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Bragg diffraction

  1. Nov 18, 2005 #1
    Hi,

    In the solid form FeO, CoO and NiO all has the NaCl-structure (simple cubic). In a series of diffraction experiments with x-rays ([tex]\lambda = 0.15406~\text{nm}[/tex]) one found reflexes from the (111), (200) and (220)-planes with the following [tex]\theta[/tex]-values ([tex]\theta[/tex] is the angle in Bragg's law, [tex]2d\sin\theta=\lambda[/tex]):

    FeO: 18.04 20.95 30.28
    CoO: 18.26 21.20 30.77
    NiO: 18.63 21.64 31.45

    The first number is the angle corresponding to the reflection from the (111)-plane, the second number corresponds to reflection from the (200)-plane and the third from the (220)-plane.

    Question: What are the axis length for the three unit cells? Any hints?
     
  2. jcsd
  3. Nov 18, 2005 #2

    StatusX

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    Well, you can use Bragg's law to solve for the d for each angle. Now you need to know how the spacing between certain lattice planes, d, is related to the lattice constant (length of a side of the cubic cell). For example, for the (100) planes, the spacing is just a, for (110), it is a*sqrt(2), and so on.
     
  4. Nov 18, 2005 #3

    Gokul43201

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    What is the general formula relating the interplanar spacing (of some hkl family) to the lattice parameter in a cubic structure ?
     
  5. Nov 19, 2005 #4
    I don't know, but man, I'd like to know that formula :!!) I'm having some trouble visualizing this, to say the least.
     
  6. Nov 19, 2005 #5

    Gokul43201

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    I'm sure it's in the text : [tex]d = \frac{a}{\sqrt{h^2+k^2+l^2}} [/tex]
     
  7. Nov 20, 2005 #6
    Thank you very much. My book is Descriptive Inorganic Chemistry by Canham and Overton and I can't find that formula in it.
     
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