Polarization-dependent X-ray six-beam pinhole topographs for a channel-cut silicon crystal

Abstract

It was pointed out in a previous paper [Okitsu et al. (2006), Acta Cryst. A62, 237-244] that an n-beam Takagi-Taupin (T-T) equation can be solved for a crystal of arbitrary shape. The procedure to integrate the n-beam T-T equation is to let all the Fourier coefficients of the electric susceptibility be zero at positions inside the Borrmann pyramid but outside the crystal. The efficiency of this simple procedure is verified in the present paper by showing qualitative and quantitative agreements between experimentally obtained and computer-simulated X-ray six-beam pinhole topographs for a channel-cut silicon crystal.

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

“…We verified these by comparing computer-simulated and experimentally obtained topographs using a six-beam case (Okitsu et al, , 2006(Okitsu et al, , 2011 and three-, four-, five-, six-, eight-and 12-beam cases (Okitsu et al, 2012). Hereafter, Okitsu et al (2006), Okitsu et al (2011) and Okitsu et al (2012) are denoted by O et al 2006O et al , O et al 2011O et al and OIY 2012 In OIY 2012, the n-beam T-T equation was derived from the n-beam Ewald-Laue (E-L) theory, and vice versa by their Fourier transformation, which explicitly revealed a simple relationship between them described by a Fourier transform. 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.…”