Making sense of Brillouin Zones - Part 1

[@dunderdemo]

Thank you! I'm only 2 minutes in but a already understand more then I have learnt the past 2 weeks in class :)

[@k9pker]

Thanks that was very clear. Not going to make any puns about crystals to say how clear.

[@whitcwa]

Thanks for your transparency, but there are opaque crystals

[@Ad_Mico]

Reciprocal lattice... that's a tricky in words and it's probably best put by wikipedia as "the lattice in which the Fourier transform of the spatial wavefunction of the original lattice is represented." In other words, imagine you have an electron wavefunction e^ikr in a crystal where the sites are in real space r. The reciprocal lattice is just that crystal transformed into momentum space k.

[@tulikatripathy]

Got it ! But I don't understand why do we need to use the concept of reciprocal lattice in forier space and imagine something complicated which is actually not der.. Rather y can't we use the direct lattice to describe all phenomena??? Similar in the case of Miller indices.. Y can't we use the real coordinates of a plane..

[@Ad_Mico]

+Tulika Reema Perhaps you can, it's just a lot more hard work to do it. Sometimes introducing a hard concept to remove a lot more hard work in living without it is worth it. Just got to face the challenge of understanding the concept and life is easy thereafter.

[@bakulvinchhi]

What is wave with the different lambdas on Brillouin Zones ? what does it mean, wavelength, wave on the Brillouin Zones ?

[@yakovhammer5739]

Man Dennis from its always sunny is really a genius

[@mohibmohib6442]

I always noticed that the points (111) became (kx=ky=kz=pi/a) and X(011) becam (Kx=Ky=pi/a , Kz=0) Is there a rule for transferring them..? please

[@flav6350]

I understand the concept of aliasing but since we are talking about the electron's dispersion relation, why does this have to do with lattice spacing? For me this concept is very clear for acoustic waves, which are "lattice waves" but I don't see any reason why electrons in a crystal could not have a wavelength smaller than the lattice.

[@mohammadarshadpathan490]

Really good question

[@sagarrawal8332]

still couldn't understood what is Brillouin zones or how they are formed.

[@shabijun]

Thanks for uploading this. Very clear explanation.... Does the same explanation apply to the plasmon dispersion relation?

[@Ad_Mico]

+Shabnam Fa For the most part, yes. There's a few differences, but physics is often like this. Similar ideas keep coming around with a few tweaks to adapt to a different physical situation.

[@sivonparansun]

Quick Q: why is the spacing in the reciprocal lattice 2*pi/a ? Is related to needing units of inverse meters in K-space?

[@Ad_Mico]

+chris s Partially. Ultimately though, it all comes down to the relationship between wavenumber and wavelength which has a factor of 2pi included k = 2*pi/l. Inverse space can be measured in multiples of wavenumber as much as real space can be measured in multiples of wavelength. All we're doing is just converting convenient units across.

[@Xz4]

When you're explaining the reduced scheme, I was taught that instead of reflecting at each brillouin zone boundary, the wave coupld simply moved the reciprocal lattice vector in either direction. Since we also used a negative k-axis, I think this is slightly easier to understand than the reflection. Admittedly, our explanation for the movement was very mathsy, so probably not really suited to video. (next comment)

[@chaudry123]

Amazing job.

[@summaratashfeen153]

the brillouin zone of reciprocaq lattice to fcc lattice ha shortest G's are eight vectors, how?????

[@ayushigrover16]

what is the reciprocal lattice ?

[@reservoirchannel5576]

just some imaginery bullshit math operations to god knows why they do it, its not the real object

[@muhammadhaidir2485]

Thank you from Indonesia

[@Xz4]

Otherwise, great video, really well explained. Perhaps some relation to what they actually are, i.e. their relation to free electron theory.

[@heathgustavo4498]

I dont mean to be so off topic but does any of you know a method to log back into an Instagram account? I was stupid lost my login password. I would appreciate any assistance you can offer me!

[@yaelrayden197]

@Heath Gustavo instablaster ;)

[@heathgustavo4498]

@Yael Rayden i really appreciate your reply. I got to the site through google and im waiting for the hacking stuff atm. I see it takes quite some time so I will get back to you later with my results.

[@heathgustavo4498]

@Yael Rayden it worked and I actually got access to my account again. I am so happy:D Thank you so much you really help me out :D

[@yaelrayden197]

@Heath Gustavo no problem :D

[@pitv1315]

Now it make sense. Thanks

[@physicsdiva1871]

Nice explanation

[@bakulvinchhi]

What is a WignerSeitz Cell ?

[@JesseSGoossens]

Thank your for saving me.

[@Ad_Mico]

Glad to be of assistance :)

[@m040ax]

What does he say at 2:55: "And so your Brillouin zones are just the _ _ _ _ _ _, okay so its the uhm set of all points closest to the point of interest..."

[@krithikaupadhya2891]

Wigner-Seitz cell

[@shchen1999]

thank you from Taiwan

[@anadrolen]

Nice! Thank you!

[@Chickerlicker]

With Fourier-Transformation.

[@JosheyG34]

Man you say words funny? are you from london?

[@kockarthur7976]

It kinda sounds like he's from south africa

[@00iCon]

It's obviously Aussie

[@flubberamoebes]

nah defo aussie

[@sodansuds]

wigner seitz cell