Diffraction physics

The main theories of diffraction are briefly described and their more important results compared. The limitations of the geometrical theory are discussed and the concept of extinction introduced. The main features of the diffraction by a perfect crystal are briefly reviewed: total reflection and Darwin width associated with the Bragg gap, standing waves, anomalous absorption, ray tracing, plane-wave and spherical-wave Pendellosung, polarization properties. Real crystals are seldom perfect. They may be nearly perfect with small strains and/or individual lattice defects faults or they may be highly deformed with large strains and a high density of defects. The diffraction by the former is handled using extensions of the dynamical theory of diffraction by perfect crystals using ray tracing. The results are analytical in the case of a constant strain gradient and are otherwise described by simulations which can be compared to the experimental results The latter case is more difficult but can be approached by more sophisticated theories such as that of Takagi and Taupin.