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The K absorption edge of pure Fe and the pre-edge Fe K absorption of FeS, (pyrite), Fe20, (hematite), and FeCO, (siderite) are investigated with single crystal absorbers of these materials using linearly polarized synchrotron X-radiation. From the angular dependence of the pre-edge K absorption the existence of predominantly ligand-field-induced dipole transitions in Fe,O, and of quadrupole transitions in FeCO, is concluded. The multipole character and the mechanism of the pre-edge K absorption are discussed.Die K-Absorptionskante von reinem Fe und die Fe K-Vorkantenabsorption von FeS, (Pyrit), Fe,O, (Hamatit) und FeCO, (Siderit) werden a n einkristallinen Absorbern dieser Materialien mit linear polarisierter Synchrotron-Rontgenstrahlung untersucht. Aus der Winkelabhangigkeit der K-Vorkantenabsorption wird auf das Aaftreten von iiberwiegend ligandenfeldinduzierten Dipolubergangen im Fe,O, und von Quadrupoliibergangen im FeCO, geschlossen. Der Multipolcharakter und der Mechanismus der K-Vorkantcnabsorption werden diskutiert.

A generalized dynamical theory has been developed that extends previous models of x-ray diffraction from crystals and multilayers with vertical strains to the cases of grazing incidence and/or exit below the critical angle for total specular reflection. This provides a common description for extremely asymmetric diffraction, surface ͑''grazing-incidence''͒, and grazing Bragg-Laue diffraction, thus providing opportunities for the applications of grazing geometries to the studies of thin multilayers. The solution, obtained in the form of recursion formulas for ͑2ϫ2͒ scattering matrices for each individual layer, eliminates possible divergences of the ͑4ϫ4͒ transfer-matrix algorithm developed previously. For nongrazing x-ray diffraction in the Bragg geometry and for grazing-incidence x-ray specular reflection out of the Bragg diffraction conditions, the matrices are reduced to scalars and the recursion formulas become equivalent to the earlier recursion formulas by Bartels et al. ͓Acta Cryst. A 42, 539 ͑1986͔͒ and Parratt ͓Phys. Rev. 95, 359 ͑1954͔͒, respectively. The theory has been confirmed by an extremely asymmetric x-ray-diffraction experiment with a strained AlAs/GaAs superlattice carried out at HASYLAB. A solution to the difficulties due to dispersion encountered in extremely asymmetric diffraction measurements has been demonstrated. Finally, the validity of Ewald's expansion for thin layers and the relation of the matrix method to the Darwin theory, as well as the structure of x-ray standing waves in multilayers are discussed. ͓S0163-1829͑98͒05408-3͔

Using the dynamical theory of Bragg diffraction, we show that there is a direct relationship between the phase of the x-ray standing-wave field and the phase of the structure factor. For an experimental demonstration, we monitor the Ga and As E fluorescence and resonant Raman scattering yields, while scanning through the (111)and (200) Bragg diffraction rocking curves of GaAs perfect single crystals. The phases of the (111) and (200) GaAs structure factors are determined from the phases of the modulations in these secondary yields. With the use of monochromatized synchrotron radiation, with a variable photon energy between 10 and 15 keV, the effect of anomalous dispersion on the structure-factor phases is clearly seen in the vicinity of the Ga and As E absorption edges. We use this feature, in conjunction with the measured absorption spectrum, for directly determining the dispersion parameters f' and f" for atoms which appear in single-crystal structures.

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