The X-ray standing wave has been studied when the real part of the scattering factor is zero. In the symmetric Laue case, the phase of the standing wave advances by % when the deviation parameter W changes from À1 to 1, which is the same variation as in the usual symmetric Bragg case when only the real part of the scattering factor exists. However, the phase in the former case is different from that in the latter by %a2. By using the standing waves, the origins of the anomalous transmission and anomalous absorption effects reported by Fukamachi & Kawamura [Acta Cryst. (1993), A49, 384±388] have been analysed. The standing wave in the Laue case can give rise to a more accurate method of site determination of a speci®ed impurity atom as well as a wider range of applications than a conventional standing-wave approach.

In the waves emitted from the entrance, back and lateral surfaces of a very weakly bent plane-parallel perfect crystal with negative strain gradient, X-ray interference fringes between two refracted beams with different hyperbolic trajectories were observed when the strain was very weak, of the order of 10−7.

We report a practical method to assign parastichy numbers to spiral patterns formed by sunflower seeds and pineapple ramenta using a discrete Fourier transform. We designed various simulation models of sunflower seeds and pineapple ramenta and simulated their point patterns. The parastichy numbers can be directly and accurately assigned using the discrete Fourier transform method to analyze point patterns even when the parastichy numbers contain a divergence angle that results in two or more generalized Fibonacci numbers. The presented method can be applied to extract the structural features of any spiral pattern.

In order to observe the effect of atomic resonant scattering on X-ray topography, topographs of a GaAs crystal with the 200 reflection have been taken using synchrotron X-rays with energy near the K-absorption edges of Ga and As. The X-ray energy has been tuned to four typical resonant scattering conditions. It is shown that the contrast of lattice defects observed in topographs changes with the resonant scattering conditions. Such topography taken under resonant scattering is useful for studying lattice defects in crystals.

By using X‐rays from synchrotron radiation, we measured the rocking curves due to only the imaginary part of the atomic scattering factor in Laue case. The interference fringes are observed which are totally different from the Pendellösung fringe. The fringes of the diffracted and transmitted rocking curves are in‐phase with each other. We studied the origin of the in‐phase fringes by using the complex dispersion surface and the electric field in the crystal, and also the relation with a coupled pendulum.