Experimentally obtained and computer-simulated X-ray asymmetric eight-beam pinhole topographs for a silicon crystal.

Kouhei Okitsu,Yasuhiko Imai,Yoshinori Ueji,Yoshitaka Yoda

doi:10.1107/s2053273319001499

Abstract

In this study, experimentally obtained eight-beam pinhole topographs for a silicon crystal using synchrotron X-rays were compared with computer-simulated images, and were found to be in good agreement. The experiment was performed with an asymmetric all-Laue geometry. However, the X-rays exited from both the bottom and side surfaces of the crystal. The simulations were performed using two different approaches: one was the integration of the n-beam Takagi-Taupin equation, and the second was the fast Fourier transformation of the X-ray amplitudes obtained by solving the eigenvalue problem of the n-beam Ewald-Laue theory as reported by Kohn & Khikhlukha [Acta Cryst. (2016), A72, 349-356] and Kohn [Acta Cryst. (2017), A73, 30-38].

Highlights

We previously reported a derivation of the n-beam Takagi– Taupin (T-T) equation and an algorithm to integrate it (Okitsu, 2003; Okitsu et al, 2006)
Ishiwata et al (2010) reported X-ray rocking curves that were obtained by fast Fourier transformation of the X-ray amplitude in a three-beam topograph, and compared them with those computed by solving the eigenvalue problem of the three-beam E-L theory
Obtained and computer-simulated asymmetric eight-beam pinhole topographs, which were in good agreement, were reported

Summary

Introduction

We previously reported a derivation of the n-beam Takagi– Taupin (T-T) equation and an algorithm to integrate it (Okitsu, 2003; Okitsu et al, 2006). We verified these by comparing computer-simulated and experimentally obtained topographs using a six-beam case (Okitsu et al, 2003, 2006, 2011) and three-, four-, five-, six-, eight- and 12-beam cases (Okitsu et al, 2012). Heyroth et al (2001) reported X-ray three-beam topographs experimentally obtained and computer simulated by coherently superposing the X-ray amplitude calculated based on the E-L theory

Results

Discussion

Conclusion