1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Interplanar spacing

  1. Sep 15, 2013 #1
    The interplanar spacing between planes labeled by miller indices (hkl) is given by:
    where G is the reciprocal lattice vector:
    Somehow I can't get this formula to work. I wonna calculate the distance between (200) planes. This should be a/2, where a is the lattice constant. But (look it up) b1=2[itex]\pi[/itex]/a (-x + y +z), where x, y and z are unit vectors. And so G= hb1 = 2[itex]\pi[/itex]/a (-x + y +z) and thus lGl = h2[itex]\pi[/itex]/a * √3
    d= a/(2√3)
    But this can't be right. I have no idea why I get that factor of √3, because I checked everything. Where did I make a silly mistake?
  2. jcsd
  3. Sep 15, 2013 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    From your expression for b1, it appears that you are working with a face-centered-cubic lattice (in real space) and that you have chosen reciprocal lattice vectors that are reciprocal to a set of primitive lattice vectors corresponding to a primitive cell. However, for fcc and bcc lattices the miller indices are often chosen to correspond to a conventional cell.
    For information on primitive and conventional cells: http://www-personal.umich.edu/~sunkai/teaching/Winter_2013/third_lecture.pdf

    The unprimed vectors (a1, a2, a3) in the diagram that I attached show lattice vectors in real space that correspond to a primitive cell of the lattice. The primed vectors correspond to a conventional cell.

    So, the Miller indices (2, 0, 0) probably correspond to the conventional cell. If so and you want to use d=2[itex]\pi[/itex]/lGl, you will need to find the reciprocal vector b'1 that is reciprocal to the conventional cell lattice vectors (a'1, a'2, a'3).

    Attached Files:

    Last edited: Sep 15, 2013
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted