Why do x-rays penetrate crystals and not reflect with longer wavelengths?

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Discussion Overview

The discussion revolves around the behavior of x-rays when interacting with crystal structures, specifically focusing on the mechanisms of scattering, diffraction, and the reasons for the lack of reflection with longer wavelengths. The scope includes theoretical aspects of x-ray diffraction and the physical principles governing these interactions.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant inquires about the scattering process of x-rays in crystals and whether they can penetrate into the interior of the crystal.
  • Another participant explains that all planes in a crystal diffract x-rays to some extent and mentions the concept of the structure factor in relation to diffraction peaks.
  • A further contribution specifies that the largest plane-spacing corresponds to the largest lattice parameter, and provides a mathematical relationship indicating that no wavelength greater than twice the largest lattice parameter can produce a diffraction peak.
  • One participant addresses the penetration of x-rays into crystals, comparing it to their penetration of human tissue, and notes that significant reflection occurs only when multiple planes contribute to the process, leading to sharp Bragg diffraction at specific angles.

Areas of Agreement / Disagreement

Participants express various viewpoints on the mechanisms of x-ray interaction with crystals, with some agreement on the role of plane spacing and diffraction, but no consensus on the specifics of penetration and reflection processes.

Contextual Notes

There are limitations regarding the assumptions made about the relationship between wavelength and lattice parameters, as well as the conditions under which diffraction occurs. The discussion does not resolve these complexities.

Who May Find This Useful

This discussion may be of interest to those studying crystallography, materials science, or anyone exploring the principles of x-ray diffraction and its applications in various fields.

photon79
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In x-ray diffraction with crystals, what actually happens with the incident x-ray beem or photon? scattering occurs due to which atoms (plane) of the crystal?(can it penetrate into the interior of the crystal?) why doesn't the reflection occur with big wavelengths?
 
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All the planes diffract the x-rays to some extent. The peaks you see in diffraction data can be index to specific planes, ie 100, 110, ...Keyword lookup: Structure factor. Of course you could use longer wavelengths but the spacing between the planes would have to be larger.
 
The largest plane-spacing will be the largest lattice parameter. All other planes are closer together. So, [itex]d \leq a[/itex]. Also, [itex]sin \theta < 1[/itex] and [itex]n \geq 1[/itex] .

Hence, [tex]\lambda = \frac {2dsin \theta}{n} \leq 2a[/tex]

So, no wavelength greater than twice the largest lattice parameter can produce a diffraction peak.
 
photon79 said:
can it penetrate into the interior of the crystal?
X-rays penetrate humans; they also penetrate crystals. A single plane of atoms absorbs very little. A single plane also reflects very little. Only when hundreds or thousands of planes contribute to the reflection, you can get sharp Bragg diffraction at certain angles (when phases add constructively).
 

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