Wide angle X‐ray dynamical diffraction by deformed crystals: recurrence relations

Abstract

Dynamical wide‐angle multiwave X‐ray diffraction from a deformed crystal was considered, for the special case when no more than one strong reflection occurs at a time. The obtained set of equations can be transformed to the Takagi two‐beam approximation if the scattering vector is close to a vector of the reciprocal lattice. The new formalism was employed to obtain recurrence relations for the amplitude reflection coefficient corresponding to laterally homogeneous multilayer structures for the case of coplanar Bragg diffraction. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Structure ofFe3Si∕GaAs(001)epitaxial films from x-ray crystal truncation rods

“…[26][27][28][29][30][31][32][33][34][35] Recently, we have shown 36 that the dynamical calculation can be extended to the whole CTR by summing up the amplitudes of the diffracted waves of the two-beam diffraction problems for all Bragg reflections along the CTR. Dynamical and kinematical scattering intensities quantitatively agree everywhere except in the vicinity of the Bragg peaks, where the kinematical intensity diverges.…”

Crystal truncation rods in kinematical and dynamical x-ray diffraction theories

“…Studies of very thin (a few atomic layers) films require the analysis of the whole CTR. The problem of an accurate calculation of the CTR intensity in the whole wave vector range has been the subject of a number of investigations, 11,12,13,14,15,16,17,18,19 but a conclusive recipe has not been given yet. It is well established that the two-beam dynamical diffraction theory is very accurate in the vicinity of the respective Bragg reflection but fails in the middle between two reflections.…”

“…The resolution of the latter problem was attempted by appropriate multibeam calculations. 12,16,17 Recently, Pavlov et al 19 proposed to calculate the diffracted intensity in a wide angular range by summing up the amplitudes of the diffracted waves for different reflections, each amplitude being the solution of the corresponding two-beam diffraction problem.…”

“…For non-grazing incidence and exit, the resulting amplitude depends on the z-component of momentum transfer q = 2πL/a, rather than the incident and the exit angles Φ in and Φ out separately. Pavlov et al 19 have arrived to an equivalent formula by solving the Takagi-Taupin equations.…”

Long-range scans and many-beam effects for high-resolution x-ray diffraction from multilayered structures: Experiment and theory

“…The systematic study on LRS with the use of a dynamical approach was started two decades ago. [10][11][12][13][14] Recently, this problem has been considered in several works [4][5][6][7]15 for deriving an effective algorithm for simulation of LRS, which can be applicable for modern HRXRD methods. Within the accuracy provided by the first order of x-ray polarizability, the problem has been resolved in Ref.…”