X-ray Takagi–Taupin dynamical theory generalized to n-beam diffraction cases

A new X-ray dynamical diffraction theory that can deal with n-beam cases comprehensively (n ∈ {3, 4, 6, 8, 12}) has been derived based on the Takagi–Taupin dynamical theory. The new theory takes into account correctly the effects of arbitrarily polarized incident X-rays and the polarization states of X-ray wavefields in a crystal. Furthermore, an arbitrary lattice displacement in the crystal can be dealt with. The new theory has a high symmetry and therefore can be written with one equation supposing that suffixes are taken in 2n ways, where the suffixes indicate ordinal numbers of waves and polarization states. This simplicity of the theory enables a computer program to solve the equations to be coded easily. A method to solve the theory numerically is also described. `Six-beam X-ray section topographs' computer simulated based on the new theory are also presented.