Symmetry Of Diffraction Patterns Research Articles

Particle size and convergent electron diffraction patterns of triangular prismatic gold nanoparticles

Convergent beam diffraction (CBED) patterns of nanoparticles are possible. CBED of triangular prismatic shaped Au nanoparticle with focus on diffraction pattern symmetry and forbidden reflections observed along [111] and [112] zone axes are reported in this work. It is well known that the CBED patterns of nanoparticles of 30 nm or less in size only show bright kinematical discs. The dynamic contrast with Kikuchi and sharp HOLZ lines within the bright discs, as observed in CBED of volumetric materials, is well observed in particles larger of 500 nm in size. In addition, it is shown that the 1/3[422] and 1/2[311] weak forbidden reflections observed in the [111] and [112] electron diffraction patterns of these particles do not modify the symmetry of the CBED patterns, but they disappear as the size of the particle increases. The symmetry of the CBED patterns are always observed in concordance with the space group Fm3m (No. 225) of the Au unit cell. The possible explanations for observing forbidden reflections are the incomplete ABC stacking due to surface termination and the stacking faults in the fcc structure.

Symmetry of diffraction patterns of two-dimensional crystal structures

Conventionally, theoretical considerations in electron microscopy employ the weak phase approximation (WPA), which is only valid for weak scattering atomic elements (C, B, N) but not for transition metal dichalcogenide (TMD) materials. This leads to many exciting phenomena being overlooked. The present theoretical study goes beyond the weak phase approximation and thus the obtained results can be applied for two-dimensional (2D) crystals made of weakly as well of strongly scattering atoms, including the TMD materials. We show that the symmetry of an electron diffraction pattern, characterized by the Friedel’s pairs, is governed by the symmetry of the exit wave distribution. For an infinite periodic crystal, the exit wave is an infinite and periodic 2D distribution which can be assigned an exit wave unit cell. The latter is determined by both the chemical composition of the crystallographic unit cell and the distance between the atomic layers. For 2D crystals of identical atoms, such as graphene, the exit wave unit cell is symmetrical and, thus, a symmetrical diffraction pattern is expected. For TMD materials, the exit wave unit cell is not symmetrical and a non-symmetrical diffraction pattern is expected for both monolayer and bilayer. Conventionally asymmetry in diffraction patterns has been explained by presence of dynamical (multiple) scattering effects. Our study shows that the asymmetry of a diffraction pattern can be explained solely by the asymmetry of the exit wave unit cell. The exit wave unit cell can be asymmetrical even in kinematic (single) scattering model. Therefore, conclusions about dynamical (multiple) scattering effects in 2D materials cannot be made based solely on asymmetry of a diffraction pattern. We also show that for hexagonally arranged atoms the second-order diffraction peaks show perfectly symmetrical intensities independently on the symmetry of the exit wave unit cell distribution.

Optical diffraction and high-energy features in three-dimensional photonic crystals

We provide a band-structure-based interpretation of the diffraction phenomena observed in three-dimensional photonic crystals. Qualitative and quantitative information about these patterns is obtained in a simple manner from the band structure. Our conclusions and experimental results explain phenomena occurring at frequencies above the first stop band that were not previously understood. Optical features observed in transmission spectra from opaline photonic crystals are now clarified by relating them to diffraction phenomena. We also observe an intriguing change in the diffraction pattern symmetry when the photonic-crystal refractive-index contrast is modified.

Molecular packing and crystalline morphologies of biodegradable poly(alkylene dicarboxylate)s derived from 1,6-hexanediol

The crystalline structures of two aliphatic polyesters derived from 1,6-hexanediol and suberic or dodecanodioic acid are studied by means of X-ray and electron diffraction and real space electron microscopy. Chain-folded lamellar crystals have been obtained by isothermal crystallization of dilute n-hexanol or n-heptanol solutions and their crystalline habit have been studied. A regular folding habit is deduced from polyethylene decoration techniques. An orthorhombic unit cell containing four chain segments with a planar zig-zag conformation is determined for the two studied polyesters. A P2 1 ab space group symmetry can be assumed taking into account the detected systematic absences and the symmetry of diffraction patterns. In addition, evidence of a second non-orthorhombic structure is found for the suberic acid derivative. The orthorhombic crystal packing of these polymers is characterized by a setting angle close to 45°, showing a similarity with polyethylene. Refinement of the X-ray fiber diffraction pattern of polyester 6-12 allows to determine the c-chain axis shift between the molecular chains, being observed an alignment of the CH 2–O methylene groups with the CH 2–O oxygen atoms of neighbouring chains. Crystallization from the melt renders spherulites with a negative birefringence and a fibrillar texture, whereas banded morphologies constituted by multilayered single crystals can be obtained by evaporation of xylene solutions. Electron diffraction patterns of ultrathin samples allow the spherulitic radial growth direction to be correlated with the crystalline structure.

The influence of ion bombardment on the composition and atomic structure of the CoNi 3(1 0 0) surface layers

The low-energy electron diffraction method with a number of original techniques has been employed to observe and study a new radiation-stimulated reconstruction transition on the CoNi 3 (1 0 0) single crystal surface. Low-energy bombardment by Ar + ions (600 eV) leads to a change of the diffraction pattern symmetry corresponding to a surface structure change f.c.c.→h.c.p. To elucidate the causes of the effect observed the changes of the surface composition and the concentration profile under the action of ion bombardment were studied. It has been found that first atomic layer of the sample is fully enriched in cobalt, and this, precisely, leads to the formation of the h.c.p. phase on the surface.

A new phase of carbon

An unknown structure with close to six-fold symmetry in diffraction patterns has been found by TEM-studies of C60- and C70-samples after different stages of thermobaric treatment. The new phase may be considered as intermediate between graphite and diamond. The value 0.51 nm of parameter a0 of this phase was found to be closed to twice the value for graphite and to twice the value of parameter d110 in diamond. The atoms situated in the nodes of (0001)-graphite planes with doubled a0-parameter take part in the connection of (0001)-planes by sp-3 bonds. The connection of (0001)-graphite planes results in splitting of these planes between the layers. Four layers form the unit cell of the new phase. The unit cell contains 24 atoms. This crystal lattice can be represented as a triclinic one with parameters: a=b=0.51 nm, c=0.745 nm, α≡β=82°, γ=120°. The density of the new phase lies in the range of carbyne densities.

Evidence of intermediate states between approximant crystal and quasicrystal

Abstract We report transmission electron microscopy investigations on the Al6Li3Cu (auasicrystal)-Al5Li3Cu (crystal) interface. This interfacial area is not sharp but displays intermediate states. A detailed analysis of the diffraction patterns reveals that the transformation involves a planar defect organization. The defect network, periodically organized at Iow defect density, becomes aperiodic when the defect density increases. This complex organization suggests that diffusion rates are very Iow in auasicrystals. New conditions for annealing Al6Li3Cu auasicrystals are then determined that subsequently improve the auasicrystalline order. Fine lines of diffuse scattering in annealed samples still remain as imperfections. We interpret these lines as a precursor state of a new rhombohedral approximant crystal. These observations provide a seauence of intermediate states to discuss in relation to the deviation from icosahedral symmetry in diffraction patterns and diffusive/displac-ive transformations.

Preliminary crystallographic data for the copper enzyme ascorbate oxidase

Ascorbate oxidase (EC 1.10.3.3) is a copper enzyme belonging to the group of so-called ‘blue oxidases’ together with laccases and ceruloplasmin. The enzyme, widely distributed in several plant species, catalyzes the oxidation of L-ascorbate, transferring the reducing equivalents to molecular dioxygen. The biological function of the enzyme is still in question. Ascorbate oxidase activity is highest in those parts of plants which grow faster; on the other hand some authors suggested a possible role of the enzyme in plant respiration [1]. The native enzyme is a non-covalent dimer, whose subunits (respectively 75,000 and 72,000 Mr) contain 8 Cu 2+ ions; these can be classified, according to their coordination environments, as of type-1, type-2 and type-3 [2, 3]. Ascorbate oxidase is known to undergo fully reversible association-dissociation phenomena. Its ultracentrifuge pattern changes as a function of pH and buffer media, while the spectroscopic properties and the activity towards ascorbate remain unchanged. Although the information available at present is not sufficient to fully elucidate the sequence of redox events which take place within the protein, there exist some evidence that the three classes of copper ions fulfil different functions. Type-1 copper is the primary site of electron acceptance; type-2 and type-3 coppers are implicated respectively in ascorbate and O 2 binding [4]. Ascorbate oxidase is thus an ideal model enzyme for the study of biochemistry and biophysics of vegetal copper proteins. In consideration of its physico-chemical properties, the elucidation of ascorbate oxidase three-dimensional structure may also contribute to the comprehension of the association-dissociation phenomena and of their biological significance. The protein employed for the crystallization experiments was purified from green zucchini squash according to the method of Avigliano et al. [5], showed absorption ratios A 280/A 610 = 25 ± 1, A 330/ A 610 = 0.8 ± 0.05 and had a turnover number of 5 × 10 5 mol/min. Several micro-buttons filled with a 15 mg/ml solution of the enzyme were used in parallel dialyses experiments against different buffers and precipitating agents, in the pH range 5–9. Under the following conditions the same characteristic blue crystals of the enzyme could be grown: 1. 1.8 M ammonium sulfate, at pH values 6.7 through 8.4 2. 1.0 M sodium citrate, at pH 7 3. 1.9 M potassium phosphate, at pH 7 The crystals obtained were subsequently used for a preliminary crystallographic. From the analysis of the diffraction pattern symmetry and of the systematic absences it was possible to conclude that ascorbate oxidase crystallizes in the orthorhombic space group P2 12 12 1 with unit cell edges a = 125.4, b = 189.8, c = 112.2 Å. The asymmetric unit can thus accommodate a dimer of the enzyme (Mr 294,000) and the (volume) solvent content of the crystals is 45%. The crystals diffract to 3.0 Å resolution; this crystalline modification is isomorphous with that reported by Ladenstein et al. [ 6] for the same enzyme, but grown under different physico-chemical conditions.

Experimental Alignment of a Spectrometer System Using Laser Diffraction

A simple technique is described to facilitate precise three-dimensional alignment of a monochromator relative to a dimensionally fixed optical feed system. This technique uses diffraction of a He-Ne laser through the entrance slit of the monochromator. Diffraction pattern symmetry serves as a sensitive visual guide. Reduction of a three-dimensional alignment problem into a simpler two-dimensional one is achieved by the utilization of a “rail and rider” approach accompanied by systematic placement and mechanical alignment of components. Considerable time savings using this approach have been realized.

Relations entre la symétrie des diagrammes de diffraction des électrons lents et celle du cristal

The very strong absorption of low energy electrons by matter has some consequences on the symmetry of diffraction patterns. The symmetry of a pattern is that of one or several structural planes according to the depth reached by the electrons. It may differ from the symmetry of the crystal unit cell. When the symmetry of the crystal is lower than that of the structural planes, the symmetry of the pattern corresponds to that of the diffracting medium whereas if the symmetry of the crystal is higher than that of the structural planes, the symmetry of the pattern is lower than that of the diffracting medium.

Observation of the breakdown of Friedel's law in electron diffraction and symmetry determination from zero-layer interactions

Detailed observations are made of the breakdown of Friedel's law in electron diffraction, using the single-crystal intensity distribution from cadmium sulfide in the [21{\bar 3}0] orientation. It has been found by experiment that no breakdown of Friedel's law occurs in the zero-order beam distribution. An analysis of the problem due to Moodie, using multiple-scattering diagrams, has also led to this result. Multiple-scattering diagrams are used here to illustrate the symmetry properties of the zero-beam distribution. Rules are given for the deduction of the other symmetry elements of the projected structure from the diffraction-pattern symmetry, and from the occurrence of dynamic extinction bands in the kinematically forbidden reflections. These are illustrated by further pictures from cadmium sulfide. This analysis is simplified in the present work by neglecting non-zero-layer interactions. Results obtained by n-beam calculation using the multi-slice method show the possibility of quantitative interpretation, and of absolute orientation determination. The limitations of the systematic dynamic approximation and also of a systematic approximation using corrected scattering potentials are examined for this substance.