The mosaic crystal model goes back to a theoretical analysis of X-ray diffraction by C. G. Darwin (1922).
An important application of mosaic crystals is in monochromators for x-ray and neutron radiation.
To describe diffraction by a thick mosaic crystal, it is usually assumed that the constituent crystallites are so thin that each of them reflects at most a small fraction of the incident beam.
When only beams within the scattering plane are considered, then they obey the Darwin–Hamilton equations (Darwin 1922, Hamilton 1957), where
are the corresponding currents, μ is the Bragg reflectivity, and σ accounts for losses by absorption and by thermal and elastic diffuse scattering.