Misleading fringes in TEM images and diffraction patterns of Si nanocrystallites

High‐resolution transmission electron microscopy (HRTEM) images and electron diffraction patterns of twinned Si nanocrystallites were recorded along various directions and analyzed in detail. We point out that special attention must be paid when interpreting HRTEM images and diffraction patterns of twinned Si nanocrystallites, because elongation of reciprocal lattice points could fabricate misleading fringes and patterns. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of calcium-containing orthophosphates of NaZr2(PO4)3 structural type by high-temperature X-ray diffraction

Orthophosphates Ca_0.5Ti₂(PO₄)₃, Ca_0.5Zr₂(PO₄)₃, Ca_0.75Zr₂(SiO₄)_0.5(PO₄)_2.5, and CaMg_0.5Zr_1.5(PO₄)₃ (structural type NaZr₂(PO₄)₃), having different occupancies of interframework positions by calcium, have been prepared by the sol-gel method with the subsequent thermal treatment of dried gels and investigated by IR spectroscopy and X-ray diffraction. The analytical indexing of X-ray diffraction patterns is performed within the sp. gr. $R\bar 3$ . High-temperature X-ray diffraction was used to investigate the behavior of the orthophosphates upon heating: thermal expansion in the temperature range of 20–610°C (up to 500°C for Ca_0.5Zr₂(PO₄)₃). The coefficients of thermal expansion are calculated from the shift of diffraction peaks. The unit-cell parameters of crystals at different temperatures are determined. The dependences of thermal expansion and its anisotropy on the occupancy of cation M positions by calcium are revealed.     

Study of the structural quality of heteroepitaxial silicon-on-sapphire structures by high-resolution X-ray diffraction,X-ray reflectivity,and electron microscopy

Heteroepitaxial silicon-on-sapphire (SOS) structures have been studied by high-resolution X-ray diffraction, X-ray reflectivity, electron microscopy, and electron diffraction. These methods yielded a large amount of complementary data on the defect structure of both the sapphire substrate and the silicon film, including integral and local (at the atomic-resolution level) information about the substrate, film, and sapphire-silicon interface.     

Optical absorption spectra and electron diffraction patterns of rare-earth oxycarbonates

The 4.2 K optical absorption spectra of Ia-(NdO)₂CO₃ and II-(NdO)₂CO₃ are reported. Type Ia exhibits, apparently, a single site for neodymium, and type II, at least two sites. Electron-diffraction patterns obtained from flakes suggest a large orthorhombic unit cell for type Ia and confirm the hexagonal symmetry of the unit cell of type II.     

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.     

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.     

Electron diffraction study of the structural features of kaolinites

The structural variations of kaolinites have been investigated based on oblique-texture electron diffraction patterns. The features of manifestation of the 2D lattice of kaolinite layers in the geometry of the 20l and 13l reflections have been revealed. The manifestation of violations in the regular alternation of layers in kaolinites in the diffraction patterns has been analyzed using a numerical simulation of the diffraction profiles along the first (02l, 11l) and second (20l, 13l) ellipses of oblique-texture electron diffraction patterns. The simulation was performed for finite sequences of ten layers using the statistical Markov model in the quasihomogeneous approximation. It is shown that oblique-texture electron diffraction patterns can be used to reveal the coexistence of two phases with different structural perfections and particle morphologies in kaolinite samples.     

Formation conditions and temperature dependence of forbidden reflections during resonant X-ray diffraction in zinc oxide single crystals

Different mechanisms of formation of purely resonant reflections hhl (h = 2n + 1) during resonant diffraction of X-ray synchrotron radiation in zinc oxide, whose intensity very strongly changes with an increase in temperature, are considered. Such reflections, forbidden in the dipole-dipole scattering, can be excited owing to the dipole-quadrupole scattering and the anisotropy of X-ray susceptibility induced by thermal motion of atoms and point defects. Different contributions are theoretically considered and it is shown that they can be separated owing to their different temperature dependences.     

The characterization of modulated structures via their diffraction patterns

The existence of a modulated structure is signified in reciprocal space by the existence of weak extra features in addition to the strong Bragg reflections of the unmodulated parent structures. These weak extra features may be sharp incommensurate satellite reflections and/or a diffuse intensity distribution. The extraction of information as regards the character of such modulated structures from a study of their diffraction patterns is reviewed. In Section 2, the structural parameters defining the deviation of modulated structures from their corresponding parent phases is discussed. In Section 3, the observation and interpretation of satellite extinction conditions is discussed. In Section 4 and 5, the qualitative features often present in the diffraction patterns of modulated structures are related to structure factor expressions.     

A contribution to the indexing of transmission electron diffraction patterns

A method for the indexing of TED spot patterns is presented. The reduced cell of the TED pattern defined by the two shortest vectors, which enclose an acute angle, serves as reference cell for the indexing. The d-values of both the cell defining vectors and of their sum and difference vectors are determined being the four largest d-values, which can be determined from the pattern. These four d-values are compared with suitable d-value sets of the possible crystalline phases and probable phase identifications are made. Generally, there exist several indexing variants for the individual d-values of the separate phase identification possibilities. It is possible to find the correct indexing by the determination of the indices of the sum and difference vectors, occasionally, for one pair of the indexing variant from the vectors defining the reference cell and by comparison of these indices with the indexing variants for the d-values of the sum and difference vectors of the corresponding phase identification variant. The measuring and calculation of the intervectorial angles formerly necessarily hasn't to be made in this method. However, the determination of the sum and difference vectors involves it. The reliability of the indexing can be increased in a strong manner if two or three different reciprocal lattice planes of the specimen under investigation are recorded in the corresponding TED patterns and if, in the following, these patterns can be indexed by the mentioned method without any doubt.     

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.     

The structural type and related concepts of crystal chemistry

A detailed historical review is presented and the difficulties arising when defining such a fundamental concept as structural type in crystal chemistry are analyzed. Particular attention is paid to the genetic relationship between different structural types and to the criteria of choosing between them. Many other terms and concepts of modern crystal chemistry defined for completeness.     

Laue diffraction of X-rays in GaAs at the zero value of the real part of the structure factor for quasiforbidden reflections

Specific features of the Laue diffraction of X-rays are considered for quasiforbidden reflections within the wavelength range between the K-absorption edges of Ga and As in a GaAs crystal. It is established that scattering for the 200 reflection is of the dynamical nature in the wavelength range where the real part of the structure factor F _r200 is zero and diffraction is determined by the imaginary part of the atomic form factor f″ (ω) alone. It is shown that the position of the minimum of the function R _i = f(λ) is sensitive to the crystal non-stoichiometry predicted by the numerical calculations within the theory taking into account both the real and the imaginary parts of the structure factor.     

Study of structural order in porphyrin-fullerene dyad ZnDHD6ee monolayers by electron diffraction and atomic force microscopy

The structure of porphyrin-fullerene dyad ZnDHD6ee monolayers formed on the surface of aqueous subphase in a Langmuir trough and transferred onto solid substrates has been studied. The data obtained are interpreted using simulation of the structure of isolated molecules and their packing in monolayer and modeling of diffraction patterns from molecular aggregates having different sizes and degrees of order. Experiments on the formation of condensed ZnDHD6ee monolayers are described. The structure of these monolayers on a water surface is analyzed using π-A isotherms. The structure of the monolayers transferred onto solid substrates is investigated by electron diffraction and atomic force microscopy. The unit-cell parameters of two-dimensional domains, which are characteristic of molecular packing in monolayers and deposited films, are determined. Domains are found to be organized into a texture (the molecular axes are oriented by the [001] direction perpendicular to the substrate). The monolayers contain a limited number of small 3D domains.     

Crystalline quality of lysozyme crystals grown in agarose and silica gels studied by X-ray diffraction techniques

The crystalline quality of hen egg white lysozyme (HEWL) crystals grown in agarose gels and in silica gels has been characterized by measuring resolution and mosaic spread. These crystals have been compared to solution grown ones. A quasi-plane-wave X-ray topography study has also been done on some crystals. The study concerns triclinic, monoclinic, orthorhombic and tetragonal forms of HEWL. One observes that the resolution is not really changed by gelling the growth medium, even for rather high gel contents (agarose 0.5% wt/wt). On the contrary, mosaicity, characterized through reflection profile recordings allows to differentiate crystals grown by different techniques: agarose gel grown crystals are, on average, better than solution grown ones but the best crystals are obtained in silica gel. X-ray topography confirms this result.     

The structural characteristics of amorphous D2O ice by neutron diffraction

Neutron diffraction measurements have been made at several wavelengths for vapor-deposited D₂O ice at 10 K. The observed structure factor exhibits more oscillatory features than corresponding measurements on liquid D₂O water, indicating an ammorphous phase which has strong intermolecular spatial correlations. A detailed examination of the data shows that this is strongly influenced by hydrogen-bonding effects and that the local environment for each molecule is very similar to that in crystalline ice. The predictions of Boutron and Alben, based on a continuous random network model, are found to be in excellent agreement with the data.     

Three-layer monoclinic 3M 2 polytype of muscovite revealed from oblique-texture electron diffraction patterns

The inhomogeneous (complex) polytype 3M ₂ of finely dispersed muscovite with the structure formed by layers with different parity of azimuthal orientations (561) or relative rotations $[11\bar 2]$ was identified for the first time using the oblique-texture electron diffraction patterns. The specimen had no rigorous order in layer alternation, which is reflected in the distortion of the reflection positions and intensities. It is shown that the most probable defects reduce to the replacement of the layer orientations characteristic of the 3M ₂ polytype by layer orientation characteristic of the 2M ₂ polytype. This fact indicates that, under certain conditions, the prismatic coordination of interlayer cations in micas is preferable.     

Complex (nonstandard) six-layer polytypes of lizardite revealed from oblique-texture electron diffraction patterns

Association of simple (1T and 3R) and two complex (nonstandard) orthogonal polytypes of the serpentine mineral lizardite from the Catoca kimberlite pipe (West Africa) association is revealed from oblique-texture electron diffraction patterns. A six-layer polytype with an ordered superposition of equally oriented layers (notation 3₂3₂3₄3₄3₆3₆ or ++??00) belonging to the structural group A and a three-layer (336 or I,I,II) or a six-layer (336366 or I,I,II,I,II,II) polytype with alternating oppositely oriented layers and semi-disordered structure are identified using polytype analysis.