What happens to X-rays if they do not meet Bragg's law?

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SUMMARY

Bragg's law, defined by the equation ##2d\sin[\theta]=m\lambda##, is essential for understanding X-ray diffraction. If X-rays do not meet this criterion due to differing energy levels, they cannot produce the same diffraction pattern at the specified angle ##\theta##. Instead, the X-rays may interact with the crystal lattice, potentially finding alternative planes for diffraction at different angles. However, if they do not meet the conditions for diffraction, the energy may be dispersed uniformly in a ##4\pi## solid angle.

PREREQUISITES
  • Understanding of Bragg's law and its mathematical formulation
  • Knowledge of crystal lattice structures and their planes
  • Familiarity with X-ray diffraction techniques
  • Basic principles of electromagnetic radiation
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  • Research the implications of varying X-ray energies on diffraction patterns
  • Study the concept of alternative diffraction angles in crystal planes
  • Explore the mathematical modeling of X-ray interactions with crystal lattices
  • Investigate the dispersion of electromagnetic radiation in solid angles
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Physicists, materials scientists, and anyone involved in X-ray crystallography or studying the properties of electromagnetic radiation in crystalline materials.

gaiussheh
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Bragg's law states that it must meet ##2d\sin[\theta]=m\lambda## for diffraction to happen. I just wonder, if you have an x-ray of slightly different energy that hits the crystal plane at the same angle ##\theta##, what would happen? It certainly can't form the same diffraction pattern at the same angle ##\theta##, but as the electrons in the crystal still vibrate, the x-ray still goes somewhere. Can they find another plane so that the diffraction happens at another angle? Or is the energy spread out evenly in ##4\pi##?
 
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For any EM radiation, each wavelength forms its own diffraction pattern independently and these are superimposed on a screen.
 

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