Normale und anomale Absorption von Röntgen-Strahlen in Germanium und Silicium/Normal and anomalous absorption of X-rays in Germanium and Silicon

Abstract

N o r m a le u n d a n o m a le A b s o r p tio n v o n R ö n tg e n -S tr a h le n in G e r m a n iu m u n d S iliciu m Normal and anomalous absorption of X-rays in Germanium and Silicon A brief discussion of G. Moliere's generalized dynamical theory is given with respect to the interpretation of the experimental data ! % 1,/Z-o I obtained by means of the Borrmann effect.In order to compare theory and experiment photoelectric absorption cross sections for Silicon and Germanium have been calculated over the X-ray energy range from 5 to 25 keV. Linear ab sorption coefficients measured by us and other authors agree with theory within a few per cent.Taking the Debye-Waller factor into account, the same theoretical data have been used to cal culate J X <l 9IX <o ! f°r Ge and Si. The agreement with extensive measurements of the Borrmann effect in Ge is very good in most cases. The experiments presented in this paper confirm the existence of the electric quadrupole transitions within the photoelectric effect.

Powder diffraction with synchrotron radiation. II. Dispersion factors of Ni

“…This is only a few percent of f b, in agreement with the calculated and observed ratio f'~/f'~ of the imaginary parts (Hildebrandt et al, 1973). It can be concluded that although the present experiment does not give any definite value for the angle-dependent part of f', it gives an upper limit and this limit is so low that it rules out any speculations that there may be significant effects of this kind.…”

“…H6nl-type calculations, which have been supported by measurements (Hildebrandt, Stephenson & Wagenfeld, 1973), suggest that f" depends only very slightly on sin O/h, in contrast to calculations, which show noticeable effects for both f' and J" (Hazell, 1975). Interferometric measurements give f' at zero angle, as do measurements of the critical angle or calculations from the absorption coefficient through the Kramers-Kronig relations (Bonse & Hartmann-Lotsch, 1984;Dreier, Rabe, Malzfeldt & Niemann, 1984;Hoyt, de Fontaine & Warburton, 1984).…”

“…The results of Hildebrandt et al (1973) indicate that f~/f~, is typically 0.01 to 0.05. The same is presumably true for the real parts, and so a ~> b.…”

Double-crystal rocking curve of the forbidden Si 222 reflection

“…Dispersion corrections and absorption were taken into account. The linear absorption coefficient/.t was taken to be 14.64cm -1 and a value for the ratio of the imaginary parts of the polarizabilities Xi(333)/xi(O) --0.6 was used (Hildebrandt, Stephenson & Wagenfeld, 1973). Initially, the intrinsic reflection curve was calculated and then the convolution of two identical curves was performed.…”

Symmetrical cases of simultaneous X-ray diffraction and the Borrmann effect. I. The analysis of photoelectric absorption

“…To calculate the photoelectric-absorption contribution to the imaginary part of the polarizability one usually uses the multipole series (Hildebrandt, Stephenson & Wagenfeld, 1973). It is enough to retain only the dipole and quadrupole terms because the remaining terms are small; then we have Xi'(k, k~)= z?…”