So during neutron scattering in a crystal, a neutron can interact with 0, 1, or more phonons. First of all, what is the actual mechanism by which they interact? My textbook just kind of glosses over that. Second of all, when a neutron goes in it can absorb a phonon and come out with more energy than it came in with. This must mean the energy comes from the crystal, right? But what energy, just the thermal energy of the atoms? So, if you scattered neutrons off a solid at 0K, would it only give energy to the crystal, not take it at all?