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

[cooev769]

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 ;)

 

[DrDu]

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/