X-ray diffraction minima?

In summary, for x-ray diffraction maxima, Bragg's law states that 2d*sinθ = mλ, where m is the order of the maximum. However, there is no analogous law for the minima, as diffraction gratings do not have a simple alternating maximum/minimum pattern. Instead, there are primary maxima that are narrow and bright, with secondary maxima and minima in between, which are not normally visible. In the case of real crystals and multiple scattering, the concept becomes more complex. For example, in surface diffraction, there is an "anti-Bragg" position.
  • #1
L_landau
27
0
For x-day diffraction maxima we have braggs law
2d*sinθ = mλ (maxima)

Is there an analogous law for the minima like
2d*sinθ = (m+1/2)λ (minima?)

Thanks!
 
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  • #2
Diffraction gratings don't have a simple alternating maximum/minimum pattern like the two-slit setup does.

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/gratint.html

What you see are the primary maxima which are very narrow and bright. You don't normally see the secondary maxima and the minima in between them.
 
  • #3
For an ideal, infinite crystal, and using the kinematic theory of x-ray diffraction, there is intensity only at the Bragg positions, and nothing in between. Once you consider real (finite and imperfect) crystals and multiple scattering (dynamical theory of x-ray diffraction), things become a bit more complicated.

As an example, in surface diffraction, you get something called an "anti-Bragg" position.

https://en.wikipedia.org/wiki/X-ray_crystal_truncation_rod
 

1. What is X-ray diffraction minima?

X-ray diffraction minima is a phenomenon that occurs when a beam of X-rays is directed at a crystalline material. The X-rays are diffracted by the atoms in the crystal, resulting in a diffraction pattern that contains areas of low intensity, known as minima.

2. How does X-ray diffraction minima help in determining crystal structure?

X-ray diffraction minima can provide information about the arrangement of atoms in a crystal, known as its crystal structure. By analyzing the pattern of minima, scientists can determine the spacing and orientation of the atoms in the crystal lattice.

3. What factors can affect the appearance of X-ray diffraction minima?

Several factors can influence the appearance of X-ray diffraction minima, including the wavelength of the X-rays, the angle of incidence of the X-ray beam, and the orientation of the crystal lattice.

4. Can X-ray diffraction minima be used to identify unknown materials?

Yes, X-ray diffraction minima can be used as a tool for material identification. By comparing the diffraction pattern of an unknown sample to known patterns of different materials, scientists can determine the composition of the sample.

5. Are there any limitations to using X-ray diffraction minima for crystallography?

While X-ray diffraction minima is a powerful technique for crystallography, there are some limitations. It is most effective for crystalline materials and may not work for amorphous materials. Additionally, the size and quality of the crystal can affect the accuracy of the diffraction pattern.

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