What happens when we rotate crystal while shooting electrons at it?

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SUMMARY

When a narrow beam of electrons is directed at a crystal, diffraction occurs according to Bragg's Law, resulting in observable minima and maxima on a detection screen. Rotating the crystal alters the angle (θ) between the incoming beam and the crystal planes, potentially changing the positions of these diffraction patterns. Unlike previous methods where sensors were rotated, rotating the crystal itself introduces new dynamics in the diffraction pattern, influenced by the crystal's geometry, particularly its thickness in different directions. This discussion highlights the complexities of electron diffraction experiments and the implications of crystal rotation.

PREREQUISITES
  • Understanding of Bragg's Law in electron diffraction
  • Familiarity with the geometry of crystals in diffraction experiments
  • Knowledge of Young's interference experiment principles
  • Basic concepts of electron beam interactions with matter
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  • Explore the mathematical derivation of Bragg's Law for electron diffraction
  • Investigate the effects of crystal geometry on diffraction patterns
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  • Study the impact of varying angles in diffraction experiments
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I know that if we shoot narrow beam of electrons at the crystal (we don't change the angle) we will get a diffraction of electrons according to the brag's law. Therefore we get minimums and maximums on the screen around the crystal.

Until now we have been dealing with problems where ##\vartheta## (this is an angle between an incoming beam and crystal planes) was constant. It meant that crystal wasn't rotating. To find maximums and minimums we have instead been rotating a sensor around the crystal.

But what would happen if we rotated the crystal? This would mean that we are changing the angle ##\vartheta##! Would minimums and maximums move around the screen or would they only appear and disappear? What is different than before?

A good picture is worth 1000 words.
 
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You can probably work it out just by figuring the conditions for diffraction ... start with the standard youngs interference experiment and see what happens when you rotate the plane bearing the slits.

In electron diffraction experiments, the crystal is usually thin in one direction and thick in the other two - so you get extra effects from the geometry.
 

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