X-ray diffraction and Bragg's law

In summary, the student is having difficulty with the Bragg condition for diffraction and does not know how to calculate the lattice plane spacing, d, from the given information.
  • #1
Martin89
25
1

Homework Statement


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The Attempt at a Solution


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Hi All,

I have two issues with this question. First of all when I put the given values into the Bragg condition for diffraction I get two different wavelengths when the question implies there is only one. Secondly, I don't know how I can calculate the lattice plane spacing, d, from the given information. Any help would be appreciated, thanks!
 

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  • #2
The correct formula is:
λ = 2 dhkl sinθhkl
In case of a cubic lattice with lattice parameter a one has :
dhkl = a / sqr(h2 + k2 + l2)
You have now to find out what (h k l ) planes give rise to the second and what (h k l ) planes give rise to the third scattering peak in the X-ray diffractogramm of CsI.
 
Last edited:
  • #3
Lord Jestocost said:
The correct formula is:
λ = 2 dhkl sinθhkl
In case of a cubic lattice with lattice parameter a one has :
dhkl = a / sqr(h2 + k2 + l2)
You have now to find out what (h k l ) planes give rise to the second and what (h k l ) planes give rise to the third scattering peak in the X-ray diffractogramm of CsI.
I have no idea how to work that out from the given information...in lectures we were shown how to calculate d when the lattice plane was known
 
  • #5
  • #6
There is no "m" in the equation λ = 2 dhkl sinθhkl. Do you understand that the scattering peaks which are observed at 10.8° and 13.3° are due to scattering from different planes with different Miller indices. This has nothing to do with mth-order reflections.
 

1. What is X-ray diffraction and how does it work?

X-ray diffraction is a technique used to study the structure of crystalline materials. It involves shining a beam of X-rays onto a crystal and measuring the angles at which the X-rays are diffracted, or scattered, by the crystal. This information can then be used to determine the arrangement of atoms within the crystal.

2. Who discovered X-ray diffraction?

X-ray diffraction was discovered by physicist Max von Laue in 1912. He showed that X-rays could be diffracted by crystals, confirming the wave nature of X-rays and laying the foundation for further studies in crystallography.

3. What is Bragg's law and how is it related to X-ray diffraction?

Bragg's law is a mathematical equation that describes the relationship between the angle of diffraction, the wavelength of the X-rays, and the spacing of the crystal lattice. It states that when X-rays are diffracted by a crystal, the angle of incidence and the angle of reflection will be equal, and the path difference between the waves must be a whole number multiple of the X-ray wavelength. This law allows us to calculate the spacing between atoms in a crystal based on the diffraction pattern.

4. What are the applications of X-ray diffraction?

X-ray diffraction has many applications in various fields such as materials science, chemistry, and biology. It is commonly used to determine the atomic and molecular structure of crystals, identify unknown substances, and study phase transitions in materials. X-ray diffraction is also an important tool in drug development, as it can help determine the structure of proteins and other biomolecules.

5. What are the limitations of X-ray diffraction?

One limitation of X-ray diffraction is that it can only be used on crystalline materials, as amorphous materials do not have a regular repeating pattern of atoms. Additionally, X-ray diffraction cannot provide information about the arrangement of atoms in the non-crystalline regions of a material. It is also important to note that X-ray diffraction cannot distinguish between different elements, so additional techniques may be needed to fully analyze a sample.

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