Extremely skew X-ray diffraction

Höche, H. R.; Brümmer, O.; Nieber, J.

doi:10.1107/s0108767386098707

Cited by 36 publications

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References 5 publications

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“…1͒: ͑i͒ The coplanar extremely asymmetric diffraction ͑EAD͒ is realized when the diffraction planes make the Bragg angle with the crystal surface and either the incident or exit x-ray wave is grazing. [5][6][7][8][9][10][11][12] ͑ii͒ Surface or ''grazing-incidence'' diffraction 13 ͑GID͒ is the geometry where the Bragg planes are perpendicular to the surface and both the x-ray waves are grazing. [14][15][16][17][18][19][20][21][22][23] ͑iii͒ Finally, grazing Bragg-Laue diffraction ͑GBL͒ is a combination of the EAD and GID.…”

Section: Introductionmentioning

confidence: 99%

Dynamical x-ray diffraction of multilayers and superlattices: Recursion matrix extension to grazing angles

et al. 1998

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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

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Section: Introductionmentioning

confidence: 99%

Dynamical x-ray diffraction of multilayers and superlattices: Recursion matrix extension to grazing angles

et al. 1998

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Dynamical Diffraction at Grazing Incidence

Authier¹

1998

Cryst. Res. Technol.

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Dynamical Diffraction

Shen¹

2002

Characterization of Materials

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Diffraction‐related techniques using x rays, electrons, or neutrons are widely used in materials science to provide basic structural information on crystalline materials. To describe a diffraction phenomenon, one has the choice of two theories: kinematic or dynamical. Kinematic theory assumes that each x‐ray photon, electron, or neutron scatters only once before it is detected. This assumption is valid in most cases for x rays and neutrons since their interactions with materials are relatively weak. This single‐scattering mechanism is also called the first‐order Born approximation or simply the Born approximation. The kinematic diffraction theory can be applied to a vast majority of materials studies and is the most commonly used theory to describe x‐ray or neutron diffraction from crystals that are imperfect. There are, however, practical situations where the higher‐order scattering or multiple‐scattering terms in the Born series become important and cannot be neglected. This is the case, for example, with electron diffraction from crystals, where an electron beam interacts strongly with electrons in a crystal. Multiple scattering can also be important in certain application areas of x‐ray and neutron scattering, as described below. In all these cases, the simplified kinematic theory is not sufficient to evaluate the diffraction processes and the more rigorous dynamical theory is needed where multiple scattering is taken into account. Dynamical diffraction is the predominant phenomenon in almost all electron diffraction applications, such as low‐energy electron diffraction and reflection high‐energy electron diffraction. For x rays and neutrons, areas of materials research that involve dynamical diffraction may include the situations discussed.

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Extremely skew X-ray diffraction

Cited by 36 publications

References 5 publications

Dynamical x-ray diffraction of multilayers and superlattices: Recursion matrix extension to grazing angles

Dynamical x-ray diffraction of multilayers and superlattices: Recursion matrix extension to grazing angles

Dynamical Diffraction at Grazing Incidence

Dynamical Diffraction

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