Why is the change in momentum of a crystal include reciprocal lattice vectors?

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SUMMARY

The change in momentum of a crystal is fundamentally linked to reciprocal lattice vectors, as it pertains to crystal momentum rather than true momentum. Phonons, which are quantized modes of vibrations in a crystal, carry crystal momentum and not true momentum. The book "Solid State Physics" by Ashcroft & Mermin provides a comprehensive explanation of these concepts. Understanding this relationship is crucial for grasping the behavior of phonons during scattering events.

PREREQUISITES
  • Understanding of crystal momentum versus true momentum
  • Familiarity with phonons and their role in solid-state physics
  • Basic knowledge of reciprocal lattice vectors
  • Awareness of the principles of scattering in crystal structures
NEXT STEPS
  • Study the concept of crystal momentum in solid-state physics
  • Read "Solid State Physics" by Ashcroft & Mermin for in-depth knowledge
  • Explore the relationship between phonons and reciprocal lattice vectors
  • Investigate the implications of momentum conservation in scattering events
USEFUL FOR

Students and researchers in solid-state physics, particularly those studying crystal dynamics, phonon behavior, and momentum conservation in crystalline materials.

cooev769
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So i don't really understand why the change in momentum of a crystal involves a reciprocal lattice vector. Surely it is just the change in momentum due to the change in the number and frequency of the phonons before and after whatever event/scattering/collision takes place. Can somebody please explain this to me in as analogous to classical mechanics way as possible, not just a purely mathematical explanation please. I'm not proficient with Fourier transformations momentum spaces etc. Thanks ;)
 
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This is a tricky question. The first important step is to realize that you are talking about crystal momentum, not true momentum. E.g. phonons do not carry true momentum but only crystal momentum.
The book by Ashcroft & Mermin is a good source on this topic.
We also had an interesting discussion in this forum before:
https://www.physicsforums.com/threads/do-phonons-conserve-momentum-or-not.611109/
 

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