Electron diffraction from crystals

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Discussion Overview

The discussion revolves around the phenomenon of electron diffraction from crystals, specifically addressing the relationship between the angles of incidence (theta i) and reflection (theta r) and the conditions under which they may differ. The scope includes theoretical aspects of diffraction and the application of the Bragg condition.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions why theta i and theta r are not necessarily equal in electron diffraction.
  • Another participant requests clarification on the definitions of theta i and theta r.
  • A participant defines theta i as the angle of incidence and theta r as the angle of reflection, providing a reference diagram for further understanding.
  • It is noted that the angle of diffraction is determined by the Bragg condition, which states that the difference in path length from one atom to the next must be an integral number of wavelengths. This condition is typically presented under the assumption that theta i equals theta r, but it is argued that this is only a special case.
  • A later reply suggests that if theta i and theta r are allowed to differ, the Bragg condition can be expressed as d(sin theta i + sin theta r) = nλ, indicating a more general formulation.
  • There is a mention that most references use the angle that the electron's path makes with the normal, which would require replacing sine with cosine in the equation.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between theta i and theta r, with some supporting the idea that they can be unequal under certain conditions, while others reference traditional assumptions that they are equal. The discussion remains unresolved regarding the implications of these differing angles on the Bragg condition.

Contextual Notes

The discussion highlights limitations in the assumptions made in various references regarding the equality of theta i and theta r, as well as the dependence of the Bragg condition on these angles. There is also a noted difference in how angles are defined in relation to the normal.

blueyellow
why is it that in electron diffraction from cystals, theta i and theta r are not necessarily equal?
 
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What are theta i and theta r? Define carefully.
 
blueyellow,

The angle of diffraction is determined by the Bragg condition, namely that the difference in path length from one atom to the next is an integral number of wavelengths. The writeup you refer to does assume that θi = θr, but this is only a special case. If you draw the same diagram and let θi and θr be different, you'll see that the Bragg condition becomes

d(sin θi + sin θr) = nλ

(Most references use instead the angle that the electron's path makes with the normal, in which case replace sin by cos.)
 

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