lately I was discussing the following situation. Let's suppose you are doing X-Ray diffraction experiments on a crystal. So what you basically do is shooting a high energy photon with a wave vector $k$ into the crystal where it will undergo diffraction according to the Bragg condition.
That is, an outgoing photon of wave vector $k'$ will emerge if there exists a reciprocal lattice vector $G$, such that $$ \Delta k = G $$ Now, we were asking ourselves the question: Where does the momentum change actually go? The crystal momentum that is produced in this process will be $ \hbar G$, but "who" carries this momentum? Will the photon induce phonons ( or excitons or whatever quasi-particle ) in the crystal carrying away the momentum? Or will the crystal as a whole take the momentum? Or a mixture of that? Or something completely different?
Thanks for any hints :)