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X-rays diffraction in a solid, Bragg's law

  1. Jul 7, 2012 #1

    fluidistic

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    Gold Member

    1. The problem statement, all variables and given/known data
    The X-rays diffraction diagramm of a cubic crystal shows lines for the following angles [itex]2 \delta = 31.47º[/itex], 39.74º, 47.58º, 64.71º and 77.59º when the X-rays have a wavelength of [itex]1.54 \times 10 ^{-10}m[/itex].
    Determine the crystal stucture of the net, the Miller indices of the diffractive planes and the parameter of the net.

    2. Relevant equations
    [itex]\left ( \frac{\lambda }{2a } \right )^2 =\frac{sin ^2 (\theta )}{h^2+k^2+l^2}[/itex] where h, k and l are Miller indices.


    3. The attempt at a solution
    First I am not sure what they mean by "2 delta's". Second, it's the first time I'm asked to solve such an exercise and I've thought on it and I don't see a direct way to solve the problem, because I don't know the "parameter of the net", which I guess is "a" in the formula, nor do I know h, k and l.
    So I've started a try. I've tested for a bcc crystal structure and the test resulted in a negative answer. Please tell me if my approach is correct.
    I considered the angle \theta = 31.47º. From the given formula, I get [itex]a = \frac{\lambda }{\sin \left ( \frac{31.47}{2} \right ) } \approx 5.68 \times 10 ^{-10}m[/itex]. I considered h=2, k=l=0 because in a bcc crystal, h+k+l must be even.
    I then tried h=k=2 and l=0 and I took the value of "a" I just obtained in order to see if I could find an angle close to 39.74º but I reached a value for theta of about 22.55º.
    I realize that there are infinitely many other possibilities for the values of h, k and l for a bcc crystal structure so that I can't really affirm that the crystal isn't bcc. So how do I solve the problem? Should I work out a lot of possible values for h, k and l?
     
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