# What is Brillouin: Definition and 52 Discussions

Brillouin scattering (also known as Brillouin light scattering or BLS), named after Léon Brillouin, refers to the interaction of light with the material waves in a medium. It is mediated by the refractive index dependence on the material properties of the medium; as described in optics, the index of refraction of a transparent material changes under deformation (compression-distension or shear-skewing).
The result of the interaction between the light-wave and the carrier-deformation wave is that a fraction of the transmitted light-wave changes its momentum (thus its frequency and energy) in preferential directions, as if by diffraction caused by an oscillating 3-dimensional diffraction grating.
If the medium is a solid crystal, a macromolecular chain condensate or a viscous liquid or gas, then the low frequency atomic-chain-deformation waves within the transmitting medium (not the transmitted electro-magnetic wave) in the carrier (represented as a quasiparticle) could be for example:

mass oscillation (acoustic) modes (called phonons);
charge displacement modes (in dielectrics, called polaritons);
magnetic spin oscillation modes (in magnetic materials, called magnons).

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1. ### I Electron scattering in the Brillouin zone boundary

I what to know what is electron scattering in Brillouin zone boundary? What exactly happen for electron in Brillouin zone boundary; what happen for it in real space and what happen for it in reciprocal space? And is electron scattering from a Brillouin zone boundary could be a source for...
2. ### Brillouin's negentropy in an Einstein solid

Hello! I would like to apply Brillouin's negentropy principle to an isolated Einstein solid, with a decreasing number of oscillators. We assume that the number of oscillators are initially N and the energy quanta (q the number) remain constant. Firstly, I would like to know if this principle is...
3. ### A Raman spectroscopy and the phonon confined in the Brillouin zone

Hello everyone, I need some confirmation on something: As far as I understood, the raman spectroscopy measures the inelastic scattering of a photon in a medium through the absorption or the emission of a phonon in the medium. The energy and the momentum is conserved...
4. ### How to think about a Brillouin Zone?

Isn't a Brillouin zone a Wigner Seitz cell in reciprocal space? Is it just a collection of wave vectors? Will you have Brillouin zone boundaries in many different places in your real space crystal, and hence standing waves there? What causes the standing waves at the zone boundaries? Isn't a...
5. ### Is first Brillouin zone the same as Wigner-Seitz cell?

Homework Statement Not a homework question, but I am attempting to understand what exactly the first Brillouin zone is. Homework EquationsThe Attempt at a Solution From my textbook, what I'm gathering is that one constructs the first Brillouin zone by constructing a "Wigner-Seitz" type cell in...
6. ### What is the purpose of Electro-Optical Modulator (EOM)?

Hello, I'm studying the setup of distributed Brillouin sensor (using fibre optics) and don't quite understand the purpose of EOM in the sensor. It says that "to generate both the pump and the probe waves from a single physical light source by using an electro-optical modulator (EOM)", but since...
7. ### A Basic questions on crystal lattice: k-vectors and Brillouin

Hi all, I’m brushing up my skills on solid state physics and I have a few questions about crystal lattices: 1. What’s the spacing between allowed kx, ky, and kz states for a lattice of dimensions La x Lb x Lc? My attempt: The spacing is kx, ky, and kz: k_x = \frac{2\pi}{L_a}, \qquad k_y =...
8. ### A Why is the Brillouin zone a torus?

Recently, topological concepts are popular in solid state physics, and berry connection and berry curvature are introduced in band theory. The integration of berry curvature, i.e. chern number, is quantized because Brillouin zone is a torus. However, I cannot justify the argument that...
9. ### Brillouin Zones: Primitive Reciprocal Lattice Vectors

Hi fellows, An FCC lattice has one atom per unit cell and a set of primitive vectors. Its 1st BZ has its distinctive 3D shape, set explicitly by the Wigner-seitz cell in the reciprocal space. What if we have a zinc-blende (GaAs) lattice with 2 atoms per unit cell? How are the primitive...
10. ### Integrating Wannier Functions: Simplifying the Prefactor Equation

Homework Statement I did not manage to get the final form of the equation. My prefactor in the final form always remain quadratic, whereas the solution shows that it is linear, Homework Equations w refers to wannier function, which relates to the Bloch function ##\mathbf{R}## is this case...
11. ### Energy gap between brillouin zones?

Homework Statement Consider a monovalent 2D crystal with a rectangular lattice constants ##a## and ##b##. Find expressions for the fermi energy and fermi wavevector in 2D. Show that the fermi surface extends beyond first zone if ## 2a > b\pi##. If the crystal is now divalent, estimate the...
12. ### Why is the volume of FCC and BCC different in reciprocal space?

Taken from http://dao.mit.edu/8.231/BZandRL.pdf BCC In real space, it has a simple cubic lattice with one basis in the centre. Total number of atoms per unit cell = 2. Volume of primitive unit cell is then ##\frac{1}{2}a^3##. In reciprocal space, BCC becomes an FCC structure. It has a simple...
13. ### Dispersion relation for the free electron model

I'm trying to get my head around what this means exactly. I've plotted the graph to help verse me with the functions that I've derived. From the free electron model, the wavefunctions are treated as planewaves of the form \psi_\mathbf{k}(\mathbf{r}) = e^{i\mathbf{k}\cdot\mathbf{r}} Due to...
14. ### What is the first Brillouin zone and how do I construct it?

HI, I read the other threads in this forum but I still didn't understand (and I have read Aschroft and Mermin as well as Kittel). So, could you pleae explain to me (preferably in a VERY detailed manner) what is the first Brillouin zone and how do I construct it? Thank you :)
15. ### Volume of Brillouin zone is the same as Fourier primitive parallelepip

In Kittel's solid state text, problem 2.3, he says that the volume of the Brillouin zone is the same as a primitive parallelepiped in Fourier space. Somehow I can't see why this is true. Can someone help me see why this is true? Also, is the same relationship true between Wigner-Seitz cells and...
16. ### What Is the Brillouin Zone in Solid State Physics?

How can I define brillouin zone?
17. ### K vector in first brillouin zone

Hey guys, I just realized that there is a gap somewhere in my understanding of K vectors and reciprocal space. My question is how can we talk about K vectors "living" in the first Brillouin Zone, when these vectors cannot be expressed on the vector form of reciprocal space ( r*=ha*kb*+lc* ...
18. ### Understanding Brillouin Zones - What do they represent physically?

Hey all, Quick question about BZ's and it's probably a really dumb one. Solid State isn't my favorite class... What does it physically represent? Like is the area of the BZ divided by the area of a k-state (2π/L) equal to the number of charge carriers in the system? So if there was an...
19. ### Acoustic Wave Velocities in Brillouin Zone

Acoustic Wave Velocities in Brillouin Zone - Phonon Spectrum of Ge Homework Statement Acoustic Wave Velocities in Brillouin Zone - Phonon Spectrum Diagram The exact problem I'm stuck on is Q3c on this exam paper. I have included an image of the problem below. I haven't had any trouble up...
20. ### Bragg and Brillouin diffraction

I'm supposed to give a seminar tomorrow for my 300 level experimental physics paper. The experiments we do our reports on are pre-determined and I pulled the short straw with the most bloody complicated on here, the acousto-optic modulator. I'm trying to get my head around it and I've spend the...
21. ### Stimulated Brillouin scattering inside an optical fiber

Hello everyone I need some one once and for all to give me the steps to have a clear step by step idea about the stimulated Brillouin scattering inside an optical fiber please and thank you
22. ### How can the band-gap structure be determined using the E-k graph?

Hi all, If you are given the real space lattice vectors (14 Angstroms in the x-direction and 8 Angstroms wit an angle of 91 degrees between them) and have to draw the reciprocal lattice and the the first Brillouin zone, and then using this data sketch the E-k graph and comment on the band-gap...
23. ### Brillouin Zones, Phonons, Energy Propagation through a Crystal

Hello, I am having quite a bit of trouble really grasping Brillouin Zones and their relation to phonons, energy propagation, etc. I've got a few questions, and there will probably be a number of misconceptions, but I figure they'll clarify what I exactly don't understand. I think a lot of the...
24. ### Fock space and the Brillouin condition

Hi there! in a recent lecture on fock space, i was given the brillouin condition for two-particle operators:- <\Phi_{0}|a^{†}_{a}a_{r}h|\Phi_{0}> = \frac{1}{2}\sum\sum<\Phi_{0}|a^{†}_{a}a_{r}a^{†}_{\lambda}a^{†}_{\mu}a_{\lambda'}a_{\mu'}|\Phi_{0}><\lambda\mu|g|\mu'\lambda'> =...
25. ### Solid State - Phonons at Brillouin Zone Boundary

Homework Statement Homework Equations {3.9b} A[2\mu -m\omega ^2 ]=2\mu Bcos(\frac{ka}{2}) B[2\mu -M\omega ^2 ]=2\mu Acos(\frac{ka}{2}) The Attempt at a Solution All I can think of is setting k =\frac{\pi}{a} so that B[2\mu -M\omega ^2 ]=A[2\mu -m\omega ^2 ] solve for omega...
26. ### Finding Distances to Brillouin Zone Borders from Origo

Hi, i have problems understanding the Brilluoin zone to the bcc lattice First, i wonder what the distances are, from the origo to the brillouin zone plane borders. I firts thought it would be half the distance of the basis vectors (mine are 2pi/a, where a is my lattice constant, BUT its only...
27. ### Why are the K points in the Brillouin zone of graphene inequivalent?

The Brillouin Zone (BZ) of both graphene and the (111) surface of metals like Ag(111) eihibit a hexagon, but I wonder why the BZ of graphene has two inequivalent ponits K and K', while the K point of BZ of the Ag(111) is equivalent. Thank you in advance!
28. ### Calculating Energy Levels for Lattice Using Analytic Continuation?

When energy levels for a lattice are constructed the Bloch wave vector is evaluated along the edges of the irruducible zone. Like \Gamma - X - M path for a square lattice. I wonder why the calculation is NOT performed for values within the zone? And how the energy corresponding to an...
29. ### Group velocity at Brillouin zone boundary

I am working on an assignment here; A linear chain with a two-atom primitive basis, both atoms of the same mass but different nearest neighbor separation and thus different force constants. I have made a rigorous calculation in order to find the dispersion relation ω(k), with extensive...
30. ### Ewald sphere vs Brillouin Zone

Is it correct to say that the Ewald sphere and Brillouin Zone are both representations of k'=k+G? I'm comfortable with the construction of the Ewald sphere, but don't quite see how a BZ represents k'=k+G. Can anyone explain how the construction of a BZ represents k'=k+G and whether it...
31. ### Brillouin zones and the E-k relation

Hi, I'm having some trouble to fully understand how energy bands are formed in Brillouin zones. Almongst a few of the questions I have are: In a 2D plane of atoms, where a is the lattice constant in the x-direction and 1.5a in the y-direction. Would the brillouin zone edge in the k_y...
32. ### Brillouin Zone Size: Debate Settled

Hi guys, Me and a few of my coursemates are revising for a solid state exam but have hit a problem. Is the area of every 2D brillouin zone (independent of lattice type) (2Pi/a)^2? For a square lattice in 2D real space with lattice constant, a, the reciprocal lattice vectors can easily be found...
33. ### First Brillouin Zone: Unravelling Why [-pi/a,pi/a)

Hey all, I have a question with first Brillouin zone. It's: It says that it's enough to consider values of K within the first brillouin zone, K= [-pi/a,pi/a). why is this easy to see, and why don't we choose the interval K= (0 , 2pi/a) instead? Why is the point K=pi/a not included (open...
34. ### Trying to understand the Brillouin zone

I am having a really hard time understanding how the Brillouin zone relates to electron states and have a couple of questions that might help clear it up for me. For a band structure like this: https://wiki.fysik.dtu.dk/gpaw/_images/silicon_banddiagram.png I know that the different...
35. ### How to show all Brillouin zones have same volume

It is quite easy to calculate the volume of the first brillouin zone to be (2pi)^3/V if V is the volume of a unit cell in the real lattice. In many places one can also find the statement that all Brillouin zones have the same volume. I have not however found a proof of this anywhere. The 3D case...
36. ### Raman vs Brillouin scattering?

I am researching smart structures using optical fibre based sensors. One type used is distributed sensors of which there are two main kinds: ROTDR (Raman Optical time domain reflectometer) and BOTDR (Brillouin Optical time domain reflectometer). The former is based on Raman scattering within the...
37. ### First brillouin zone construction

Hi All, Is there any software or program to show the first brillouin zone and the miller index of zone boundary plane ? I use Mercury, but there is no such function.
38. ### Brillouin Zone & K Point Explained

what is Brillouin zone and K point?
39. ### Brillouin zone: reciprocal lattice

Can somebody explain me how can we visualise reciprocal lattice of a crystal lattice. Also what do we mean by wavevectors of a reciprocal lattice. What is its physical significance?
40. ### Calculating Electron Mass at Band Bottom & Brillouin Corner

Homework Statement What is the effective mass of the electron at the bottom of the band and at the corner of the Brillouin Zone? What is the significance of these results? Atoms lie on a square lattice of side a. Homework Equations E(kx,ky) = C{1 - cos(kxa) - cos(ky)} The Attempt...
41. ### Proof that the n brillouin zones are of equal areas?

proof that the "n" brillouin zones are of equal areas? i'm trying to find a way to prove that the brillouin zones are indeed of equal areas. if i draw, for examle, the first 3 or 4 brillouin zones of a cubic 2-dimensional lattice, then it is relatively easy to show geometrically how the parts...
42. ### Energy Bands and Brillouin Zones

I've been studying electronic band structure in the NFE model, but first the free electron bands. I'm just a bit curious as to the exact interpretation of energy vs. wavevector plots. The free electron plot is parabolic. I know all physically distinct solutions lie in the 1st Brillouin Zone...
43. ### Brillouin zones and energy bands

In the semi-classical model, i noticed that all the electrons with values of k that are in the same brillouin zone are considered to be at the same energy band, but i can't quite understand why it is so. i know that in each brillouin zone the number of allowed states (of k) is the same as the...
44. ### Solid State in tight binding approximation, Brillouin zone, Fermi

Hello, In few days, I have an examination, and I still have some dark zone in my head! If somebody could help me by giving me some advices/answers/way of reflexion/books to consult, it could be very great! Here is my questions: How to determine energy levels and wavefunction of the...
45. ### Brillouin Zone of BCC lattice?

I'm answering a question where it becomes necessary to know the closest face of the BZ in a bcc structure. The answer is given as +/- (2*pi) / (sqrt(2)*a) where a is the cubic lattice parameter. I would have thought the Answer would have been sqrt(3)*a / 4. Where does the pi come from...
46. ### Solid state - Energy of electron in Brillouin zone

Homework Statement Using geometrical arguments or otherwise, derive how the energy of an electron in the second Brillouin zone may be less than the energy of an electron in the first zone. [3] Homework Equations The Attempt at a Solution I'm thinking this has something to do...
47. ### Wigner-Seitz = Brillouin Zone?

I am confused about the relation between the Wigner-Seitz cell and the first Brillouin zone. My teacher explained that to find the Wigner-Seitz cell in real space, one draws lines between the lattice points and connects the perpendicular bisecting planes. This constructs the volume nearer to...
48. ### How Does the Brillouin Zone Influence Electron Wavefunctions in Solids?

Hi, I'm following the book of Kaxiras on solid state physics and I'm a bit confused about Brillouin zone and solving Schroedinger equation in BZ. Please let me to write the logical statements I've understood (maybe correct ot not): 1. Crystals are made up of atoms located periodically in...
49. ### Copper oxide plane and brillouin zone

I am having trouble understand the crystal structure or copper oxide and what the first brillouin zone looks like.
50. ### Understanding Brillouin's Entropy Decrease

I do not quite understand how Brillouin goes from k\cdot \Delta (\log P) to -k\cdot \frac{p}{P_0} in this context: from "Maxwell's Demon cannot operate: Information and Entropy", L. Brillouin, 1950. Could anybody offer a meaningful explanation? [I added the "The entropy decrease is...