[Pw_forum] What's meaning of the origin of the first BZ and which planes are corresponding to it in the real lattice space?

[degironc]

BZ has to do with the symmetry properties of a lattice (described by a 
infinite discrete-translation group).
k points in the BZ label possible periodicity of wfc, phonons, or other 
function defined for this lattice.
They give you the complex phase factor involved in a discrete lattice 
translation.
Gamma points means that all these phase faqctors are equal to 1... why 
do you want to see it as a plane in real space?
Any how if you want to see it pictorially the question is: find the set 
of points in real space such that the accumulated phase shift is pi !
Start with a small k vector and approach gamma ... what happens to the 
plane?
If I rememeber correctly this subject is covered in a basic geometry or 
linear algebra course as "projective geometry" ... at least it was so 25 
yrs ago...

hope this helps,

 stefano

Hongyi Zhao wrote:

>Hi all,
>
>I can understand the concept of the first Brillouin Zone, but I cann't 
>figure out the meaning of the origin of the first BZ and which planes 
>are corresponding to it in the real lattice space.  I mean, the origin 
>coordinate of the first Brillouin Zone is (0, 0, 0), so the 
>corresponding plane(s) to it in the real lattice space should have the 
>index (/infty /infty /infty ).  But what does this plane index mean, I 
>just cann't understand.  Would anyone give me some hints on this?
>
>Thanks in advance.
>
>---
>Hongyi Zhao
>GnuPG DSA: 0xD108493B
>
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