Questions tagged [phonons]
Collective excitations in periodic, elastic arrangements of atoms or molecules in condensed matter, like solids and some liquids. They are quasiparticle quantum modes of vibration of elastic structures of interacting particles.
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Why does kinetic energy below molecule bond energy break bonds?
I was thinking about why bullet can break molecular bonds when it hits solid target despite the fact that the kinetic energy of the individual atoms that make up the bullet is less that the molecule ...
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Are sound waves in fluids also Goldstone modes?
One usually says that sound waves in a crystal, ie. phonons, are Goldstone modes of the broken translation symmetries. However, fluids have sound waves and also translation invariance. In fact, it's ...
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Questions about scattering matrix theory of non-free particles
Hi，I have a problem for scattering matrix theory.
Currently, the book I've read is about collision between free particles.
What if collision between non-free particles? For example, in lattice, only ...
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Why does silicon have 6 phonon modes instead of 24?
As is known, silicon has a structure made up of two intertwined face-centered cubic (FCC) lattices, with bases $[000]$ and $[\frac 1 4,\frac 1 4,\frac 1 4]$.
This equates to $\frac{1}{8}\cdot 8 + \...
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How does heat is generated during nuclear reaction
In a nuclear reaction 235-U is being constantly divided under high neutron flux. After the division we get 2-3 neutrons with high energy and fission products with its own energy. My question is from ...
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How many atoms are in the primitive unit cell for diamond?
The primitive unit cell for diamond is pictured (the parallelepiped inside the cube). How many atoms are in the unit cell? My first guess is 3.5 and i know this must be wrong as the number of atoms in ...
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Phonons in quantum dots
If my understanding is correct, quantum dots are tiny crystals where the confined electronic degrees of freedom have discrete energy levels. In this paper Phys. Rev. B 65, 195313 (2002), and many ...
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High temperature phonon heat capacity and equipartition theorem
I have seen the derivation of the high temperature heat capatcity sing integration of the density of states. The heat capacity is $C=3Nk_B$ with $N$ the number of atoms in the lattice. According to my ...
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Why the phonon modes may not be horizontal at the brillouin zone boundary?
In the book Principles of the Theory of Solids by Ziman, it says:
The exact behaviour then will be rather complicated. In general, (the
phonon mode) $\nu_q$ bends over, as in the linear case, ...
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Harmonic Approximation for dynamical matrix in 3D fcc-lattice
I have maybe a basic misunderstanding of how the harmonic approximation is working. I have the following problem:
Given a fcc-lattice with lattice constant $a$ and a radial-symmetric
potential
...
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How do normal modes have group velocity?
Considering phonon dispersion curves in crystals, the group velocity is given by the derivative of frequency with respect to wave vector.
But these modes on the dispersion represent normal modes, ...
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How can I meaningfully diagonalize the eigenvector subspace of a degenerate phonon mode?
It often occurs to find phonon modes which are degenerate by symmetry. In such occasions the eigenvector is usually not physically insightful, as is is a linear combination of the n degenerate ...
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Is the absorption of photons instantaneous?
I'd like to know if the excitation of chlorophyll by photons $$Chl+ h\nu \rightarrow Chl^*$$
is instantaneous. I imagine a photon arriving $0.5$ Angstroms away from the molecule, and then disappearing ...
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From a gravitational wave detector perspective, what is the difference between a gravitational wave and a phonon?
I already asked a question but it seemed that it was not precise enough. My problem is that I cannot see how gravitational waves have anything to do with spacetime. An EM wave or a phonon can put ...
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Why isn't the dispersion of the phonon spectrum of two atomic basis with equal masses the same as for the one atomic basis?
The solution for the two atomic basis is given by
\begin{align*}
\omega^{2}=\gamma\left(\frac{1}{M_{1}}+\frac{1}{M_{2}}\right) \pm \gamma\left[\left(\frac{1}{M_{1}}+\frac{1}{M_{2}}\right)^{2}-\frac{...
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Deriving effective interactions, e.g. phonon-mediated electron-electron interaction
Upshot of the question: how can I derive the effective electron-electron interaction brought about by the electron-phonon interaction?
I've read derivations of the electron-phonon interaction and ...
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Why do purely harmonic interatomic interactions result in infinite thermal conductivity?
When interatomic interactions are purely harmonic, normal modes cannot interact, and therefore no phonon scattering occurs, thus resulting in infinite thermal conductivity.
But why is anharmonicity ...
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Mossbauer effect: neglectable recoil or absolute no recoil?
I stumbled on the Mossbauer effect. From the wikipedia article, I cannot tell for sure if the momentum of recoil is really zero, or only neglectable.
From what I do (think I) understand, the ...
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Should phonon energy be undefined at zero frequency?
The energy carried by phonons of frequency $\omega$ is given by
$$
E = \hbar \omega n_b(\beta \hbar \omega) = \hbar \omega \frac{1}{exp(\beta \hbar \omega) - 1}
$$
So when $\omega = 0 $, the energy ...
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The difference between optical phonons and acoustic phonons in terms of energy absorption
Why can the energy of a photon be directly absorbed by an optical phonon but not by an acoustic phonon？
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Heat capacity due to Phonon Vibrations
Why does the speed of sound come, in the expression of Heat capacity, from phonon vibrations?
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Calculate phonon density of states
I need to calculate phonon density of states for a cuprate superconductor. I know there is a general formula for the calculation of phonon density of states by Einstein models like this
$$D(\omega)=(\...
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Optical and acoustic branch
Does a diatomic crystal posses both optical and acoustic branch simultaneously; Or, whether the vibration is either optical or acoustic?
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Why optical phonons are called “optical”? [duplicate]
In diatomic lattice vibration, acoustical phonons correspond to vibration. But I could not understand the relevance of term optical in this context.
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Vibrational Energy at T = 0 K using the Debye model
I mm trying to estimate the vibrational energy at $T=0$ for a 3-D lattice using the Debye model.
My plan is to sum over all the frequencies using:
$$U = \int_0^{\omega_D} d\omega D(\omega)\epsilon(...
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Approximations in article on phonon-assisted emission
I am trying to reproduce the calculations from an old article by J.J. Hopfield (J. Phys. Chem. Solids, vol.10, pp.110-119 (1959) - A theory of edge emission phenomena in CdS, ZnS and ZnO - found here)....
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Elastic X-ray diffraction: Where does the Photon Momentum go to?
lately I was discussing the following situation. Let's suppose you are doing X-Ray diffraction experiments on a crystal. So what you basically do is shooting a high energy photon with a wave vector $k$...
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Why phonon density of state depends on velocity autocorrelation?
We know that if we take the Fourier Transformation of velocity autocorrelation function, we will get the phonon density of state. But why phonon density of state depends on this? What is the physical ...
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Thermalizing bulk superconductors
I have been discussing with some friends whether or not (or how) bulk superconductors thermalize when placed in an environment far below their transition temperature.
Suppose you have a cube of pure ...
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Derivation of the dynamical matrix
I am following a derivation of the dynamical matrix given at http://physik.uni-graz.at/~pep/Lehre/PP/DynMat.pdf. Here T and W are kinetic and potential energies.
$T=\sum_{n\alpha i}\frac{M_{\alpha}}{...
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How does Bohmian Mechanics explain superconductivity?
I'm looking for sources that discuss how Bohmian Mechanics explains superconductivity. Are there still Cooper pairs? Phonons? I saw one vague reference to vortices, but no details. This is my first ...
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Is this equation for the density of states of an elastic isotropic material an approximation?
The density of states of phonons can be calculated with
$$
Z(\omega)=\frac{V}{(2\pi)^3}\int_{\omega=\text{const}}\frac{d\vec{f}_\omega}{|\vec\nabla\omega|}
$$
where $\omega$ is the phonon frequency ...
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Doppler shift in Acousto-Optic modulators
The interaction between a beam of light and an acoustic wave is commonly modelized as a photon-phonon scattering phenomenon. Applying the conservation of energy we have that
$$ \hbar\nu_1=\hbar\nu_0\...
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Long-ranged Coulomb Interaction $\Rightarrow$ Longitudinal Plasmon Modes?
I am currently taking a lecture on quantum theory of condesed matter systems. In the lecture notes it is stated that
For long-ranged Coulomb interactions only longitudinal plasmon modes are ...
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Are acoustic phonons always the lowest energy vibrational modes in solids?
In solids with unit cells containing more than one atom, the normal modes show acoustic and optical branches. The number of optical branches is proportional to the number of atoms in the unit cell, ...
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Can we consider oscillation of air column in the wind instruments as phonons subject to Bose- Einstein statistics ?
A flute is a wind instrument, which could be modelled as a resonance cylinder open at both ends. Any cylinder resonates at multiple frequencies. A skilful player produces a standing wave in the flute ...
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What is the difference between acoustic photon and acoustic phonon?
In the book Biomedical Photonics Handbook, 3 Volume Set edited by Tuan Vo-Dinh, it is written : Brillouin Scattering is caused by the interaction of the photon with the acoustic phonon. As the result ...
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Why the chemical potential of phonon gas in Einstein 's solid model is not zero
In Einstein’s model of solid, each atom in the solid is considered to be an independent three-dimensional quantum harmonic oscillator with characteristic frequency $ω$ that is constant. Each degree of ...
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Understanding what the Bose-Einstein distribution
I'm currently studying Kittel's Solid State Physics and in his chapter on Phonon heat capacity, we need to first calculate the total energy $U$. Phonons have energy $E_n = (n+1/2)\hbar\omega$ and he ...
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Understanding the technical bits of quantising elastic waves
I'm reading Kittel's Solid State book and I have a number of 'simple-ish' questions regarding phonons. He starts with the hamiltonian
$$H=\sum_{s=1}^N\left[\dfrac{1}{2M}p_s^2+\dfrac{1}{2}C(q_{s+1}-q_s)...
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Spontaneous symmetry breaking in fluids
BACKGROUND:
One can think of solids as spontaneously breaking translational symmetries in the sense that each atom in a lattice has to pick a particular position. Yet, as with everything in our ...
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What is the phonon/lattice interaction?
To my understanding, phonons in solids are an excited state of a lattice, i.e., a lattice of atoms oscillate at a certain frequency. Phonons are quasipartices.
But what should the phonon/lattice ...
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Debye Temperature for Copper
I am trying to calculate the Debye temperature, $\theta_D$, of copper using the following:
$$
\theta_D = \frac{\hbar v_s}{k_B} \left( \frac{6\pi^2N}{V} \right)^{1/3}
$$
I have the following values: $...
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Why does acoustic imepdance increase when mass density and bulk modulus increaes?
If we take some material and (somehow) increase its mass density or bulk modulus then its acoustic impedance will increase as $z = \sqrt{\rho \kappa}$. That is, it What is the physical reasoning ...
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Allowed k value for maximum and minimum phonon frequency in a diatomic lattice
I've got an expression for the phonon frequency in a diatomic lattice where the atoms are of mass $m$ and $5m$. The expression is $\omega^2=(12Cm\pm\sqrt{(144C^2m^2-20m^2C^2(1-\cos(ka)})))/(10m^2)$. I ...
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Can light cool down materials?
I was studying Raman scattering and I computed the probability of anti-Stokes scattering (with density of states n, at the numerator) over Stokes (n+1 at denominator). The densities are based on the ...
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In phonon theory, what is the physical significance of the force constants tensors?
I want to compute phase equilibria of crystalline solids using First-principle methods (DFT in particular). The methodology for this computation is described in this chapter.
In order to calculate ...
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Can the periodicity in k-space of the electronic band structure be understood as a result of aliasing?
Discrete sampling in the case of phonons
In the case of phonons in periodic solids, the picture is quite intuitive. The motion of the atoms in the lattice is described as a continuous wave (amplitude ...
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How many types of phonons are there, and what are their characteristics?
I've skimmed through Wikipedia's article, as well as as PSE question What is a phonon?, but I am still entirely left in confusion as to the types of phonons and their corresponding characteristics and ...
asked Aug 28 '18 at 8:02
thermomagnetic condensed boson
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Pauli principle for “Phonons”
I'm reading in Feynman's "Statistical Mechanics" Chap. 6.4 about a system of $M$ interacting particles, they may be bosons or fermions. Let the hamiltonian be
$$ H=\sum_i^{3M}p_i^2+\sum_{ij}^{3M}U_{...
