Is there an electron wind?

A not uncommon question in electron microscopy is what happens to the momentum transferred by the electron beam to a crystal. If the beam passes through a crystal and is preferentially diffracted in one direction, is the momentum ’lost’ by the beam transferred to the crystal? Newton’s third law implies that this must be the case. Some experimental observations also indicate that this is the case; for instance, with small particles if the particles are supported on the top surface of a film they often do not line up on the zone axis, but if they are on the bottom they do. However, if momentum is transferred to the crystal, then surely we are dealing with inelastic scattering, not elastic scattering and is not the scattering probability different? In addition, normally we consider inelastic scatter as incoherent, and therefore the part of the electron wave that is inelastically scattered will not coherently interfere with the part of the wave that is scattered; but, electron holography and high resolution electron microscopy work so the wave passing through a specimen must be coherent with the wave that does not pass through the specimen.