Small-angle Peak Research Articles

Glories, hidden rainbows and nearside-farside interference effects in the angular scattering of the state-to-state H + HD → H2 + D reaction.

Yuan et al. [Nat. Chem., 2018, 10, 653] have reported state-of-the-art measurements of differential cross sections (DCSs) for the H + HD → H2 + D reaction, measuring for the first time fast oscillations in the small-angle forward region of the DCSs. We theoretically analyse the angular scattering dynamics in order to quantitatively understand the physical content of structure in the DCSs. We study the H + HD(vi = 0, ji = 0, mi = 0) → H2(vf = 0, jf = 0,1,2,3, mf = 0) + D reaction for the whole range of scattering angles from θR = 0° to θR = 180°, where v, j, m are the vibrational, rotational and helicity quantum numbers respectively for the initial and final states. The restriction to mf = 0 arises because states with mf ≠ 0 have DCSs that are identically zero in the forward (θR = 0°) and backward (θR = 180°) directions. We use accurate quantum scattering matrix elements computed by Yuan et al. at a translational energy of 1.35 eV for the BKMP2 potential energy surface. The following theoretical techniques are employed to analyse the DCSs: (a) full and nearside-farside (NF) partial wave series (PWS) and local angular momentum theory, including resummations of the full PWS up to third order. We also use window representations of the scattering matrix, which give rise to truncated PWS, (b) six asymptotic (semiclassical) small-angle glory theories and four N rainbow theories, (c) we introduce "CoroGlo" tests, which let us distinguish between glory and corona scattering at small angles for Legendre PWS, (d) the semiclassical optical model (SOM) of Herschbach is employed to understand structure in the DCSs at intermediate and large angles. Our conclusions are: (a) the small-angle peaks in the DCSs arise mainly from glory scattering. For the 000 → 020 transition, there is also a contribution from a broad, or hidden, N rainbow, (b) at larger angles, the fast oscillations in the DCSs arise from NF interference, (c) the N scattering in the fast oscillation region contains a hidden rainbow for the 000, 020, 030 cases. For the 000 → 020 transition, the rainbow extends up to θR ≈ 60°; for the 000 and 030 cases, the angular ranges containing a N rainbow are smaller, (d) at intermediate and backward angles, the slowly varying DCSs, which merge into slow oscillations, are explained by the SOM. Physically it shows this structure in a DCS arises from direct scattering and is a distorted mirror image of the corresponding probability versus total angular momentum quantum number plot.

Formation of the Structure of Aqueous Solutions of Manganese, Nickel, Copper, and Zinc Chlorides, According to X-ray Diffraction Data

The structure formation in the aqueous solutions of manganese, nickel, copper, and zinc chlorides is studied via X-ray diffraction in a broad range of concentrations. Small-angle peaks are interpreted. The change in their intensity and position is analyzed, depending on the concentration and nature of cations. The X-ray scattering intensity curves for the studied solutions are compared to the corresponding data for the solutions of lanthanide chlorides investigated earlier.

Condensation of free volume in structures of nematic and hexatic liquid crystals

ABSTRACTEight novel liquid crystalline materials were prepared containing highly branched terminal chains, either 2,4,4-trimethylpentyl or 3,5,5-trimethylhexyl. All materials exhibit nematic mesophases, with additional smectic (Sm) C, hexatic B and SmI phases for certain homologues. Analysis by small- and wide-angle X-ray scattering reveals continual build-up of the correlation length within the nematic phases, where we also observe splitting of the small angle peak into four lobes, indicating pretransitional Sm fluctuations. Connoscopy confirms the nematic phase to be uniaxial and optically positive. We observe that in the solid state, the molecules exist as staggered antiparallel pairs as a consequence of the sterically demanding bulky terminal group, and this would also appear to manifest in the hexatic B phase, where the layer spacing was found to be greater than the molecular length. If true, this is an example of pair formation driven by sterics rather than dipole–dipole interactions and suggests that reentrant systems driven purely by steric frustration may be found.

Structural changes in water clusters during methane adsorption

The structure of water clusters that have adsorbed from one to six methane molecules is studied by molecular dynamics simulation. Characteristic structural units of Voronoi and hybrid polyhedra are employed to reveal the structural changes resulting from the attachment of CH4 molecules to the clusters. The most significant changes in topological properties are associated with variations in the number of faces of simplified polyhedra. A change is unambiguously detected in the small-angle peak intensity in the angular distribution of nearest geometrical neighbors determined with the use of the Voronoi polyhedra. The results of two different calculations of the number of hydrogen bonds in the clusters are compared, and the “nonsphericity” coefficients are calculated for the polyhedra.

Effect of concentration on the structure of aqueous solutions of gadolinium chloride and gadolinium nitrate as probed by X-ray diffraction

Aqueous solutions of gadolinium chloride and gadolinium nitrate are studied by X-ray diffraction over wide ranges of concentrations under standard temperature and pressure. Small-angle peaks on measured scattering intensity curves are interpreted. Small-angle peaks are found not only on the intensity curves for concentrated solutions, but also on those for dilute systems, and this proves that these systems retain a long-range order. Diverse types of ion-ion interactions are shown to be the major contributors to the overall scattering pattern that are responsible for the appearance of pre-peaks.

Concentration dependence of the structure of aqueous solutions of samarium trichloride according to X-ray diffraction

Aqueous solutions of samarium chloride in a wide range of concentration under ambient conditions are studied by X-ray diffraction analysis. The small-angle peaks in experimental scattering intensity curves are interpreted. It is shown that highly concentrated solutions are characterized by a unique structure that differs heavily from the structure of dilute systems. It is found that small-angle peaks also appear in the intensity curves of dilute solutions, indicating that the so-called long-range order is preserved in these solutions. It is revealed that the contributions to the total scattering pattern that govern the appearance of prepeaks are interionic interactions of different types (e.g., cation-cation, anion-cation, and anion-anion interactions) in concentrated systems and the distances between the cations in dilute solutions.

Microstructure, texture and mechanical properties of aluminum processed by high-pressure tube twisting

The new severe plastic deformation technique known as high-pressure tube twisting (HPTT) is a continuous process to obtain grain refinement in bulk metallic materials of tubular geometry. HPTT was applied to commercially pure aluminum up to a shear strain of 24. The mechanical properties were enhanced markedly and were characterized by compression and ring-hoop tensile tests. It was shown that the axial force during HPTT does not contribute to the plastic flow of the material; it is only controlled by the shear component of the applied stress. The microstructure and the crystallographic texture were examined in detail by electron backscatter diffraction, transmission electron microscopy, and X-ray diffraction, and these showed the existence of a gradient within the cross-section of the tube. The next-neighbor grain misorientation distribution showed a bimodal nature, of which the small-angle peak was attributed to the “internal” new grains originating from the interior of the initial grains and the second one from the new grains situated at the grain boundaries of the initial grains. The measured textures were typical shear textures with specific tilts in the sense of the shear direction at large strains, which can be attributed to the effect of strain rate sensitivity of slip. The main component of the textures was the C component, which continuously strengthened with the shear. The results obtained suggest that HPTT is an efficient processing way to transform the microstructure of Al tubes into ultra-fine-grained structures in one single operation.

Multi-Length Scale Morphology of Poly(ethylene oxide)-Based Sulfonate Ionomers with Alkali Cations at Room Temperature

A series of Li-, Na-, and Cs-neutralized polyester ionomers with well-defined poly(ethylene oxide) (PEO) spacer lengths between sulfonated phthalates have been investigated by X-ray scattering at room temperature. As the spacer lengths are increased the PEO segments crystallize, as evidenced by multiple crystal reflections that are identical to those of pure poly(ethylene glycol) oligomers. This crystallization also produces multiple small-angle peaks, which correspond to the well-defined thickness of PEO crystallites. The ionomer peak (q = 1−5 nm−1) is absent in the Na- and Cs-neutralized ionomers, while the Li-neutralized ionomers show peaks at q = 2−3 nm−1, reminiscent of conventional ionic aggregates in ionomers. Detailed analysis of the normalized X-ray scattering intensity from these ionomers reveals a variety of ionic states that are highly dependent on the cation size. The states of ionic groups change from a majority of isolated ion pairs to aggregated structures as the cation size decreases from...

Influence of Electrostatic Interactions on Chain Dynamics and Morphological Development in Perfluorosulfonate Ionomer Membranes

ABSTRACTSeveral high temperature methods of processing Nafion® have been developed using various alkylammonium ion forms of the ionomer, and the choice of counterion has been shown to have a significant effect on the thermal and mechanical properties of this material. In particular, it has been shown that neutralization gives rises to two high-temperature mechanical relaxations as observed in dynamic mechanical analysis (DMA). While several studies in the literature have attempted to explain the molecular origins of these mechanical relaxations, the assignments were based primarily on limited DMA results and have at times been contradictory. The study presented here is a fundamental investigation into the molecular origins of the thermally induced morphological relaxations and dynamics of alkylammonium forms of Nafion® membranes as studied by variable temperature small-angle x-ray scattering (SAXS) and solid-state 19F NMR spectroscopy. The intensity of the small-angle ionomer peak at ca. q = 2 nm–1 was monitored as a function of temperature for each alkylammonium neutralized sample in unoriented and oriented states. In the case of the oriented samples, the degree of anisotropic scattering from the oriented ionomer morphology was quantified using the Hermann's orientation function and monitored as a function of temperature. Changes in intensity of the ionomer peak and the Hermann's parameter as a function of temperature were shown to correlate well with relaxations observed in DMA. Several variable temperature solid-state 19F NMR techniques (including spin diffusion, side-band analysis and T1ρ experiments) were used to investigate the dynamics of the Nafion® chains. Side band analysis indicated that the side-chain is more mobile than the main chain and that the mobility is greatly affected by the size of the counterion. Changes in side-band intensity as a function of temperature were shown to correlate well with DMA data. Results from T1ρ experiments show strong counterion dependence and suggest coupled main- and side-chain motions. A two-component relaxation process was also observed for the main-chain fluorines. The results of the NMR investigations, along with the SAXS data, have led to the development of a more detailed description of the dynamics of Nafion® and the molecular origins of the mechanical relaxations. With this information, the continuing goal to determine how the strength of the electrostatic interactions in perfluorosulfonate ionomers affects the chain dynamics and developing morphology may be realized for the purpose of controlling the morphology to create more efficient ionomeric membrane materials.

Melting Behavior of Poly(Tetramethylene Succinate) as Studied by Time-Resolved Small Angle X-Ray Scattering

To elucidate the morphological origin of the multiple melting endothermic peaks found in DSC scans of poly(tetramethylene succinate), a time-resolved small angle X-ray scattering study utilizing a synchrotron radiation source was conducted. The results suggested that low-temperature endothermic peak can be attributed to the melting of secondary lamellae inserted between the primary lamella stacks, while the middle and high-temperature endothermic peaks were to the melting of primary lamellae. The middle one, however, was associated only with the original ones but the high endothermic peak was with both the original ones and lamellae reorganized through the recrystallization process. A new small angle peak was observed in addition to the original peak during the late stage of melting process. The origin of the new peak was interpreted as a transient phenomenon resulted from the partial melting of primary lamellae prior to the complete melting.

Interaction of Short-Chain Alkanes with the Surface and Interfaces of Multilayer Films Built from Amphiphilic Molecules: An in-Situ X-ray and Neutron Scattering Probe

Partially deuterated Cd−arachidate Langmuir−Blodgett multilayers were subjected to a gas atmosphere of n-pentane and n-hexane at room temperature. The gas−film interaction was studied by in-situ X-ray and neutron specular scattering through a gas-flow box. Both methods show an increase of the small-angle Bragg peak intensities during the gas treatment while the intensities of Kiessig oscillations decrease at the same time. The change of intensities is partially reversible after purging with air. Neutron scattering reveals that the increase of structural Bragg peaks is also accompanied by a decrease of superstructure peaks originated by the scattering length density difference between the sequentially stacked deuterated and nondeuterated chains. This indicates a gas-assisted intermixing of amphiphilic molecules in the vertical direction. The observed effect is much larger than in the case that the short-chain molecules occupy defect sites of the virgin Langmuir−Blodgett film. It can be explained by assumin...

A 45 Å equatorial long period in dry dragline silk of Nephila clavipes

A small-angle peak has been found by X-ray scattering measurements on the dry dragline silk of Nephila clavipes. The weak peak, located on the equatorial axis, yields a long period of approximately 45Å. Probably it corresponds to the lateral spacing of the crystals and is determined kinetically during the formation of the nanofibers.

Structure formation during the crystallization induction period of a short chain-molecule system: A molecular dynamics study

A molecular dynamics simulation has been performed for a short chain-molecule system to study structure formation during the crystallization induction period. A model simulating n-alkane having 20 methylene units was used for the short-chain molecule. A model system containing either 250 or 2000 chains was quenched from a high temperature, and the structure formation was examined at constant temperature and pressure. The model system containing 250 chains eventually forms an ordered phase after the induction period, during which macroscopic quantities, such as volume, remain almost constant. In spite of these small changes in the macroscopic quantities, development of local parallel order is significant during the induction period. We also found that the development of local parallel order causes density fluctuations which appear as a weak small-angle peak in the structure factor. A characteristic length scale corresponding to the density fluctuations becomes larger as time elapses in the induction period. These features are qualitatively in accord with recent experimental findings on a different polymer system [M. Imai et al., Phys. Rev. B 52, 12 696 (1995)].

Static and dynamic scattering by concentrated systems: theory

Significant progress has been made concerning the understanding of several aspects of microstructure and dynamics of concentrated suspensions. Among these aspects are the proper description of the small-angle peak observed in scattering from aggregating colloids, the theories for the phase behaviour of colloid-polymer mixtures as well as of binary hard-sphere suspensions and the quantitative calculation of the effects of hydrodynamic interaction on the short dynamics of charge-stabilized colloids. There have been several theoretical and experimental investigations on possible generalizations of the Stokes Einstein relation to concentrated suspensions. Mode-coupling theory for the glass transition describes nearly monodisperse hard-sphere systems well, but is found to fail partially for other systems.

RELATIVISTIC EFFECT IN INELASTIC COLLISION OF ELECTRON WITH ATOM OR ION

Based on relativistic Born approximation theory, we have calculated the relati-vistic and non-relativistic generalized oscillator strengthes (GOS) of the Li-liks iso-electron sequence. The difference between the two calculations shows the relativistic effect of both the target and impact electron in the inelastic collision process. For low Z target (e.g. Li), the relativistic effect is negligible. For the 2s?p transition of Au+76, the relativistic GOS is 27.1% smaller than the non-relativistic one. At high impact energy, the contribution of transverse term of GOS to the differential cross section is important at certain angle. At extremely high impact energy (e.g. 106, 107eV), the transverse term of GOS becomes dominant at forward small angle and such forward peak makes overwhelming contribution to the totalinelastic cross section.

Low-dimension structural properties and microindentation studies of ion-beam-sputtered multilayers of Ag/Al films

Artificially modulated silver/aluminum multilayer films with modulation wavelengths Λ between 1.35 and 21.3 nm, and total film thickness of 1 μm were prepared by ion-beam sputtering. The mechanical properties of these films were investigated by a low load muhardness indentation technique. The films displayed increased hardness as the modulation wavelength decreased. X-ray diffraction scans showed well-defined small angle peaks and satellite peaks for high angles indicating a coherent multilayer structure. The hardness enhancement as the modulation wavelength decreases may be partially attributed to the Ag 2Al formation at the interfaces. The high quality of the well-defined layer structure is confirmed by the presence of interference maxima corresponding to the number of bilayers in the low angle diffraction data for films with total film thicknessesess than 33.0 nm.

Synthesis and structural characteristics of ion‐beam sputtered multilayer Ag/Al thin films

Multilayers of Ag/Al with layer thickness ratio of 1.7:1.0 have been deposited on Si and glass substrates using ion‐beam sputtering with composition modulation wavelengths λ ranging from 13.5 to 213 Å. Spatial distribution and angular dependence of deposition rates were determined by analysis of x‐ray diffraction scans which showed several orders of distinct satellite peaks and well defined small angle peaks. At high modulation wavelengths (λ≳35 Å), the multilayer film showed (111) preferred orientation normal to film plane. For short modulation wavelengths (λ<35 Å), other orientations appeared and peaks corresponding to Ag2Al intermetallic phase were also observed. One satellite peak corresponding to Ag2Al(100) peak was observed and gave the same modulation wavelength as the parent Ag/Al multilayer. The computer simulation analysis using square wave model is in good agreement with the observed satellite peak positions for high modulation wavelengths. The average lattice parameter of the Ag/Al multilayer reduces by 1.1% as the modulation wavelengths drops below 35 Å, which may be partially attributed to the presence of a significant proportion of Ag2Al interphase layers at the interface.

Structural, elastic and transport properties of Ag/Al multilayer thin films prepared by ion-beam sputtering

Abstract Multilayers of Ag/Al with composition modulation wavelengths λ between 13.5 and 210 A were deposited onto silicon substrates using ion-beam sputtering. X-ray diffraction scans showed well defined small angle peaks and satellite peaks at high angles indicating coherent multilayers. The average lattice parameter showed a 1.1% reduction with decreasing modulation wavelengths from 90 to 25 A. Brillouin-scattering measurements showed a moderate 5% enhancement of surface velocity (elastic constant) with decreasing wavelengths. This elastic hardening and interplanar structural contraction may be partially attributed to the observed formation of Ag2Al at the multilayer interfaces. Although deposited only 10° from a normal incidence, the electrical resistivities, measured between 77 and 300 K in a van der Pauw configuration, showed a temperature independent in-plane anisotropy of up to 90% and the room temperature resistivity was an order of magnitude greater than expected from the bulk average. The temperature coefficient of resistivity showed a “U” shaped dependence with λ and the lower up turn occurred at λ ≈ 50 A.

Short-range clustering and long-range periodic decomposition of an electron irradiated Ni-Cu alloy

Diffuse and small-angle neutron diffraction studies of the null matrix 62Ni-41 at.% 65Cu have been performed after thermal treatment and after irradiation with 3 MeV electrons at temperatures between 373K and 640K. Besides an increase in the short-range clustering, a periodic decomposition with a wavelength around 45 AA is observed after irradiation at temperatures between 373K and 480K. The decomposition structure was found to be stable against thermal annealing and irradiation, at least up to 510K. Upon thermal treatment above 600K dissolution of the long range decomposition takes place. By extrapolation of the short-range clustering data from high temperatures, the critical temperature of the coherent miscibility gap is obtained at 527K and that of the incoherent gap at 575K. The decomposition kinetics within the gap can be described satisfactorily by Cook's clustering model (1969, 1970) for large scattering wavevectors, i.e. for the short-range clustering. The small-angle peak kinetics show several specific deviations from the predictions of the common spinodal decomposition theories. The possibility cannot be excluded that the observed long-range decomposition is a radiation-induced phase transformation.

Large- and small-angle peaks in slow H+-H collisions

The probability against impact-parameter curve for H(2p) production in slow H+-H collisions is considered with particular reference to its double-peak structure The inner large-angle peak has already been described by Bates and Sprevak (1970) in simple physical terms, as strong rotational coupling at the point of closest approach on a Coulomb trajectory. The outer small-angle peak is now simply described in terms of an approximate 2p sigma -2p pi symmetrical resonance arising out of perturbed-united-atom degeneracy. Both peaks are encompassed by one of the authors' previously proposed phase-integral formulae.