When it comes to measuring the phonon dispersion at the edge of a Brillouin zone, why are neutrons chosen and not photons?
Phonons have energies in the range 10-100 meV. The wave vector of photons with energies close to the energies of phonons is very small compared to the typical size of a Brillouin zone. Therefore, photons can mostly probe zone-center phonons (e.g. Raman or IR spectroscopies). To probe zone-boundary phonons you need a large wave vector with an energy in the 10-100 meV scale, and this is what neutrons provide.