X-ray interference fringes from a weakly bent plane-parallel crystal with negative strain gradient.

Under the anomalous transmission condition in the Bragg mode, X-ray interference fringes were observed between two beams with different hyperbolic trajectories in a very weakly bent plane-parallel perfect crystal with negative strain gradient. The origin of the fringes was analysed based on the dynamical theory of diffraction for a distorted crystal. In the reflected beam from the entrance surface, the interference fringes were observed between once- and twice-reflected beams from the back surface. In the transmitted beam from the back surface, the interference fringes were observed between the direct beam and once-reflected beam from the entrance surface. In the emitted beam from the lateral surface, the interference fringes were observed between the beams after different numbers of reflections in the crystal. The multiply reflected beams were formed by a combined result of long propagation length along the beam direction with large divergence of the refracted beams when the strain gradient was negative. The period of these interference fringes was sensitive to very weak strain, of the order of 10-7.

Erratum: An X-ray diffractometer using mirage diffraction. Erratum.

Errors in the article by Fukamachi, Jongsukswat, Ju, Negishi, Hirano & Kawamura [J. Appl. Cryst. (2014), 47, 1267-1272] are corrected.[This corrects the article DOI: 10.1107/S1600576714012114.].

An X-ray diffractometer using mirage diffraction.

Some characteristics are reported of a triple-crystal diffractometer with a (+, -, +) setting of Si(220) using mirage diffraction. The first crystal is flat, while the second and third crystals are bent. Basically, the first crystal is used as a collimator, the second as a monochromator and the third as the sample. The third crystal also works as an analyzer. The advantages of this diffractometer are that its setup is easy, its structure is simple, the divergence angle from the second crystal is small and the energy resolution of the third crystal is high, of the order of sub-meV.

Strain distribution in an Si single crystal measured by interference fringes of X-ray mirage diffraction.

In X-ray interference fringes accompanied by mirage diffraction, variations have been observed in the spacing and position of the fringes from a plane-parallel Si single crystal fixed at one end as a function of distance from the incident plane of the X-rays to the free crystal end. The variations can be explained by distortion of the sample crystal due to gravity. From the variations and positions of the fringes, the strain gradient of the crystal has been determined. The distribution of the observed strain agrees with that expected from rod theory except for residual strain. When the distortion is large, the observed strain distribution does not agree with that expected from rod theory.

Moiré pattern from a multiple Bragg-Laue interferometer.

In X-ray section topography of Si 220 diffraction in a multiple Bragg-Laue mode, a moiré pattern is observed when the incident beam is divided into two parts by inserting a platinum wire in the middle of the beam. The moiré pattern can be explained by the summation of two interference fringes corresponding to the two incident beams. The coherency of the X-rays from the bending-magnet beamline is estimated using the moiré pattern.

Interference fringes in multiple Bragg-Laue mode.

Interference fringes in multiple Bragg-Laue mode have been measured from the lateral surface of an Si plane-parallel crystal by changing the distance L between the incident point of X-rays and the crystal edge for two sample crystals with different thicknesses H. The period of the interference fringes becomes large when the distance L becomes large or the thickness H becomes small. When the ratio L/H is larger than 15, a shorter period of oscillation appears in addition to the interference fringes. These variations are explained by considering the beams in multiple Bragg-Laue modes based on the dynamical theory of diffraction. When L/H is less than 15, the measured fringes are well reproduced by taking account of interference between beams in the Bragg-Laue and the Bragg-Bragg-Laue modes. The short period of the oscillations observed for L/H > 15 is reproduced by adding the intensities of the beams in higher-order Bragg-Laue mode. The interference fringes calculated by taking the visibility into account show good agreement with the measured ones.