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

Riichirou Negishi,Keiichi Hirano,Tomoe Fukamachi,Dongying Ju,Takaaki Kawamura,Sukswat Jongsukswat

doi:10.1107/s2053273319011859

Abstract

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.

Highlights

If the crystal is small along the incident azimuth direction (x) compared with the propagation length of the X-ray, interference fringes can be observed in the emitted beams from the lateral surface both in the diffracted- (IFLSD) and the transmitted-wave directions (IFLST)
The trajectory of the X-ray refracted beam in a very weakly bent perfect crystal with negative strain gradient shows a hyperbolic form opening down, while it shows a hyperbolic form opening up when the strain gradient is positive
In the wave emitted from the entrance surface IFRB were observed between once- and twice-reflected beams from the back surface

Summary

Introduction

If the crystal is small along the incident azimuth direction (x) compared with the propagation length of the X-ray, interference fringes can be observed in the emitted beams from the lateral surface both in the diffracted- (IFLSD) and the transmitted-wave directions (IFLST). Both IFLSD and IFLST have been observed by Fukamachi et al (2004, 2005) from a thin Ge plane-parallel crystal. BbB and B3bB are the angles of the refracted beams in the BbB and the B3bB modes from the surface, respectively

Experimental

Beam trajectory

Interference fringes between two reflected beams from the back surface

Comparison between measured and calculated interference fringes

Coherent condition and energy width of IFRB

Findings

Summary

Funding information