Genetic algorithm for solution of the inverse problem in high-resolution X-ray reflectometry

The method of high-resolution X-ray reflectometry with application of the genetic Differential Evolution algorithm for global minimization of the error function is developed. The optimization of the computational process is performed by combining the genetic algorithm with the Levenberg-Marquardt method. This optimization reduced the computational time by a factor of 3–4. The structural properties of multilayer systems Al_xGa_1?x As/GaAs/Al_xGa_1?x As (x ～ 0.2) grown on GaAs(001) are investigated. The density profiles along the normal to the surface are obtained and the sizes of the transition layers are determined with a resolution of 0.1–0.2 nm.     

Diffraction methods analysis of the approximation of the real glass structure

X-ray and electron diffraction methods are discussed and the results of an analysis of glass structure are reported.Experimental methods were employed to analyse the structures of a series of complex oxide glasses of the type:

$\text{SiO}{}_2\text{(～72\%)+}\text{Na}{}_2\text{O}\text{(～14\%)+}\text{CaO}\text{(～8\%) +}\text{MgO}\text{(～4\%)+R}{}_2\text{O}{}_3\text{(～2\%)}$

.In calculating the structural parameters of the real glass structure the assumed effective molecule was approximated which included from two (SiO₂) to five (SiO₂Na₂OCaOMgO) groups of various atoms. The structural parameters obtained allowed the real internal structure to be established and were employed in the construction of a space model of the glass.The most probable structural models are presented, obtained by successive approximation with individual oxide groups added one after another. The models' structural and physicochemical parameters were chosen to be consistent with those of the nodal model which is near to the real glass structure. The parameters required to construct the nodal model in question were established by analysing radial distribution functions and by the differentiation of the adequate radial distribution functions by subtraction and successively approximating the effective molecule including the oxide groups (SiO₂, Na₂O, CaO and MgO) added one after another.An aperiodic model of a nodal lattice is presented in a scheme, stressing the structural parameters and local orderings in groups describing the internal structure of complex oxide glasses. Also, an approximate nodal space model of great importance for the construction of a structural model of glass is presented and discussed with regard to its utility and accuracy in the determination of its parameters.     

Model approach to solving the inverse problem of X-ray reflectometry and its application to the study of the internal structure of hafnium oxide films

The key features of the inverse problem of X-ray reflectometry (i.e., the reconstruction of the depth profile of the dielectric constant using an experimental angular dependence of reflectivity) are discussed and essential factors leading to the ambiguity of its solution are analyzed. A simple approach to studying the internal structure of HfO₂ films, which is based on the application of a physically reasonable model, is considered. The principles for constructing a film model and the criteria for choosing a minimal number of fitting parameters are discussed. It is shown that the ambiguity of the solution to the inverse problem is retained even for the simplest single-film models. Approaches allowing one to pick out the most realistic solution from several variants are discussed.     

Neutron and X-ray diffraction studies of the structure of non-crystalline materials

Neutron and X-ray diffraction experiments have provided useful information about the topological and chemical short-range order in non-crystalline materials. The availability of new sources and detectors for X-rays and neutrons has greatly improved the statistical accuracy of the scattered intensity and extended its range in momentum (Q) space, yielding high-resolution atomic distribution functions. The methods of isotopic and isomorphous substitution have been used to determine the partial atomic structure factors and their corresponding atomic pair distribution functions in binary metallic systems, and to evaluate the nearest-neighbor interactions in more complicated inorganic glasses. Recent results of structural investigations on Ni-based amorphous alloys and on halide glasses are discussed.     

Effects of structure instability of a V3Si single crystal from X-ray scattering data

Diffuse X-ray scattering from a V₃Si single crystal was studied at room temperature. It was demonstrated that the structure possesses instability regions associated with the formation of a new phase. The characteristic features of the q dependence of diffuse scattering are indicative of the presence of two-types of domains— those randomly distributed over the crystal and those forming a spatially periodic distribution.     

Development of methods of X-ray diffraction analysis for determining the composition and structure of sillenite-family crystals

A methodology for refining the crystal structure of sillenites of nominal composition Bi₂₄ M ₂O₄₀ based on the choice of the correct initial model and thermal atomic parameters is reported. The validity of the approach proposed is demonstrated by examples of crystals with M = Si, Fe, or V, for which the real composition is found with allowance for the composition of each structural site. Individual structural details are confirmed by IR and Raman spectroscopy data.     

Comparison of lead solubility in NaCl crystals from data obtained by different methods

The solvus of the NaCl: Pb²⁺ system was found in the concentration range from 1.5 × 10⁻³ to 1.9 × 10⁻² mol% at temperatures ranging from 375 to 430 °C from the data of flotation measurements of the crystal density. The heat of impurity dissolution equal to 2.0 ± ± 0.6 eV and the change in the vibrational entropy in the formation of the solid solution S_v/K= 20 ± 10 were determined. Reasons for a difference in the estimates of lead solubility in NaCl, obtained from temperature dependences of light scattering and by other methods: measurement of the density, electric conductivity, and the electron-microscopic decoration of the same crystals are discussed.     

Method for estimating the morphological significance of simple forms of crystals from X-ray data

When developing V.I. Mikheev and I.I. Shafranovskiĭ’s method for estimating the morphological significance of faces of different simple forms from X-ray reflection intensities, a way to approximately evaluate the morphological significance of simple forms on crystals from the structure amplitudes of the corresponding atomic planes is proposed. The potential for this approach is demonstrated by the examples of marcasite and zircon.     

A method for automated determination of the crystal structures from X-ray powder diffraction data

An algorithm is proposed for determining the crystal structure of compounds. In the framework of this algorithm, X-ray powder diffraction patterns are compared using a new similarity index. Unlike the indices traditionally employed in X-ray powder diffraction analysis, the new similarity index can be applied even in the case of overlapping peaks and large differences in unit cell parameters. The capabilities of the proposed procedure are demonstrated by solving the crystal structures of a number of organic pigments (PY111, PR181, Me-PR170).     

Difference method for solution of the inverse problem of reflectometry of multilayer films

A schematic of a reflectometric experiment whose results make it possible to reconstruct the structure of multilayer films on substrates is proposed. A mathematical apparatus is developed that allows for determining the numerical values of the main parameters (electron density, thickness, and roughness) for each layer of the model film. Until now, there have been no methods for determining the structure of multilayer films from experimental data, and the problem has been solved by the trial-and-error method. Some model examples of reconstruction of the film structure are reported.     

Local 3D real space atomic structure of the simple icosahedral Ho11Mg15Zn74 quasicrystal from PDF data

We present a new complementary strategy to quasicrystalline structure determination: The local atomic structure of simple icosahedral (si) Ho₁₁Mg₁₅Zn₇₄ [a(6D) = 5.144(3)Å in a sphere of up to r = 17Å was refined using the atomic pair distribution function (PDF) from in‐house X‐ray powder diffraction data (MoKα₁, Q_max = 13.5Å⁻¹; R = 20.4%). The basic building block is a 105‐atom Bergman‐Cluster {Ho₈Mg₁₂Zn₈₅}. Its center is occupied by a Zn atom – in contrast to a void in face centred icosahedral (fci) Ho₉Mg₂₆Zn₆₅. The center is then surrounded by another 12 Zn atoms, forming an icosahedron (1st shell). The 2nd shell is made up of 8 Ho atoms arranged on the vertices of a cube which in turn is completed to a pentagon dodecahedron by 12 Mg atoms, the dodecahedron then being capped by 12 Zn atoms. The 3rd shell is a distorted soccer ball of 60 Zn atoms, reflecting the higher Zn content of the si phase compared to the fci phase. In our model, 7% of all atoms are situated in between the clusters. The model corresponds to a hypothetical 1/1‐approximant of the icosahedral (i) phase. The local coordinations of the single atoms are of a much distorted Frank‐Kasper type and call to mind those present in 0/1‐Mg₂Zn₁₁. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of the data of X-ray microtomography and fluorescence analysis in the study of bone-tissue structure

The possibility of localizing clusters of heavy atoms is substantiated by comparing the data of X-ray microtomography at different wavelengths, scanning electron microscopy, and X-ray fluorescence analysis. The proximal tail vertebrae of Turner??s thick-toed gecko (Chondrodactylus turneri) have been investigated for the first time by both histological and physical methods, including X-ray microtomography at different wavelengths and elemental analysis. This complex methodology of study made it possible to reveal the regions of accumulation of heavy elements in the aforementioned bones of Turner??s thick-toed gecko.     

Study of the defect structure of paratellurite crystal using multiwave diffraction and normal X-ray diffractometry methods

Multiwave X-ray diffraction has been used to study the structure of crystalline samples. A cycle of local measurements of rocking curves (RCs) of the (220) and (371) reflections under conditions of multiwave diffraction (MD) has been carried out in a paratellurite crystal. The data obtained are used to compare the sensitivity to structure defects of two-beam diffraction with that of MD, which makes it possible to study the X-ray wave phase. The comparison has revealed a higher ability of the phase-sensitive method to detect defects.     

Three-dimensional structure of the Arg32His mutant of the human tumor necrosis factor determined at 2.5 Å resolution from X-ray data for a twin crystal

The three-dimensional structure of the Arg32His mutant of the human tumor necrosis factor (TNF-α) was established at 2.5 Å resolution by the molecular replacement method. The crystals of the mutant belong to sp. gr. R3. The specimen has a hemihedral twinning fraction of approximately one half with the twin law corresponding to an additional twofold axis along the a-or b-axis of the crystal lattice. The model analysis of interactions between functionally important loop 29–36 of the mutant and the receptors p55 and p75 was performed.     

Geometrical aspect of solving the problem of real structure growth on the model of alkali metal halides of the NaCl type

The formation of a nanoscale packing polyhedron of layer-by-layer model-structure growth using a specified system of bonds between structural units, which determines the space partition in crystalline or quasicrystalline state of matter, was described in [1]. In a continuation of these studies, the application of the mechanism of sectorial layer-by-layer growth of the structural unit neighborhood graph to the formation of the spectrum of model coordination packing growth polyhedra of NaCl-type alkali metal halides is considered. A computer experiment based on the cell content clusterization and application of the radial algorithm of neighborhood graph growth showed that the existence of small (NaCl)₂ clusters in the form of planar dimers is preferential for the equilibrium growth shape of sodium chloride crystal as a regular cube in the precrystallization state of vapor phase.     

Crystal structure of nacrite from the electron diffraction data

The crystal structure of the nacrite mineral of the kaolin group (space group Cc; R = 2.76%; 634 unique reflections) is refined from the digital oblique-texture electron diffraction patterns obtained with the use of imaging plates. The maxima characterizing the locations and potentials of the hydrogen atoms of the hydroxyl groups are revealed from the difference Fourier-potential syntheses. The O-H interatomic distances and the angles of inclination of the O-H bond with respect to the ab plane are equal to 0.97 Å and ?18.3° for the inner hydroxyl group and 0.92, 0.85, 0.93 Å and 60.8°, 67.8°, 58.4° for the outer hydroxyl groups, respectively. The O_donor-O_acceptor interatomic distances are 2.940, 2.949, and 3.121 Å. It is established that the electrostatic potential distributions of the hydrogen atoms of the inner hydroxyl group and one of the outer hydroxyl groups located in the vicinity of the symmetry pseudoplane m of the layer are characterized by anisotropy, which can indicate a statistical distribution of these hydrogen atoms.     

Crystal structure of celadonite from the electron diffraction data

The crystal structure of the dioctahedral celadonite mica 1M (space group C2/m; R, 2.98%; 184 unique reflections) is refined from the oblique-texture electron diffraction patterns obtained with the use of imaging plates. The maximum characterizing the location and potential of the hydrogen atom of the hydroxyl group oriented into the unoccupied trans octahedron at an angle of 4.4° with respect to the ab plane is revealed from the difference Fourier-potential syntheses. The O-H interatomic distance is equal to 0.98 Å. The superstructure reflections observed in the selected-area electron diffraction patterns for a number of particles arise from the superposition of two cells, namely, the main cell with a broken base-centered symmetry and the base-centered supercell with the triple parameter a. These reflections are caused by the ordered distribution of the trivalent and divalent cations Fe and Mg over the octahedral cis positions.     

Development of methods for ultrasonic scanning of X-ray wavelength

The method for X-ray wavelength tuning using an adaptive element (a quartz monolithic resonator modulated by a standing longitudinal low-frequency ultrasonic wave) has been proposed and implemented. This method is characterized by high tuning accuracy and possibility of scanning X-ray beam parameters with a time resolution of up to 3 μs.