Neutron diffraction from sound-excited crystals

A longitudinal sound wave modulates the regular arrangement of the atomic planes of a crystal in two ways: first, the spacing between the atomic planes is modified in the regions of compression and expansion introducing a macroscopic strain and, second, the lattice planes acquire a velocity in the oscillating strain field. Bragg reflection in a strained crystal maintains the energy of the radiation, whereas Bragg reflection by a moving lattice provokes a Doppler shift of the radiation. In a diffraction experiment both these effects lead to an enlarged bandwidth of the reflection curve. The relative importance of strain and Doppler depends mainly on the radiation used. For thermal neutron scattering the profile of the rocking curve of a Bragg reflection may permit to separate the two effects. Atomic amplitudes of the sound field of 136 Å peak to peak in the bulk of the crystal can be deduced from the rocking profile. The enlarged bandwidth of a sound-excited crystal opens a possibility for diffraction-based optical elements where the trade-off between resolution and intensity can be readily modified.