1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Brillouin zone

  1. May 27, 2010 #1
    Hi, I just can't understand the basics with BZ.

    How do I find the shortest distance to the BZ boundary, how do I compare the electron energy between the last electron in the 1st BZ with the first electron in the 2nd BZ?

    I think I need a visual how to calculate these things, does anyone know any good site with illustrations?

    Here's an example:
    Q: For what minimum electron concentration Z does the free electron Fermi sphere touch the first Brillouin zone boundary of a BCC metal?
    A: Calculating the primitive reciprocal lattice vectors b_i of BCC we find the shortest distance to the BZ boundary |b_i|/2 = √2(π/a).

    How do I know the shortest distance is |b_i|/2? From here I know how to finish.

    If someone could show me some examples how to solve these types of questions I would be grateful!

    Sorry for any grammatic errors, English is not my native language.
     
  2. jcsd
  3. May 27, 2010 #2

    Astronuc

    User Avatar

    Staff: Mentor

    Perhaps this will help.

    http://www.msm.cam.ac.uk/doitpoms//tlplib/brillouin_zones/zone_construction.php [Broken]
     
    Last edited by a moderator: May 4, 2017
  4. May 27, 2010 #3
    Thanks for your reply.

    Actually I know how to draw the BZ in 2D-lattice, it's just like the WZ-cell.

    How do I apply this to calculate the shortest distance to the 1st BZ for a BCC or FCC?
    Is it always half of the reciprocal lattice vectors b_i? Or is that specific for a BCC?

    Do I understand this correct:
    For a BCC is the shortest dist to the 1st BZ .5*(2pi/a)*|0,1,1|=sqrt(2)*pi/a
    and for FCC .5*(2pi/a)*|1,1,1|=sqrt(3)*pi/a?
     
  5. May 28, 2010 #4
    The shortest distance to the BZ doesn't necessarily mean it will have the lowest energy. Only if you make the assumption that the Fermi surface is a sphere (for free electrons), which isn't true when you have a potential.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Brillouin zone
  1. 1st Brillouin zone (Replies: 0)

  2. Brillouin Zone Size (Replies: 3)

Loading...