Phonon Definition and 106 Threads

The low temperature heat capacity was experimentally shown to go as T^3 for low temeperatures (and as T for even lower temperatures for metals). This result came out of Debye's model after he modified Einstein's model, relaxing some of his assumptions. I have a few questions on Debye's model...

Good day everyone. I would like to know about the lower limit of the frequency range of active acoustic phonon modes. Textbooks say it can reach zero. But I am curious about whether it can be very small, such as 1 micro volt or the like. Would a phonon mode of so small energy be of any...

I am conducting an experiment on the parabolic trough that concentrates the solar light and heats up water. I am using different metal sheets (zinc, aluminium, copper, tin...) for the parabolic trough to see the differences in temperature change. I researched on a few things and I understand...

In a metal, can one electron decay into one lower-energy electron plus one phonon? (i.e., can the attached Feynman diagram occur?) If we replace phonons by photons and consider the process in a vacuum, I guess this is prohibited because you can always boost to a frame where the incoming and...

Phonons are quantized lattice vibrations. They are traveling waves of the form exp(ikr) taken to satisfy periodic boundary conditions. I'm guessing periodic boundary conditions are equivalent to demanding the waves to be zero at the boundary. which is what characterizes standing waves (right...

This occur when two phonons interact and the sum of their momenta add to a new wavevector outside the new Brillioun zone. The resulting wavevector is then mapped back into the Brillioun zone by subtraction of a suitable reciprocal lattice vector. I don't think I understand the physics in all of...

We have studied elastic waves in solids, standing waves in solid, heat capacity due to oscillation modes of individual atoms in a solid etc etc. And all these are put in the chapter called phonons in my book. So what are phonons basically? Are they just any kind of wave oscillatory motion that...

Hi guys, I'm reading solid state physics, I have some doubts about phonons. Here is the question, if we heated up a material, based on the the thermal equilibrium of occupancy of phonons given in Kittel's Introduction to Solid State Physics, <n> = 1/(e^(\hbar\omega/kBT)-1) so as T...

Hi everyone Homework Statement The frequence for phonons between two atoms with mass M1 and M2 is given by: \Omega^2 = C (\frac{1}{M_1} + \frac {1} {M_2}) \pm C*[(\frac{1}{M_1} + \frac {1} {M_2})^2 - \frac {4} {M_1 M_2} sin^2(\frac {Ka}{2})]^{\frac 1 2} Show that for Ka <<1 the...

Hi, can someone help me about rotating phonon eigenvectors? Say I have a primitive cell with 3 atoms, so for each point in reciprocal space, there are 9 eigen frequency and eigenvectors. Each eigenvector is a 9-dimensional complex vector. I calculated eigenvectors from a transverse branch...

Can we simply understand a softened phonon mode as one having reduced energy/frequency? Does "soft" indicate smaller value of the spring coefficient like the k in f=kx, where f is force and x is displacement of a spring, so a "soft" spring has a smaller k value? Thanks...

While practicing for an upcoming exam, i ran into this question that has truly got me stumped. A phonon dispersion graph is given for NiAl (attached), and then they ask you to schematicaly plot the density of modes graph. I have the result of what is should look like, but i do not understand how...

So during neutron scattering in a crystal, a neutron can interact with 0, 1, or more phonons. First of all, what is the actual mechanism by which they interact? My textbook just kind of glosses over that. Second of all, when a neutron goes in it can absorb a phonon and come out with more...

I found a lecture on the internet where a LCAO assumptions are used to calculate the phonon band structure. In this lecture (Here) we can find that the true Hamiltonian: H = \frac{p^2}{2m}+V_0(x) where V_0(x)=V_0(x+a) is replaced with the following aproximate hamiltonian: H\cong \sum_n...

Hey Everyone, I've a quick a question regarding the make-up of bosonic Green's functions, taking the free propagator for phonons as example. According to Mahan, 3rd ed. it is given by: D(q, \lambda, t-t')=-i\langle0|TA_{q}(t)A_{-q}(t')|0\rangle with A_{q}=a_{q}+a^{+}_{q} [ Eqs...

I am doing a basic introduction to solid state physics and I have come across a question which asks What the difference between two phonon interactions and three phonon intereactions. I know that Normal colission and Umklapp colissions are part of the three phono interactions since it tells me...

Hello, As you all know, if a crystal contains a phonon of frequency \omega, it means that the Fourier decomposition of the physical vibration of that crystal lattice contains a plane wave of frequency \omega, and the more phonons of a given frequency, the bigger the amplitude of that component...

I understand that the relationship between the phonon frequency and its wavenumber is the phonon dispersion. But is there a much more indepth definition of phonon dispersion and if i was asked to explain in a few lines (and in english not mathematical equations) what the phonon dispersion...

Homework Statement In a simple cubic lattice of spacing 0.2nm a phonon traveling in the {1 0 0} direction with wavelength 0.42nm collides with another phonon of the same wavelength which is traveling in the {1 1 0} direction. Draw a reciprocal space diagram to show the magnitude and...

Homework Statement If all the heat transport is by phonons, estimate the mean free path of phonons in Germanium at 300K using the following data. Thermal conductivity=80W/K m; Debye temperature=380K; atomic weight=72.6; sound velocity=4500m/s; density=5500kg m^{-3} Homework Equations...

hello I am new in this forum.. and i would like to ask first this is statement that i confused about 'At low values of k (i.e. long wavelengths), the dispersion relation is almost linear, and the speed of sound is approximately ω a, independent of the phonon frequency. As a result, packets of...

Homework Statement There is a Ar cube crystal with Lenard jones potential: V^{L.J.}=-\alpha/r^{6}+\beta/r^{12} We know the volume V, the parameters of the L.J. potential, and the mass of the Ar atom (m_{Ar}). Determine the phonon density of state. (D(ω)=?) Homework Equations...

I've got a question about interpreting these - mainly about how the horizontal axis works. See attached file - On the leftmost panel, it has a form of the wavevector q plotted from left to right, labeled as (000) on the left and (100) on the right. What does this mean? Does it mean that...

I mean how can i analysis the thermal conductivity of two structures with their phonon spectrum. thank you!

I'm doing a literature review on dispersion relations, and I've been told that if i can derive the phonon dispersion relation, it would help my review. So i was wondering if anybody could help me with the derivation either through Quantum-mechanical approach or Semi-classical treatment of...

We all know that there exist pseudogap in superconductors and in metals (semimetals). Were there the experiments, aimed to find gaps analogues to pseudogap in phonon spectrum? Is pseudogap T* is connected with some change in phonon spectrum in some direction? The same question for...

Dear friends of physics forum I have calculated the phonon dispersion of an fcc phase using PHONON software. the fcc phase I am talking about is a metastable phase of Zr. Zr, as we all know exists in hcp and bcc phases. I wanted to calculate the heat capacity at constant volume using the...

Hello, I am constructing a 2d atomistic mass spring Hamiltonian with nearest neighbor bonds (harmonic potential) in an attempt of calculating the phonon dispersion. I solve the eigenvalue system and calculated the eigenvalues or phonon energy levels (y-values of dispersion). I am fine up to...

Hi there! So I'm aware that the phonon contribution is proportional to T^3 and for electrons it is T (this is for metals where the first result comes from the Debye model). I was wondering where the electron contribution is derived from and why it is such a low dependence.

When exciting a phonon mode with an evanescent wave possessing a wavevector ~100-200X larger than freespace but still ~10X smaller than fermi wavevector, would one expect a different resonance frequency for the phonon mode? I would think not.. but experiment seems to say yes. More specifically...

Hello all, What does it mean when two phonon branches get crossed in phonon dispersion relation ? Also, in certain high symmetry direction, one can find only one transverse branch and other direction two separate branches, what do these response mean? (Ref. Solid state physics by...

I have searched this topic in our forums. no answer about that. I have obtained the phonon dispersion curve by applied a numerical simulation. However, how can I obtain the phonon density of state from such a curve? generally speaking, g(q)dq = g(w)dw, here q is the wave-vector; w is...

Question 1: If we consider that each atom in a cristal solid is a harmonic oscillator with the energy eigenvalues (n+1/2) \hbar \omega and if one oscillator has for example an energy (1+1/2) \hbar \omega, does this mean that there is a phonon located on this atom? Question 2: If this is true...

Hello, I seem to be having a problem with an assignment :confused: : I need to calculate the electric field at which optical phonons will be emitted. Here's what I have been given: Semiconductor with effective mass m=0.26*m0. The optical phonon energy is 50 meV. The mean scattering time...

Hello guys... Can anyone tell me where I can find a detailed calculation of the phonon self energy for an electron phonon interaction in graphene... The expression I need to get is in T. Ando paper: Journal of the Physical Society of Japan Vol. 75, No. 12, December, 2006, 124701 Equation...

Do you know the meaning of the Zero phonon or phonon-assisted?

Could You describe me what it is phonon replica. regards rafal

Hello everyone. This question may sound naive, but since I am relatively new to the subject, I would like to ask for some clarification related to phonon and electrical resistivity. As most of you might be aware of, electrical resistivity of crystalline metals increases due to increase in...

Hi In almost every reference I have found the phonon part of the frohlich electron phonon interaction hamiltonian is given by (b_{q}+b^{\dag}_{-q}) notice the +, where b_{q} is a phonon creation operator and b^{\dag}_{-q})is the destruction operator of a phonon. however in a paper on...

The electron-lattice interaction potential is given by V(r)=\sum_{i} Q_{i}\nabla V_{ei} \left( r- R_i\right) where i is a summation over lattice sites, Q_i is the lattice site displacement, and V_{ei} is the coulombic interaction Now According to Mahan's book Many particle physics...

http://qm-web.library.qmul.ac.uk/exams/science/physics/2008/PHY108.pdf Questions 9) and 10). The resources on them are scarce, can't seem to find understandable explanations for it, could anyone give me a hand here?

Hi, I'm trying to distinguish phonon branches in the case of branch crossings in some complex phonon dispersions, like in the below example: http://cmt.dur.ac.uk/sjc/thesis/thesis/img354.gif My question is, how can I know which portions near the crossing belong to the same branch? I've...

Hello there, my physics friends. I was hoping ye could answer a wee question I have on the phonon spectrum. Mainly,what is it? I know one of the mediations is sound but that's about it. If possible could you put it in terms similar to that of the electromagnetic spectrum. Thanks in...

is there any book discussing goldstone mode? i am not very familiar with field theory. Could anyone suggest some books accessible to a non-field-theory theorist? i guess the acoustic phonon is a goldstone mode but the optical phonon is not. Since a goldstone mode is associated with a...

Hello all, I have calculated the phonon energies and frequencies in some code for bulk GaAs. Now I want to analyse these frequencies, I do not know which ones are the acoustic ones which are the optical and how I can recognize the LOTO splitting ?? Here is the calculated phonons: Phonon at...

Hi! I was looking at the high- and low-temperature limits of the specific heat in the quantum theory of cristals (Ashcrof&Mermin, Chap. 23). To get the behavior under these limits, one consider first the case where T is large compared with all the phonon frequencies and second, when T is low...

Well again I'm very new to the field of solid state physics. I understand that phonons are the lattice vibrations which are transferred from one atom to another. In case of harmonic vibration, the phonons are similar to the elastic spring and the atoms are considered like the balls attached to...

Homework Statement Ok, I need to show that in an acoustic mode of vibration in a diatomic lattice, for small k, \omega \propto k, and find the constant of proportionality. Homework Equations A_1\left(\omega^2M-\frac{2T}{a}\right)+A_2\left(\frac{2T}{a}cos(ka)\right)=0 , and...

Homework Statement My solid-state physics book (Kittel) talks about the phonon mean free path (on page 122) but never defines it. Can someone please give me a definition? I know what a mean free path is for a non-quasi-particle but I do not see how that extends to phonons. Homework Equations...

Hi , i need some scientific source (book, article etc.) on phonon condensation in solids. Google scholar seems to fail in this topic. Can anyone advice me some source ?