Finding Distances to Brillouin Zone Borders from Origo

[rubertoda]

Hi, i have problems understanding the Brilluoin zone to the bcc lattice

First, i wonder what the distances are, from the origo to the brillouin zone plane borders.
I firts thought it would be half the distance of the basis vectors (mine are 2pi/a, where a is my lattice constant, BUT its only true for 2-D calculations for square lattices.

I know that the distances in 3D should be |G-vector|/2, and i take the smallest possible G.


But i still don't know

ANyone who knows how to find the distances from origo to the first BZ zone boundaries, knowig that the basis vector in the reciprocal space is 2pi/2?are they all the same??

 

[hokhani]

I think if the direct lattice constant is a, then the reciprocal lattice constant would be$2\pi/a$ hence your favorite distance is $(\pi/\sqrt2)a$.

 

[rubertoda]

Thanks a lot. and this goes eveforryone of the 12 directions in the BZ?

 

[hokhani]

No, it was for the four direction located in the middle of the figure 4.16 Ashcroft & Mermin. you can easily calculate it for remained 8 directions (see the figure).

 

[rubertoda]

ok thanks. I am jut interested in the 110-direvtion, from origo to N,in the Ʃ-direction