X-ray diffraction from ideal mosaic crystals in external fields of certain types, part III: Changes in space symmetry and symmetry of diffraction pattern

The change in the space symmetry and the symmetry of the corresponding diffraction pattern occurring under the effect of uniform electric and magnetic fields applied to a crystal have been analyzed. The tables of point symmetry groups for various directions of applied magnetic fields are constructed. It is shown that in the absence of an external field, the diffraction patterns are described by nine possible point groups; in an electric field, they are described by eleven point groups; and in a magnetic field, by only five point groups. The theoretically calculated diffraction parameters are compared with the corresponding experimental values.     

X-ray diffraction by polydomain crystals modulated by transverse waves of atomic displacements. 1. Single-wave modulation in crystals

The intensity distributions of diffuse X-ray scattering caused by domains characterized by the transverse wave of atomic displacements polarized in the (010) plane and propagating along the [001] direction are calculated by numerical methods analyzed in the kinematical approximation. The regular changes in the intensity and half-width of the satellite peaks are revealed as functions of the wave amplitude and the average domain size. The characteristic features of diffraction are considered in the case where the defect-density wave in the crystal affects the parameters of the displacement wave.     

Low temperature X-ray diffraction study of CdI2 crystals

Solid state structural transformations in polytypic crystals of cadmium iodide have been investigated at low temperatures using X-ray diffraction techniques. The crystals were cooled to liquid nitrogen and liquid helium temperatures employing three different methods. The results obtained are discussed on the basis of bond dissociation energies of interlayer and intralayer bonds and the possible mode of layer displacements in MX₂-type polytypic crystals.     

Local lattice strains in the system of cubic Zn0.999Fe0.001S x Se1 − x (0 ≤ x ≤ 1) crystals

The structure of cubic Zn_0.999Fe_0.001S _x Se_{1 ? x} (0 ≤ x ≤ 1) crystals obtained by vapor-phase chemical transport has been investigated by thermal-neutron diffraction. The diffraction patterns of these crystals are found to exhibit previously unknown diffuse-scattering effects related to local static atomic displacements in the metastable fcc lattice. It is substantiated that the tendency to form polytypes, which is characteristic to a greater extent of zinc sulfide, can be a key factor of instability in the lattice of compounds belonging to the series of anion-substituted solid solutions under study.     

Determination of the parameters of a rough surface from the dynamical X-ray diffraction data

A new method is proposed for determining the roughness parameters from X-ray diffraction data. The method is based on a controllable displacement of reflecting planes under an external tangential pressure. It is shown that the displacement of atomic planes near the rough surface upon sample compression increases in proportion to the applied stress and strongly depends on the roughness parameters. Rough surfaces with determinate periodic and random reliefs are considered together with the corresponding features of X-ray rocking curves.     

Atomic structure and enormous anisotropy of thermal expansion in NiSi single crystals. I. Refinement of structure models

The atomic structure of NiSi single crystals has been studied by the methods of X-ray diffraction analysis at 295 and 418 K. The refinement of the structure models with due regard for anharmonicity of atomic vibrations revealed the pronounced anisotropy of thermal vibrations and the considerable contribution of the fourth-order anharmonicity. The maps of the probability density function of atomic displacements and single-particle potentials of both atoms were constructed.     

Structural conditionality of the piezoelectric properties of langasite family crystals

The atomic displacements upon isomorphic substitutions in crystals of the langasite family have been analyzed. The thermal parameters are determined and the probability density function of atoms is analyzed. Local potential energy minima are found which can be occupied by atoms under external effects. The contributions of cations in all four independent crystallographic positions and anions in all three such positions to the piezoelectric properties are established. One specific structural feature is the constant (at isomorphic substitutions) or possible (under external effects) but always opposite displacements of two cations along symmetry axis 2. Large cations in eight-vertex polyhedra make the main contribution to the piezoelectric properties. The cations in the tetrahedra on symmetry axis 2 weaken these properties. The cations in the octahedra in the origin of coordinates and in the tetrahedra on symmetry axes 3 only slightly affect the piezoelectricity.     

X-ray diffraction from ideal mosaic crystals in external fields of certain types, part II: Changes in the temperature factor and diffraction pattern

The changes in the X-ray temperature factor of a single crystal in external fields of running electromagnetic and acoustic waves has been analyzed. The evaluation of these changes shows the importance of a thorough choice of crystals and experimental conditions for recording the variations in the structure factors (intensities). The relationships derived allow one to predict the type of a diffraction pattern formed in a field of a standing wave applied to the crystal. The position, shape, and the height of the main and auxiliary peaks are analyzed as functions of the applied-field parameters.     

Measurement of piezoelectric constants of lanthanum-gallium tantalate crystal by X-ray diffraction methods

A method for measuring piezoelectric constants of crystals of intermediate systems by X-ray quasi-multiple-wave diffraction is proposed and implemented. This technique makes it possible to determine the piezoelectric coefficient by measuring variations in the lattice parameter under an external electric field. This method has been approved, its potential is evaluated, and a comparison with high-resolution X-ray diffraction data is performed.     

Precision electron diffraction structure analysis and its use in physics and chemistry of solids

The present level of the precision electron diffraction provides the quantitative analysis of the electrostatic potential and electron density in crystals and allows us to approach the direct study of properties of solids by electron diffraction. This is demonstrated by examples of ionic compounds with an NaCl structure and a covalent Ge crystal. Using the analytical structure models of crystals, one can quantitatively characterize chemical bonding and study topological characteristics of the electrostatic potential by electron diffraction data. It is established that the internal crystal field is well structurized, whereas the topological analysis revealed some important characteristics of its structure. These data considerably enrich our knowledge on atomic interactions in crystals.     

X-ray diffraction and X-ray standing-wave study of the lead stearate film structure

A new approach to the study of the structural quality of crystals is proposed. It is based on the use of X-ray standing-wave method without measuring secondary processes and considers the multiwave interaction of diffraction reflections corresponding to different harmonics of the same crystallographic reflection. A theory of multiwave X-ray diffraction is developed to calculate the rocking curves in the X-ray diffraction scheme under consideration for a long-period quasi-one-dimensional crystal. This phase-sensitive method is used to study the structure of a multilayer lead stearate film on a silicon substrate. Some specific structural features are revealed for the surface layer of the thin film, which are most likely due to the tilt of the upper layer molecules with respect to the external normal to the film surface.     

X-ray diffraction analysis of modulated crystals: Review

The state of the art of X-ray diffraction analysis of modulated crystals is reviewed. The review begins with a brief historical overview followed by the consideration of the main concepts and notations used in this field. Then, methods of structural analysis of modulated crystals are considered with emphasis on recent achievements. The most interesting objects are listed, and the directions of investigation are outlined. Examples of analysis of both individual structures and families of modulated and incommensurate composite structures are given in terms of superspace symmetry.     

X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

The two-wave dynamical diffraction in the Laue geometry has been theoretically considered for a plane X-ray wave in a crystal with a third-order nonlinear response to the external field. An analytical solution to the problem stated is found for certain diffraction conditions. A nonlinear pendulum effect is analyzed. The nonlinear extinction length is found to depend on the incident-wave intensity. A pendulum effect of a new type is revealed: the intensities of the transmitted and diffracted waves periodically depend on the incidentwave intensity at a fixed crystal thickness. The rocking curves and Borrmann nonlinear effect are numerically calculated.     

New schemes for recording electron diffraction patterns of hexagonal and monoclinic crystals

Some new schemes for recording electron diffraction patterns of hexagonal crystals rotating around the axes lying in the (hk0) plane of the reciprocal lattice and monoclinic crystals rotating around the a and b axes of the direct lattice and the a* axis of the reciprocal lattice have been developed. Formulas for interpreting electron diffraction patterns are reported. The electron diffraction patterns obtained based on these schemes were used to solve the 2H and 3R polytypes of CdInGaS₄ crystals and the 3R polytype of Zn_1.5In₃Se₆ crystal with the parameters a = 4.046 and c = 59.292 Å, sp. gr. R3m.     

Accurate X-ray diffraction studies of KTiOPO<Subscript>4</Subscript> single crystals doped with niobium

Single crystals of potassium titanyl phosphate doped with 4% of niobium (КТР:4%Nb) and 6% of niobium (KTP:6%Nb) are studied by accurate X-ray diffraction at room temperature. The niobium atoms are localized near the Ti1 and Ti2 atomic positions, and their positions are for the first time refined independent of the titanium atomic positions. Maps of difference electron density in the vicinity of K1 and K2 atomic positions are analyzed. It is found that in the structure of crystal КТР:4%Nb, additional positions of K atoms are located farther from the main positions and from each other than in КТР and KTP:6%Nb crystals. The nonuniform distribution of electron density found in the channels of the КТР:4%Nb structure is responsible for ~20% increase in the signal of second harmonic generation.     

Size effect in X-ray and electron diffraction patterns from hydroxyapatite particles

High-resolution transmission electron microscopy (HRTEM), electron microdiffraction, and X-ray diffraction were used to study hydroxyapatite specimens with particle sizes from a few nanometers to several hundreds of nanometers. Diffuse scattering (without clear reflections in transmission diffraction patterns) or strongly broadened peaks in X-ray diffraction patterns are characteristic for agglomerated hydroxyapatite nanocrystals. However, HRTEM and microdiffraction showed that this cannot be considered as an indication of the amorphous state of the matter but rather as the demonstration of size effect and the morphological and structural features of hydroxyapatite nanocrystals.     

Scaling in the Optical Characteristics of Aperiodic Structures with Self-Similarity Symmetry

The properties of diffraction gratings and multilayered systems constructed using 1D models of quasicrystals are considered based on numerical simulation. It is shown that there is a direct relationship between the self-similarity symmetry of quasicrystals and scaling in the characteristics of the above-mentioned optical devices. The degree of structural correspondence between the graphical representations of the geometric properties of crystals, light diffraction patterns of gratings, and the transmission spectra of multilayered systems is estimated. It is shown that certain types of self-similarity symmetry make the characteristics of aperiodic diffraction gratings highly stable to a change in the size ratio of forming elements.     

Effect of strain in crystal on the forbidden reflections in the resonant diffraction of synchrotron radiation

The effect of strain (either static or caused by long-wavelength acoustic oscillations) on the energy spectrum and the azimuthal dependence of the intensity of “forbidden” reflections in crystals at the energy of incident radiation close to the absorption edge is considered. It is shown that a strain causing a weak change in the unit-cell symmetry may additionally contribute to the tensor atomic factor. Examples of changes in the azimuthal dependence of forbidden-reflection intensity in zinc oxide ZnO and potassium dihydrogen phosphate KH₂PO₄ are considered.     

掺杂对GaN晶体力学性能影响的研究

对GaN单晶力学性能的研究有助于解决其在生长、加工和器件应用中的开裂问题。本文围绕掺杂对GaN单晶力学性能的影响,通过纳米压痕法测试了不同掺杂类型(非掺、Si掺和Fe掺)GaN单晶的弹性模量和硬度,测试结果表明掺杂对GaN单晶的硬度有重要影响。Si掺、Fe掺GaN较非掺样品硬度有所提升,用重掺杂的氨热GaN单晶作为对照,也证明了这一结论。通过高分辨X射线衍射分析和原子力显微镜表征实验发现,晶体结晶质量、接触面积等因素对GaN单晶硬度的影响较小。对GaN表面纳米压痕滑移带长度和晶体晶格常数进行测试,结果表明,掺杂影响GaN单晶硬度的主要原因是缺陷对GaN位错增殖、滑移的阻碍作用和掺杂引起的GaN晶格常数的变化。