A Detailed Observation of the Nonprojectiveness of X-ray Moiré-Fringed Diffraction Images

Abstract

It has been shown in recent years that X-ray moir6 fringes are not given exactly as a projection of the intensity pattern on the exit surface of the crystal but oscillate spatially along the beam path behind the crystal. Experiments to reveal the real state of this moir6 image's nonprojectiveness have been conducted using synchrotron-radiation plane-wave topography, an Si bicrystal specimen and a simultaneous recording of moir6 topographic images onto a set of multilayered X-ray films. This paper reports the following experimental results: intensity prof'des revealing an unusual striking figure of the space wave field of moir6 fringes; qualitative analysis of the fringe profile change in its manner of occurrence and in the effect on the fringeposition variation; plots of oscillating fringe position and fringe direction. The amplitudes of the fringe oscillation determined over the whole field of the moir6 pattern exhibit a non-uniform characteristic distribution pattern that can be related to a specific feature of the intensity pattern on the specimen.

Theoretical study of the properties of X-ray diffraction moiré fringes. I

“…[the sign is reversed compared to the definition in Yoshimura (1996a)]. From equations (39) and (37c), the equation for the fringe line (i.e., the equi-phase line) when ¼ 0 is given by…”

“…1 (Yoshimura 1996b(Yoshimura , 1997b, which was taken in a previous experiment on the moiré -fringe oscillation (Yoshimura, 1996a). This moiré image, though nearly of rotation moiré, has a feature of lowcontrast vertical bands extending from the top to the bottom of the image.…”

“…Polcarová (1978aPolcarová ( ,b, 1980, largely based on this theory by Kato, calculated diffraction intensities from a crystal having a misfit boundary, to a final form, but did not deal with moiré fringes. Yoshimura performed a full calculation of moiré fringes on the basis of Kato's theory above, and has published part of the results as an appendix (Yoshimura, 1989(Yoshimura, , 1996a and a short note (Yoshimura, 1997a). Although omitting to publish the entire results is regretted now, the full description would have had to be very long, and it was not the main investigative theme of the author at that time.…”

Additional comments on the theoretical formulation of X-ray moiré fringes

“…The calculation with these Xg factors yields the extra phase term -2zri(Ag. ro) in equations (5a) and (5b) in Yoshimura (1996a). The equations concerned are rewritten here for the wave fields on the exit…”

“…In theory, the result of a full calculation of moir6 fringes by the conventional dynamical diffraction theory has been formulated in Yoshimura (1996a), while a satisfactory theory of moir6 fringes with X-rays has not been given since the early work by Hashimoto, Mannami & Naiki (1961) for electron diffraction moir6 fringes. The theory in Yoshimura (1996a), however, was too briefly described with the emphasis on the explanation of the theoretical projectiveness of moir6 fringes and other aspects of the theory were not well explained. It is the purpose of this paper to give supplementary explanations for the main results of the theory, to advance our understanding of moir6 fi'inges.…”