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X-ray Diffraction and Bragg's Law

  1. Mar 18, 2009 #1
    1. The problem statement, all variables and given/known data
    On a crystal (cubic) a set of diffraction lines (θ) was obtained with CuKα (1.54 Å) radiation:
    13.70, 15.89, 22.75, 26.91, 28.25, 33.15, 36.62, 37.60 and 41.95 degrees. Using
    the following table to determine which peaks are expected to be absent in a cubic
    P-, I-, and F-lattice, what type of lattice does this crystal have and what is the lattice parameter
    of this crystal?
    *Table of Bravais Lattice selection conditions*

    2. Relevant equations
    Bragg's Law:
    2d*sin(theta) = n*lambda

    d = a/Sqrt(h^2 + k^2 + l^2)
    where h, k, l are integers related to the plane you are reflecting off, n is an integer number of wavelengths and a is the lattice parameter (size of the cubic unit cell)

    3. The attempt at a solution
    In a spreadsheet i threw together ratios of the sines of all the thetas (squared) and looked for things that were (within some error due to rounding) numbers which could be whole number ratios, but I'm not sure how to go from here to constraining the selection criteria since n and the sum of the squares of h, k and l vary from theta to theta.

    It seems like all the list of 'working' thetas gives me will end up being is ratios of sine squares, but unless I'm misunderstanding the question, even if I could find a nice whole number ratio of two sines, since it looks like I have 6 free parameters in a ratio I don't have enough information. Also with only two decimal places the angles don't give 'clear' ratios in many of the cases, even if they should be whole number ratios.

    I think I cracked it, I was looking at the nice large whole number ratios (like 8) but the more informative ones are the small ones it seems when you consider the very few ways you can make a ratio of 4/3, and 3 guarantees n = 1 for that theta, and thus the sum of the squares is 3, which can only be if h,k,l are all equal to 1, and that gave me a 'key' to the rest of the problem as well as ruling out the I-lattice.

    Although it seems that in this form, you could never guarantee it isn't just a cubic P-lattice unless you were told that it includes such and such angles and no-others.
     
    Last edited: Mar 18, 2009
  2. jcsd
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