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Calculate lattice constant from x-rays

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data
    When x-rays are diffracted off NaCl, constructive interference is observed at an angle of 16.3 degrees. Determine the lattice constant of NaCl.

    Frequency of the X-ray is 1.948 x 10^18 hz
    Theta = 16.3 degrees



    2. Relevant equations
    (As far as what we're told to use and what's in the book)
    2d * Sin (Theta) = m * Lambda


    3. The attempt at a solution

    After looking through the problem it is very clear that I am unable to find the "lattice constant" from the information given in the book.

    I've found the following equations:

    1) d = a/sqrt(h2+k2+l2)
    2) Lambda/2a= sin 2 Theta/h2+k2+l2

    I've tried deriving #2 down to where it is usable and I get:

    a2 = (Lambda2/4) * (h2+k2+l2/Sin2 Theta)

    I've been unable to figure out what the miller indices are (h k and l), but everything I've tried doesn't get anywhere near the values expected online of 5.63-5.65.

    Am I going about this completely wrong or am I just overthinking the problem?

    Any help would be much appreciated.
     
    Last edited: Dec 7, 2008
  2. jcsd
  3. Dec 8, 2008 #2

    turin

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    Homework Helper

    I don't think you can figure out the Miller indices if you don't know the orientation of the crystal anyway, right? (It's been a while since I took solid state.)

    EDIT: I don't get 5.63 (Angstoms?) either (for any value of m).
     
    Last edited: Dec 8, 2008
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