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Homework Help: Reciprocal crystal lattice

  1. Sep 4, 2006 #1
    I know this might be a really stupid question, but to convert a crystal lattice 2D representation to a 2D reciprocal lattice do you justdo you just invert the scaling. I know this is a pretty poor explanation so I will try and illustrate what I mean.

    Let's say that you have a reciprocal lattice like the one below:

    . 020 . 120 . 220

    . 010 . 110 . 210

    . 000 . 100 . 200

    . 25 nm^-1

    Is the crystal lattice just a similar drawing with the spacing inverted, that is, 4 nm??? By the way the above diagram is meant to have the vertical and horizontal spacings equal so they are both 0.25 nm^-1.

    I'm sorry but I just haven't really found anything on this at all and I'm preparing for my test this week. The only example question I could find was converting from reciprocal lattice to crystal lattice, but I imagine the process will be the same if you were trying to convert from crystal lattice to a reciprocal lattice.

    Thanks for any assistance.
  2. jcsd
  3. Sep 4, 2006 #2


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    Staff Emeritus
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    Gold Member

    To find the reciprocal lattice vectors you use the following equation.

    [tex] \mathbf{b_1} = 2\pi \frac{\mathbf{a}_2 \times \mathbf{a}_3} {\mathbf {a}_1 \cdot \mathbf{a}_2 \times \mathbf{a}_3} [/tex]

    For a 2D case the vector [tex] \mathbf{a}_3[/tex] becomes just the z unit vector.

    To get the vector [tex]\mathbf{b}_2[/tex] you just cyclically permute the numerator.

    You are of course correct that the unit of the reciprocal lattice is length-1 but its a little more complicated than simply inverting the lengths.
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