Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Basic cubic centered lattice

  1. Aug 15, 2009 #1
    Do yoh have some nice picture to show why the primitive vectors of basic cubic lattice are

    [tex]\vec{a}_1=\frac{a}{2}(-\vec{e}_x+\vec{e}_y+\vec{e}_z)[/tex]

    [tex]\vec{a}_2=\frac{a}{2}(\vec{e}_x-\vec{e}_y+\vec{e}_z)[/tex]

    [tex]\vec{a}_3=\frac{a}{2}(\vec{e}_x+\vec{e}_y-\vec{e}_z)[/tex]

    Thanks!
     
  2. jcsd
  3. Aug 15, 2009 #2
  4. Aug 17, 2009 #3
    I'm afraid I don't have a diagram to show you, but it's pretty easy to visualize the primitive vectors by just thinking about it. A primitive vector simply connects two identical lattice points.

    So, for instance, the a3 vector translates one-half a lattice parameter in the +x direction, one-half a lattice parameter in the +y direction, and one-half a lattice parameter in the -z direction. If you start at a corner atom in the BCC structure, this will take you to the body center.

    I don't know if this helps at all--and it doesn't really answer your question--but it was useful to me when I first learned crystal structures.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook