Brillouin Zones

[thetrooper]

From various threads in OT lately I can safely assume that there are physicists around here.

Could someone explain to me what a Brillouin zone is (in layman terms and a minimum of mathematical formulas)?

 

[Catharsis]

Let's see if this works:

[wiki]Brillouin zone[/wiki]

Brillouin zone

Just trying out the wiki and define tags. The wiki one's got some info on it, if that helps.

 

[thetrooper]

Let's see if this works:

[def]Brillouin zone[/def]

Apparently not. Nice try though.

Edit: are you kidding me? Linking to wiki?

 

[Sidhe]

http://www.applet-magic.com/brillouin.htm

http://en.wikipedia.org/wiki/Brillouin_zone

http://people.deas.harvard.edu/~jones/ap216/lectures/ls_2/ls2_u7/sse_tut_1/solid1.html


Never heard of them in my life, not never, but here's three links I found.

 

[thetrooper]

Alright, alright. I see where this is heading...

I appreciate that you're trying to help. But I'm not in the mood to check out random things found on the web. I'd like to hear something from people that actually know something about it.

And I'm not saying that just to be a dick.

Sorry.

 

[Catharsis]

Edit: are you kidding me? Linking to wiki?

But Wikipedia knows everything!

 

[thetrooper]

Ain't that the fact?

 

[Mise]

What in particular do you need to know about them? Where is the question coming from? (i.e. what context do you need to know the information from?)

When we learnt about them on my degree, they weren't introduced in the way that Wiki describes them; they were introduced from the "particle in a box" model of the atom, but if you're coming from a Chemist's perspective then perhaps the Wiki article is more apt.

 

[Chairman Meow]

I'm not sure how much you already know about lattices, etc. Also, I have not had sufficient amounts of caffeine today. So, this may or may not help:

A Brillouin Zone is a cell in a reciprocal lattice. What that means is that if you have a lattice - for example, a cubic lattice - then you can find the reciprocal lattice, and then use that to find the Brillouin Zone. The reciprocal lattice is (IIRC) the Fourier transform of the original lattice, meaning that it represents frequencies in the spacings of points, as opposed to an ordinary lattice, which gives distances between lattice points.

The First Brillouin Zone is the smallest possible cell in the reciprocal lattice. It's usually found by taking the shortest lines between a point in the reciprocal lattice and its neighbors, and drawing a perpendicular plane (or line, in 2D) at the midpoint of each line. The space enclosed by the planes/lines is the First Brillouin Zone.

 

[thetrooper]

@Mise: Chemist's perspective for diffraction purposes.

It's just the kind of evil question that might come up at our exam; it's of no real value to us (i.e. as chemists) but the bastards love to ask about it anyway.

 

[Mise]

@Mise: Chemist's perspective for diffraction purposes.

It's just the kind of evil question that might come up at our exam; it's of no real value to us (i.e. as chemists) but the bastards love to ask about it anyway.

Ah. I was never too sure about the chemist's perspective, and even less sure about diffraction... something to do with the particle's final momentum being the vector sum (i.e. gives its direction => diffraction) of the its initial momentum and the reciprocal lattice vector? Don't quote me on that . I'm not going to be much help to you

 

[thetrooper]

@Chairman Meow: I had to chew one that for a while, but it makes sense. I think that the most problematic part of it was the Fourier transform.

Thanks!

And I know enough about lattices.

 

[thetrooper]

@Mise: , no I'm not going to quote you on that.

The good thing about being a chemist is that we usually just use what you physicists come up with. But in some cases we have to explain it...

 

[Goa]

Edit: are you kidding me? Linking to wiki?

Why don't you like the wiki entry? It's correct and concise, without to much unnecessary blabla

@ Chairman Meow: You're working in low temperature physics? Just asking because of your Location...

 

[Chairman Meow]

I'm a physics undergrad. The location in my profile was selected because it sort-of fit with the "Kelvin" avatar/sig theme.