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### Topic: Bravais Lattices [HELP]  (Read 448 times)

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##### Bravais Lattices [HELP]
« on: May 15, 2023, 01:22:46 AM »
The lecturer who was teaching me didn't go into the trouble of explaining what Bravais lattices are and instead jumped right into the types of Bravais Lattices in 2D and 3D. Trouble is, without understanding the concept, I can't move forward with Solid State Physics.

Below, I explain what I understand so far, I would request you to point out anything wrong in there.

Now, I know
Bravais Lattices are a periodic arrangement of lattice points such that they are translationally symmetric. These lattices have even distances between consecutive lattice points and they have the same surroundings.

Question 1: I don't understand why there are only 5 types of Bravais lattices, I mean, why that particular number? I asked this question to ChatGPT and here's what it said:

*Q: now why are there only 5 2d bravais lattices?

A: There are only five 2D Bravais lattices because they are the only unique ways
to arrange points in a 2D plane with translational symmetry.

In general, a Bravais lattice is defined as a mathematical framework that
describes how points in space are arranged with translational symmetry.
In 2D, a Bravais lattice is defined by two primitive lattice vectors
that span the lattice. The shape of the unit cell is determined by the
primitive lattice vectors and the lattice symmetry.

Now, I know better than to take ChatGPT's word for it. So, I need your help to verify it. Is it right in everything it had said so far. Can I know how Bravais discovered these 5 lattices to be the only bravais lattices?

#### Borek

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##### Re: Bravais Lattices [HELP]
« Reply #1 on: May 15, 2023, 03:20:52 AM »
I don't understand why there are only 5 types of Bravais lattices, I mean, why that particular number?

That's in 2D, in general there are more.

Take it with a grain of salt, when it comes to crystallography I am not necessarily better than ChatGPT: technically there is an infinite number of infinite lattices. However, if you look at their symmetries they can be classified into groups in which all lattices are considered equivalent (exhibit similar symmetry - there is a well established math behind that classification). It happens that there are 5 such groups. In this sense there are 5 lattices only.

Could be there is some more advanced logic behind this number, but from what I remember it is just "that's the way it happens to be".
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