Why Does n=2 Not Produce an Equally Strong Peak in X-ray Diffraction?

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SUMMARY

The discussion centers on the observation that n=2 in Bragg's law (nλ=2d sinθ) does not yield an equally strong peak in X-ray diffraction as expected. While Bragg's law suggests that n=2 should produce a peak, the presence of the structure factor and atomic scattering factors influences the intensity of the peaks observed. Reference to B.D. Cullity's work highlights the importance of these factors in understanding diffraction patterns. Additionally, the determination of the origin of the r vectors in the Fourier transform of the lattice is deemed non-essential for the analysis.

PREREQUISITES
  • Understanding of Bragg's law in X-ray diffraction
  • Familiarity with structure factors in crystallography
  • Knowledge of Fourier transforms in the context of wave phenomena
  • Basic concepts of atomic scattering factors
NEXT STEPS
  • Study the impact of structure factors on X-ray diffraction patterns
  • Explore the relationship between Fourier transforms and diffraction in crystallography
  • Review B.D. Cullity's "Elements of X-ray Diffraction" for deeper insights
  • Investigate the role of atomic scattering factors in determining peak intensities
USEFUL FOR

Researchers in materials science, physicists studying crystallography, and anyone involved in X-ray diffraction analysis will benefit from this discussion.

thcommj
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1. In satisfying the Bragg's law, [tex]n\lambda=2d\sin\theta[/tex], n is typically assumed to be one, which explains why we see only one peak for a particular plane (say [400] plane for silicon). But I really don't see why n=2 should not appear as an equally strong peak..?

2. Is the Fourier transform effect of X-ray scattering comparable to that of a Fraunhoffer diffraction by multiple slits?

3. In calculating the Fourier transform of the original lattice, how is the origin of the r vectors determined? Or it doesn't matter?

Thanks!
 
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(1) Purely according to Bragg's law it should be an equally strong peak. However there is also a matter of the structure factor and atomic scattering factors. See B.D. Cullity chapter 4.

(2) I don't know

(3) It doesn't matter. The lattice vectors describe the translational periodicity of the crystal. Sometimes it is conceptually convenient to define one of the atoms as the origin, but this isn't necessary.
 

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