Bcc lattice

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 dont 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[itex]2\pi/a[/itex] hence your favorite distance is [itex](\pi/\sqrt2)a[/itex].

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. im jut interested in the 110-direvtion, from origo to N,in the Ʃ-direction