Is There an Analogous Law for X-ray Diffraction Minima?

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SUMMARY

The discussion centers on the existence of an analogous law for X-ray diffraction minima, akin to Bragg's Law for maxima, expressed as 2d*sinθ = mλ. Participants explore the concept of minima potentially represented by 2d*sinθ = (m+1/2)λ. It is established that diffraction gratings do not exhibit a simple alternating pattern of maxima and minima, unlike the two-slit setup. The conversation highlights the complexity introduced by real, finite crystals and multiple scattering, referencing the kinematic and dynamical theories of X-ray diffraction.

PREREQUISITES
  • Understanding of Bragg's Law in X-ray diffraction
  • Familiarity with kinematic and dynamical theories of X-ray diffraction
  • Knowledge of diffraction gratings and their behavior
  • Concept of anti-Bragg positions in surface diffraction
NEXT STEPS
  • Research the implications of finite and imperfect crystals on X-ray diffraction
  • Study the kinematic theory of X-ray diffraction in detail
  • Explore the dynamical theory of X-ray diffraction and its applications
  • Investigate the concept of anti-Bragg positions in surface diffraction
USEFUL FOR

Physicists, materials scientists, and researchers in crystallography seeking to deepen their understanding of X-ray diffraction phenomena and the behavior of diffraction patterns in various crystal structures.

L_landau
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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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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.
 
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
 

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