A new approach to wide-angle dynamical X-ray diffraction by deformed crystals (original) (raw)
Related papers
Journal of Applied Physics
We propose a digital model for high quality superlattices by including fluctuations in the superlattice periods. The composition and strain profiles are assumed to be coherent and persist throughout the superlattice. Using this model, we have significantly improved the fit with experimental X-ray diffraction data recorded from the nominal InAs/GaSb superlattice. The lattice spacing of individual layers inside the superlattice and the extent of interfacial intermixing are refined by including both (002) and (004) and their satellite peaks in the fitting. For the InAs/GaSb strained layer superlattice, results show: (i) the GaSb-on-InAs interface is chemically sharper than the InAs-on-GaSb interface, (ii) the GaSb layers experience compressive strain with In incorporation, (iii) there are interfacial strain associated with InSb-like bonds in GaSb and GaAs-like bonds in InAs, (iv) Sb substitutes a significant amount of In inside InAs layer near the InAs-on-GaSb interface. For support, w...
Wide angle X-ray dynamical diffraction by deformed crystals: recurrence relations
Physica Status Solidi a Applications and Materials Science, 2007
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.
Acta Crystallographica Section A Foundations of Crystallography, 2004
X-ray diffraction in continuously deformed crystals is considered by application of Fourier optics and from the viewpoint of the analogy between X-ray dynamics and the motion of two-level systems in quantum mechanics. Different forms of Takagi's equations are traced back to a common framework and it is shown that they are different ways to represent the same propagation equation. A novel way to solve Takagi's equations in the presence of a constant strain gradient is presented and approximation methods derived from quantum mechanics are considered. Crystal deformation in X-ray interferometry and two-crystal spectrometry are discussed and it is demonstrated that Si lattice-parameter measurements depend on the diffracting plane spacing on the crystal surface.
Journal of Applied Crystallography, 2020
Dynamical X-ray diffraction simulations from crystals with surface undulations are reported. The Takagi–Taupin equations are applied and used to derive results in good agreement with experimental data reported in a separate paper [Macrander, Pereira, Huang, Kasman, Qian, Wojcik & Assoufid (2020). J. Appl. Cryst. 53, 789–792]. The development of Uragami [J. Phys. Soc. Jpn, (1969), 27, 147–154] is followed. Although previous work by Olekhnovich & Olekhnovich [Acta. Cryst. (1980), A36, 22–27] treated a crystal in the shape of a round cylinder, there do not seem to be any reports of previous dynamical X-ray diffraction treatments specifically for surface undulations. The significance of the present work is that it bridges the diffraction treatment of more classical dynamical diffraction theory, which assumes a flat surface, and the simple kinematic diffraction theory. The kinematic theory has, to date, been the primary means of simulating X-ray diffraction from surfaces.
Applied Physics A, 2012
Your article is protected by copyright and all rights are held exclusively by Springer-Verlag. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your work, please use the accepted author's version for posting to your own website or your institution's repository. You may further deposit the accepted author's version on a funder's repository at a funder's request, provided it is not made publicly available until 12 months after publication.
Physical Review B
The generalized statistical dynamical theory of x-ray scattering by imperfect single crystals with randomly distributed Coulomb-type defects has been extended to characterize structure imperfections in the real multilayers of arbitrary thickness in Bragg diffraction geometry. The recurrence relations for the coherent amplitude reflection and transmission coefficients of such multilayers, which consist of any number of layers with constant strain and randomly distributed defects in each one, have been derived within the concept of the dynamical wave field, i.e., the so-called Ewald-Bethe-Laue approach, with rigorous accounting for boundary conditions at layer interfaces. The analytical expression for the differential dynamical diffuse component of the reflection coefficient of an imperfect multilayer system has been obtained as well. This expression establishes direct connection between the distribution of the diffuse scattering intensity in a momentum space and statistical characteristics of defects in each layer. In addition, the integrals from differential diffuse scattering intensity over the Ewald sphere and over vertical divergence have been found, which correspond to diffuse components in measurements of rocking curves and reciprocal space maps, respectively. The developed theory provides the dynamical description for the one-and two-dimensional angular distributions of the mutually consistent coherent and diffuse components of x-ray scattering intensities, which are measured by the high-resolution double-and triple-crystal diffractometers, respectively, from imperfect films, multilayer structures, superlattices, etc. Examples of simulated rocking curves for the imperfect superlattice with defects of several types and reciprocal space map for the ion-implanted sample of yttrium iron garnet film with defects are given and discussed.
Dynamical effects in Bragg coherent x-ray diffraction imaging of finite crystals
Physical Review B, 2017
We present simulations of Bragg Coherent X-ray Diffractive Imaging (CXDI) data from finite crystals in the frame of the dynamical theory of x-ray diffraction. The developed approach is based on numerical solution of modified Takagi-Taupin equations and can be applied for modeling of a broad range of x-ray diffraction experiments with finite three-dimensional crystals of arbitrary shape also in the presence of strain. We performed simulations for nanocrystals of a cubic and hemispherical shape of different sizes and provided a detailed analysis of artifacts in the Bragg CXDI reconstructions introduced by the dynamical diffraction. A convenient way to treat effects of refraction and absorption supported by analytical derivations is described. Our results elucidate limitations for the kinematical approach in the Bragg CXDI and suggest a natural criterion to distinguish between kinematical and dynamical cases in coherent x-ray diffraction on a finite crystal.
A dynamical theory for the X-ray diffraction from the partially relaxed layers
physica status solidi (a), 2009
The dynamical theory for X-ray diffraction from the bilayer crystal structure with different lateral periods of the crystal unit cells (lateral mismatch) is considered in the present paper. The amplitudes of the principal diffraction waves and all harmonics conditioned by the lateral mismatch are calculated. The formation of the Bragg peaks is analysed taking into account the sphericity of the incident beam wave front set. The connection between the parameters of the coherent diffraction potential in the partially relaxed (epitaxial) crystals and the microscopic characteristics of the dislocations is also discussed.
X-ray diffraction of bent crystals in Bragg geometry. I. Perfect-crystal modelling
Journal of Applied Crystallography, 1992
X-ray reflectivity, widths, centroid shifts and profiles for curved perfect crystals are calculated from a model. The crystal is approximated by a stack of perfectcrystal lamellae or blocks with a gradually changing (mean) orientation. A computer program has been developed to calculate the above quantities in the Johann geometry for the composite crystal from the dynamic theory of diffraction. Focusing and defocusing aberrations and the use of photographic detection methods are included. Correction of omissions from earlier theory and modelling is noted, together with observed effects. Incoherent scattering can give dramatic changes in diffracted intensities and significant shifts of final parameters. Effects of depth penetration on shifts, cosine ratios and other parameters are included. Assumptions of the model and implementation are detailed. It is shown that interference effects between waves of roughly equal amplitudes require use of lamellar thicknesses greater than those corresponding to the Darwin range. Internal tests demonstrate agreement with the literature at extremes. The theory is applied to first-and fourth-order spectra in differential Lyman ~ wavelength measurements. Resuits for pentaerythritol 002 crystals are presented. Paper II of this series extends this model to nonideally imperfect crystals and other crystals of interest and discusses experimental agreement.