Computer simulations of X-ray six-beam diffraction in a perfect silicon crystal. II

This paper reports computer simulations of X-ray six-beam (000, 220, 242, 044, -224, -202) diffraction in a perfect silicon crystal of large thickness where the super-transmission effect prevails, i.e. about 2 cm or more for an X-ray photon energy of 8 keV. Both the plane-wave angular dependence and the six-beam section topographs, which are obtained in experiments with a two-dimensional slit, are calculated. The angular dependence is computed by means of an eigenvalue problem in accordance with Ewald's theory. The section topographs are calculated by means of a fast Fourier transformation procedure from the angular to real space. It is shown that under the effect of X-ray super-transmission the quadrupole part of the photoelectric absorption as well as the Compton scattering give apparent contributions to the minimum absorption coefficient. Comparison of experimental and theoretical results by means of measuring the effective absorption coefficient is proposed. The section topographs for a thick crystal are asymmetric and polarization sensitive. These properties are explained through the angular dependence and the stationary phase method.

Computer simulations of X-ray six-beam diffraction in a perfect silicon crystal. I

This paper reports computer simulations of the transmitted-beam intensity distribution for the case of six-beam (000, 220, 242, 044, -224, -202) diffraction of X-rays in a perfect silicon crystal of thickness 1 mm. Both the plane-wave angular dependence and the six-beam section topographs, which are usually obtained in experiments with a restricted beam (two-dimensional slit), are calculated. The angular dependence is calculated in accordance with Ewald's theory. The section topographs are calculated from the angular dependence by means of the fast Fourier transformation procedure. This approach allows one to consider, for the first time, the transformation of the topograph's structure due to the two-dimensional slit sizes and the distance between the slit and the detector. The results are in good agreement with the results of other works and with the experimental data. This method of calculation does not require a supercomputer and it was performed on a standard laptop. A detailed explanation of the main features of the diffraction patterns at different distances between the slit and the detector is presented.

On the dilatation of synthetic type Ib diamond by substitutional nitrogen impurity

Sequences of high Bragg-angle (0 B = 74°) double-crystal X-ray topographs taken at the SRS (Daresbury, U.K.) have yielded precise measurements of lattice parameter differences between growth sectors of different crystallographic forms in a large undoped synthetic diamond whose type Ib infrared absorption spectrum (principal peak at 1130 cm -1 ) indicated atomically dispersed nitrogen, singly substituting for carbon, as the only detectable impurity. The plate-shaped specimen, polished parallel to (110), 5.0 x 3.2 mm 2 in area, 0.7 mm thick, possessed an unusually well developed (110) growth sector containing nitrogen impurity concentration of only ca. 10 -6 , which served as an internal standard of pure-diamond lattice parameter with which lattice parameters of nitrogen-containing growth sectors were compared. The specimen’s suitability for precision diffractometry was checked by comprehensive tests using optical microscope techniques, cathodoluminescence and single-crystal X-ray topography. The double-crystal combination was silicon reference crystal, asymmetric 175 reflection, with diamond specimen symmetrical 440 reflection. The principal measurement was the increase of the lattice parameter, a 0 , of the (111) growth sector (nitrogen content 88 + 7 parts per 10 6 atomic) relative to that of the (110) sector: Aa 0 / a 0 = 1.18 + 0.07 x 10 -5 . In terms of measured infrared absorption coefficient at 1130 cm -1 , this gives Aa 0/a 0 = (2.95 + 0.27) x 10 -6 [p(1130 cm -1 )/cm -1 ], which is believed to hold for growth sectors of all crystallographic forms. Combination with the nitrogen assay findings of Woods, van Wyk & Collins ( Phil. Mag. B 62. 589-595 (1990)) provides a direct relation to c N , the fractional atomic concentration of substitutional nitrogen, as A a 0 / a 0 = (0.14 + 0.02) c N , which indicates that the effective volume of a single substitutional nitrogen atom in diamond is 1.41 +0.06 times that of the carbon atom it replaces. This substantial dilatation conflicts with several models for the substitutional nitrogen structure.