Photon Factory Activity Report 2005 #23 Part B (2006)
Crystallography

15C/2004G234

Observation of X-ray Interference Fringe in Bragg-(Bragg)m-Laue Casefrom Thin Finite Crystal
Tomoe FUKAMACHI*1, Riichirou NEGISHI1, Masami YOSHIZAWA1, Kenji HIRANO1,Toshiyuki TANAKA1, Tsuyoshi OBA1, Keiichi HIRANO2 and Takaaki KAWAMURA3
1Saitama Institute of Technology, 1690 Fusaiji, Fukaya, Saitama 369-0293, Japan
2
Institute of Material Structure Science, KEK-PF, High Energy Accelerator Research Organization,Oho-machi, Tukuba, Ibaraki 305-0801, Japan
3Department of Mathematics and Physics, University of Yamanashi,Kofu, Yamanashi 400-8510, Japan
In the Bragg case of an absorbing thin crystal, it has been
confirmed experimentally [1,2] that part of the incident
X-rays are confined in the crystal at a certain angle when
the absorption factor is effectively diminished by thedynamical effect (Borrmann effect). In the thin finite
crystal as shown in Fig. 1, the confined X-rays can comeout from the side edge. The diffraction condition in Fig. 1
is called as “Bragg-(Bragg)m-Laue case” (BBmL case forshort). The first “Bragg” means the first diffraction in theBragg case, the second “(Bragg)m” a sequence of “m”
diffractions in the region between the top and bottom
surfaces of the crystal and the final “Laue” the lastdiffraction in the Laue case before emitting from the edge.
The experiment was carried out at beam line 15C, Photon
factory (PF), KEK, Japan. X-rays from synchrotron
radiation were monochromated by a Si 111 double crystal
monochromater and Ge 220 monochromater, σpolarization was used. The used X-ray energy was
11100±0.5eV which was 3eV below the Ge K-absorption
edge (11103eV). The vertical and horizontal widths of theincident beam are 25 and 500µm respectively. The
distance between the incident point of X-rays and edge ofthe crystal L is 907µm. The photographs of the 220
reflection from the Ge thin crystal whose thickness is
32µm are shown in Fig. 2. The upper part shows thetransmitted beam (IT) and the emitted beam (IT’) fromthe side edge of the crystal in the transmission direction.
The lower part shows the reflection beam (IR) and theemitted beam in the reflecting direction (IR’). Theinterference fringes can be seen in IT’ and IR’. The
photographs show: 1) The period of the fringe in IR’ issmaller and that in IT’ is larger in each upper side. 2) The
period increases as distance L increases. 3) It decreases
when the crystal thickness increases.
It is possible to calculate the rate of X-ray
confinement in the thin crystal by the resonant dynamical
theory [3], but it is still not easy to analyze the flux of theconfined X-rays. Quantitative analysis of the origin of theinterference fringe in BBmL case should be a future work.
It is noted that many applications to precise X-ray optics
such as those seen in the interference fringe of an X-ray
interferometer would be expected, once the origin is fully
analyzed.

References[1] T. Fukamachi et al., JJAP 43,L865(2004).
[2] T. Fukamachi et al., JJAP 44,L787(2005).
[3] T. Fukamachi et al., JJAP 45,2830(2006).
*tomoe@sit.ac.jp

Fig. 1. Schematic diagram of Bragg-(Bragg)m-Laue case.

Fig. 2. Photographs of IT and IT’ (upper part) and IRand IR’ (lower part).

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