Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCrystal truncation rods in kinematical and dynamical x-ray diffraction theories
203
0
0.0
(
0
)
Authors
Vladimir M. Kaganer
Ask ChatGPT about the research
No Arabic abstract
Crystal truncation rods calculated in the kinematical approximation are shown to quantitatively agree with the sum of the diffracted waves obtained in the two-beam dynamical calculations for different reflections along the rod. The choice and the number of these reflections are specified. The agreement extends down to at least $sim 10^{-7}$ of the peak intensity. For lower intensities, the accuracy of dynamical calculations is limited by truncation of the electron density at a mathematically planar surface, arising from the Fourier series expansion of the crystal polarizability.
rate research
Read More
Miscut surfaces of layered crystals can exhibit a stair-like sequence of terraces having periodic variation in their atomic structure. For hexagonal close-packed and related crystal structures with an {alpha}{beta}{alpha}{beta} stacking sequence, there have been long-standing questions regarding how the differences in adatom attachment kinetics at the steps separating the terraces affect the fractional coverage of {alpha} vs. {beta} termination during crystal growth. To demonstrate how surface X-ray scattering can help address these questions, we develop a general theory for the intensity distributions along crystal truncation rods (CTRs) for miscut surfaces with a combination of two terminations. We consider half-unit-cell-height steps, and variation of the coverages of the terraces above each step. Example calculations are presented for the GaN (0001) surface with various reconstructions. These show which CTR positions are most sensitive to the fractional coverage of the two terminations. We compare the CTR profiles for exactly oriented surfaces to those for vicinal surfaces having a small miscut angle, and investigate the circumstances under which the CTR profile for an exactly oriented surface is equal to the sum of the intensities of the corresponding family of CTRs for a miscut surface.
The zero-temperature dynamical structure factor $S(q,omega)$ of one-dimensional hard rods is computed using state-of-the-art quantum Monte Carlo and analytic continuation techniques, complemented by a Bethe Ansatz analysis. As the density increases, $S(q,omega)$ reveals a crossover from the Tonks-Girardeau gas to a quasi-solid regime, along which the low-energy properties are found in agreement with the nonlinear Luttinger liquid theory. Our quantitative estimate of $S(q,omega)$ extends beyond the low-energy limit and confirms a theoretical prediction regarding the behavior of $S(q,omega)$ at specific wavevectors $mathcal{Q}_n=n 2 pi/a$, where $a$ is the core radius, resulting from the interplay of the particle-hole boundaries of suitably rescaled ideal Fermi gases. We observe significant similarities between hard rods and one-dimensional $^4$He at high density, suggesting that the hard-rods model may provide an accurate description of dense one-dimensional liquids of quantum particles interacting through a strongly repulsive, finite-range potential.
Unique intensity features arising from dynamical diffraction arise in coherent x-ray nanobeam diffraction patterns of crystals having thicknesses larger than the x-ray extinction depth or exhibiting combinations of nanoscale and mesoscale features. We demonstrate that dynamical scattering effects can be accurately predicted using an optical model combined with the Darwin theory of dynamical x-ray diffraction. The model includes the highly divergent coherent x-ray nanobeams produced by Fresnel zone plate focusing optics and accounts for primary extinction, multiple scattering, and absorption. The simulation accurately reproduces the dynamical scattering features of experimental diffraction patterns acquired from a GaAs/AlGaAs epitaxial heterostructure on a GaAs (001) substrate.
Small-angle X-ray scattering from GaN nanowires grown on Si(111) is studied experimentally and modeled by means of Monte Carlo simulations. It is shown that the scattering intensity at large wave vectors does not follow Porods law $I(q)propto q^{-4}$. The intensity depends on the orientation of the side facets with respect to the incident X-ray beam. It is maximum when the scattering vector is directed along a facet normal, as a reminiscence of the surface truncation rod scattering. At large wave vectors $q$, the scattering intensity is found to be decreased by surface roughness. A root mean square roughness of 0.9~nm, which is the height of just 3--4 atomic steps per micron long facet, already gives rise to a strong intensity reduction.
The diffraction technique is widely used in the determination of crystal structures and is one of the bases for the modern science and technology. All related structure determination methods are based on the assumption that perfect single crystal X-ray diffraction (SXRD) can determine a structure uniquely. But as the structure factor phases are lost in SXRD and even more information is lost in powder X-ray diffraction (PXRD), this assumption is still questionable. In this work, we found that structures with certain characteristic can have its sister structure with exactly the same PXRD or even SXRD pattern. A computer program is developed to search the ICSD database, and about 1000 structures were identified to have this characteristic. The original structure and its sister structures can have different space groups, topologies, crystal systems etc. and some may even have multiple sisters. Our studies indicate that special caution is needed since a structure with reasonable atomic positions and perfect match of experimental diffraction intensities could still be wrong.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
