes via the discrete
> fourier transform (with the atoms in the lattice acting as sampling
> points).
>
> In this interpretation, a phonon only has 'location' in reciprocal space
> -- its corresponding wave vector. But then I encounter statements that
> don't seem to correspond to this understanding of what a phonon is, such
> as: "Shiren described an experiment in which a beam of longitudinal
> phonons of frequency 9.20 GHz interacts in an MgO crystal with a parallel
> beam of longitudinal phonons at 9.18 GHz. The interaction of the two
> beams produced a third beam of longitudinal phonons at 18.38 GHz." What
> is a beam of phonons, and how would one be produced? What does it mean
> for a phonon to have a physical location?
>
A phonon is a discrete quantum of vibrational energy. It is an isolated
disturbance of atoms in the medium. Look up supersound to see the
effects of "one" photon. It is hard to make just one phonon over a long
time scale. Shiren is probably just describing the progation of phonons
away from the sources he is using to making them. (Most likely a
pizoelectrical structure.) He probably have two sources with some angle
between the progation vector. He is mixing them in a non-linear material
(any pizoelectric material is non-linear). Just as with other waves
interacting together in a non-linear material they produce mixed waves
where two strongest usually have frequencies of w1+w2 and w1-w2. Where
w1 and w2 are the frequencies of the photon from the two sources.
>
> thanks,
> Tobin Fricke
>
Tobin Fricke
> You're right so far. Just make the next step now.
> A phonon is a sound wave. In this experiment they were able to
> mix two sound waves.
Yes, but is a phonon localized in space? I can see a continuous 'beam' of
sound being represented as a phonon, but a burst of sound would require a large
number of phonons in interference --- I think I have something wrong.
Tobin
Mark Folsom
news:400D550B...@grc.nasa.gov...
I never had a course in solid state physics, but I've imagined that each ion
in the lattice sits vibrating in some orbit about its equilibrium position.
Given that the motion of the ion is a deBroglie wave, there are allowed
orbits and prohibited orbits. That might explain why the propagation of
heat phonons is so excruciatingly slow compared to the speed of sound--a hot
ion has to stimulate a neighboring ion into an allowed energetic state. Of
course, I'm sure my simplistic picture will be "corrected" forthwith.
Mark Folsom
Franz Heymann
"Tobin Fricke" <to...@splorg.orgNOSPAM> wrote in message
news:bujq22$joc$1...@overload.lbl.gov...
> Rene Tschaggelar wrote:
>
> > You're right so far. Just make the next step now.
> > A phonon is a sound wave. In this experiment they were able to
> > mix two sound waves.
>
> Yes, but is a phonon localized in space?
The uncertainty principle says that if you know the momentum of a phonon
well, you do not know much about where it is. delta x * delta p > hbar
Franz Heymann
"Mark Folsom" <folsom_...@redshift.com> wrote in message
news:100qv72...@corp.supernews.com...
Sorry Mark, that was so much garbage that it is not worth correcting at all.
Franz
Mark Folsom
news:buk4ml$8j6$1...@titan.btinternet.com...
Well, if you put in interatomic spacing as the mean free path of a phonon,
and then look at what the thermal diffusivity of a solid is, the average
speed of propagation has to be a very small fraction of the speed of sound
in the same solid. What's your explanation?
Mark Folsom
Rene Tschaggelar
A beam of light consists of many photons. Likewise a beam of sound
also consists of many phonons.
I have no idea what the energy of a phonon is though.
A photon is hv, aka heisenberg constant times the frequency.
Reme
Joseph.D.Warner
Joseph.D.Warner wrote:
>
Every place I used photon please replace with phonon. Slip of the mind
and fingers.
Joseph.D.Warner
Mark Folsom wrote:
>
>>
>>Sorry Mark, that was so much garbage that it is not worth correcting at
>
> all.
>
> Well, if you put in interatomic spacing as the mean free path of a phonon,
> and then look at what the thermal diffusivity of a solid is, the average
> speed of propagation has to be a very small fraction of the speed of sound
> in the same solid. What's your explanation?
>
> Mark Folsom
Heat flow is a random step process while sound is a coherent process.
An analogy is to have a flow of water and then to pulse it. The wave
moves faster than the flow of the water but the wave contains must less
energy. Basically it just moves the water up and down. Sound wave does
the same thing. As the phonon passes an atom it bumps the atom or cell
up to a slightly different energy and then the atom goes back down to
the state it was before if the the interaction is elastic. Heat though
travels from onearea to the other raising the average energy level of
all the atoms or cells and lowering the average energy level from the
group behind it. This is a multiple phonon random walk problem while
sound can be thought as a coherent multiple phonon process with the
scattered phonons givig rise thermal phonons in the region the orginal
phonon is scattered.
It is the random walk of non-coherent phonons that slows the speed of
heat transfer as compared to the speed of sound.
Mark Folsom
I understand that it's a random walk. But if you model a random walk
mathematically and make a worst case assumption about the mean free path,
the necessary speed of propagation, to match actual thermal diffusivity
values, turns out to be quite slow.
Mark Folsom
Tobin Fricke
> > Yes, but is a phonon localized in space? I can see a continuous 'beam'
> > of sound being represented as a phonon, but a burst of sound would
> > require a large number of phonons in interference --- I think I have
> > something wrong.
>
> A beam of light consists of many photons. Likewise a beam of sound
> also consists of many phonons.
Right, but that doesn't really answer my question.
> I have no idea what the energy of a phonon is though.
> A photon is hv, aka heisenberg constant times the frequency.
The energy of a phonon of frequency v is the same as a photon at that
frequency: hv. If you have n phonons at frequency v, then the total
energy E = (n + 1/2)hv. This result for phonons comes from treating the
crystal lattice as a network of simple harmonic oscillators, with the
energy quantization coming directly from the SHO.
Tobin
Tobin Fricke
> A phonon is a discrete quantum of vibrational energy. It is an isolated
> disturbance of atoms in the medium. Look up supersound to see the
> effects of "one" photon.
I only found one relevant hit with Google for 'supersound' and 'phonon'
together -- does this phenomenon go by any other name?
Also, do phonons exhibit any other particle-like behavior other than their
energy quantization?
> It is hard to make just one phonon over a long
> time scale.
Is this mainly due to the non-linearities (higher order terms) in the
material, as you described, or some other effect?
thanks,
Tobin
Joseph.D.Warner
Tobin Fricke wrote:
> On Tue, 20 Jan 2004, Joseph.D.Warner wrote:
>
>
>>A phonon is a discrete quantum of vibrational energy. It is an isolated
>>disturbance of atoms in the medium. Look up supersound to see the
>>effects of "one" photon.
>
>
> I only found one relevant hit with Google for 'supersound' and 'phonon'
> together -- does this phenomenon go by any other name?
look under bosons, bosonic systems, helium 4, cryogenics ...
>
> Also, do phonons exhibit any other particle-like behavior other than their
> energy quantization?
They care discreet amount of momentum. They relect from boundaries as a
wave does. It is hard to separate the particle from wave behaviour. But
for you question they look and feel most like a wave.; thinking of a
photon as wavepacket is probably better.
>
>
>>It is hard to make just one phonon over a long
>>time scale.
>
>
> Is this mainly due to the non-linearities (higher order terms) in the
> material, as you described, or some other effect?
Their energy levels are usually so small. It is hard to excite just one.
It has more to do with instrumentation and engineering than physics.
Tobin Fricke
> The uncertainty principle says that if you know the momentum of a phonon
> well, you do not know much about where it is. delta x * delta p > hbar
Ah, I think that was what I was missing. A phonon of wavevector K has
momentum p=h*K/(2 pi) (by definition?), so if we know the wavevector
exactly, then we don't know anything about position --- the phonon is
spread out over the whole crystal. But if we know that the phonon has
wavevector K +/- delta K then the resulting wave packets can be said to
have a position and (group) velocity. How's that?
I think this also clears up some confusion I had about the de Broglie
wavelength --- it seemed contradictory that the de Broglie wavelength is a
single wavelength but a particle is actually represented as a wave packet.
But, analagous to the phonon case, the de Broglie wavelength lambda = h/p
will be the wavelength of a continuous beam of coherent particles. K=(2
pi)/lambda, so I suppose that's where the definition of phonon momentum
comes from?
thanks,
Tobin
Tobin Fricke
> > I only found one relevant hit with Google for 'supersound' and 'phonon'
> > together -- does this phenomenon go by any other name?
>
> look under bosons, bosonic systems, helium 4, cryogenics ...
ah, superfluid helium. thanks for the link.
I was amused to see that there are websites http://bosons.com/ and
http://fermions.com/ with the basics about bosons and fermions.
Phonons are quasi-particles that behave like bosons. Are there any
quasi-particles that behave like fermions?
> thinking of a photon as wavepacket is probably better.
Yes, it's helped a lot.
Tobin
Franz Heymann
I have a feeling that you are mixing up the rate at which heat diffuses in
solid with the speed of a phonon, as a coherent wave, in the solid.
Franz
Franz Heymann
>
>
> Joseph.D.Warner wrote:
> >
> Every place I used photon please replace with phonon. Slip of the mind
> and fingers.
I did it too, but hopefully I spotted it in time.
Franz
Pieter Kuiper
> I understand that it's a random walk. But if you model a random walk
> mathematically and make a worst case assumption about the mean free path,
> the necessary speed of propagation, to match actual thermal diffusivity
> values, turns out to be quite slow.
The order of magnitude should be the speed of sound in the material. Or
somewhat less, because the group velocity decreaes for higher phonon
energies.
One can measure phonon velocities by going to low temperatures
("ballistic phonons").
Something general about what waves are:
<http://acoustics.mines.edu/~jscales/papers/nature_wave.pdf>
--
"Electrons damage the brain," said Farish. (Donna Tartt)
Thomas Palm
@grc.nasa.gov:
>
>
> Joseph.D.Warner wrote:
>>
> Every place I used photon please replace with phonon. Slip of the mind
> and fingers.
A very useful slip. Photons and phonons are in many ways equivalent, and
most people are a lot more used to thinking about the wave-particle duality
for photons. Had it instead been mixing two lightbeams in a non-linear
crystal producing a beam with the sum frequeny it wouldn't have seemed as
mysterious.
Franz Heymann
"Tobin Fricke" <fri...@ocf.berkeley.edu> wrote in message
news:Pine.SOL.4.58.04...@conquest.OCF.Berkeley.EDU...
> On Tue, 20 Jan 2004, Franz Heymann wrote:
>
> > The uncertainty principle says that if you know the momentum of a phonon
> > well, you do not know much about where it is. delta x * delta p > hbar
>
> Ah, I think that was what I was missing. A phonon of wavevector K has
> momentum p=h*K/(2 pi) (by definition?), so if we know the wavevector
> exactly, then we don't know anything about position --- the phonon is
> spread out over the whole crystal. But if we know that the phonon has
> wavevector K +/- delta K then the resulting wave packets can be said to
> have a position and (group) velocity. How's that?
More or less.
>
> I think this also clears up some confusion I had about the de Broglie
> wavelength --- it seemed contradictory that the de Broglie wavelength is a
> single wavelength but a particle is actually represented as a wave packet.
> But, analagous to the phonon case, the de Broglie wavelength lambda = h/p
> will be the wavelength of a continuous beam of coherent particles. K=(2
> pi)/lambda, so I suppose that's where the definition of phonon momentum
> comes from?
That is so.
Franz
Franz Heymann
> On Tue, 20 Jan 2004, Joseph.D.Warner wrote:
>
> > A phonon is a discrete quantum of vibrational energy. It is an isolated
> > disturbance of atoms in the medium. Look up supersound to see the
> > effects of "one" photon.
>
> I only found one relevant hit with Google for 'supersound' and 'phonon'
> together -- does this phenomenon go by any other name?
Phonons are quantised lattice vibrations. See if you can find goog googles
with that.
>
> Also, do phonons exhibit any other particle-like behavior other than their
> energy quantization?
>
> > It is hard to make just one phonon over a long
> > time scale.
>
> Is this mainly due to the non-linearities (higher order terms) in the
> material, as you described, or some other effect?
>
Franz
Franz Heymann
> On Wed, 21 Jan 2004, Joseph.D.Warner wrote:
>
> > > I only found one relevant hit with Google for 'supersound' and
'phonon'
> > > together -- does this phenomenon go by any other name?
> >
> > look under bosons, bosonic systems, helium 4, cryogenics ...
>
> ah, superfluid helium. thanks for the link.
>
> I was amused to see that there are websites http://bosons.com/ and
> http://fermions.com/ with the basics about bosons and fermions.
>
> Phonons are quasi-particles that behave like bosons. Are there any
> quasi-particles that behave like fermions?
No. Fermions really are real particles.
>
> > thinking of a photon as wavepacket is probably better.
>
> Yes, it's helped a lot.
Franz
Gregory L. Hansen
Tobin Fricke <fri...@ocf.berkeley.edu> wrote:
>On Wed, 21 Jan 2004, Joseph.D.Warner wrote:
>
>> > I only found one relevant hit with Google for 'supersound' and 'phonon'
>> > together -- does this phenomenon go by any other name?
>>
>> look under bosons, bosonic systems, helium 4, cryogenics ...
>
>ah, superfluid helium. thanks for the link.
>
>I was amused to see that there are websites http://bosons.com/ and
>http://fermions.com/ with the basics about bosons and fermions.
>
>Phonons are quasi-particles that behave like bosons. Are there any
>quasi-particles that behave like fermions?
I would think not. Angular momentum changes in units of hbar. A
quasi-particle fermion would require changes of 1/2 hbar. You can have
spin 1/2 particles, but not 1/2 integral changes.
--
"And don't skimp on the mayonnaise!"
Pieter Kuiper
> Phonons are quasi-particles that behave like bosons. Are there any
> quasi-particles that behave like fermions?
Sure: the holes in a semiconductor. Also the negative charge carriers
are "dressed" electrons - you can see that their effective mass is
different.
Then there is the fractional quantum Hall effect, which can be explained
in different ways. One can use fractional charges:
<http://www.nobel.se/physics/laureates/1998/press.html>.
One can also construct anyons (Jain's combination of flux quanta with
electrons), quasiparticles that are neither fermions nor bosons.