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 in [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.
A solution of the X‐ray `phase problem'
The phases of X-ray reflections are lost in the diffraction process in conventional two-beam diffraction. It is shown that the phases are not lost when three beams diffract simultaneously, and that phase information can be extracted from knowledge of the spatial distribution of the diffracted intensities about the three-beam point. In centrosymmetric crystals, the distribution is a sensitive function of the invariant phase of the product of the structure factors involved in simultaneous diffraction. High-resolution divergent-beam photographs illustrating the intensity differences associated with positive and negative triplet-phase products are shown.
Polarization phenomena in X-ray diffraction
Because of the dielectric properties of most crystals in the X-ray frequency region, polarization phenomena such as birefringence and optical activity are not found with X-rays in simple transmission. It can however be deduced from the dynamical theory that such effects occur in crystal diffraction. An experiment is described which proves that under certain conditions all four branches of the dispersion surface can be excited by linearly polarized incident waves. This means that elliptically polarized X-rays can also be produced by crystal diffraction. Therefore in principle all polarization experiments that can be performed with visible light are also possible with X-rays.