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Bravais lattice 
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#1
Nov3013, 05:02 PM

P: 1,005

My book has an awful lot of text about these special lattices where everything looks the same from every lattice point. But why are these lattices so important? I mean, surely in some crystals the atomic arrangement must be such that the crystal lattice is not a bravais lattice? Edit: maybe you could also point me to a derivation of the 14 different bravais lattices as I cant really see intuitively why these exhaust all space symmetry possibilities.



#2
Nov3013, 06:17 PM

P: 669

The only crystals that do not form in one of the 14 Bravais lattices are Quasicrystals, which are nonperiodic.
All other crystals, from simple rock salt and silicon to protein crystals with huge unit cells for in Bravais lattices with repeating unit cells. Real crystals are of course finite and have imperfections, but the important properties are derived from the periodicity and the unit cell  band structure (conductivity, semiconducting behaviour, etc), magnetism, birefringence, ... everything. That's why it is a big deal. Ashcroft and Mermin has a pretty good discussion of crystal lattices. 


#3
Dec113, 02:37 AM

P: 1,005

But I mean, can't you draw a periodic lattice without it being a bravais lattice?



#4
Dec113, 05:22 AM

P: 669

Bravais lattice
No, you cannot. That is the whole point.



#5
Dec113, 06:49 AM

P: 1,005

What about the honeycomb lattice? It is clearly periodic in some way, but it is not a bravais lattice. What exactly do you mean by periodic?



#6
Dec113, 07:32 AM

P: 669

The honeycomb lattice is a triangular Bravais lattice with a twopoint basis.
http://wwwpersonal.umich.edu/~sunka...honeycomb.html 


#7
Dec113, 12:59 PM

P: 1,005

So by twopoint basis you mean it is a bravais lattice where we don't put an atom in the middel of the hexagons.



#8
Dec113, 02:09 PM

Sci Advisor
P: 3,596

I think there are many books on group theory who show how and why there can only be 14 lattices. 


#9
Dec213, 03:45 PM

P: 316

Can you give one of them. For me is very interesting to see point groups. There is 32 point groups. When I see rotation of 1,2,3,4,6 order. Is this 5/32 point groups?
And what is liquid crystal? Do they form some crystal lattice? 


#10
Dec213, 05:18 PM

P: 669

Liquid crystals are not crystals in the sense that they do not have a regular periodic lattice. In most cases they consist of long molecules that have orientational order (i.e. they point into a defined direction), but no translational order.
http://en.wikipedia.org/wiki/Liquid_crystal The five groups you mention are all crystallographic point groups. Trivially, you also have to consider the group that contains only the identity. Additional symmetries that can be added to form the remaining groups are space inversion and 2fold axes perpendicular to the "main" axis. For the cubic point groups, you combine 3fold axis about the body diagonals of the cube with 2 or 4fold axes about the faces, and sometimes 2fold axes about the face diagonal and/or space inversion. http://en.wikipedia.org/wiki/Crystal...ic_point_group 


#11
Dec313, 06:29 AM

P: 316

Thanks. One more question. What is reflection group?



#12
Dec313, 01:50 PM

P: 669

Sorry, no clue. The Wiki page is not all that helpful...



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