Low Angle Region Research Articles

Anomalous dispersion effects, anharmonic thermal vibrations and bonding charges in indium antimonide

Upon the inclusion of dispersion corrections in the structure factor expressions for the ZnS structure, Friedel's law is violated for all odd and all even index reflections due to bonding effects in the low angle regions and anharmonicity in the high angle regions in this type of crystals. Systematic and precise X-ray diffraction intensity measurements were carried out using a spherical single crystal of indium antimonide at 300 K. From the least squares refinement of the experimental data we obtain the Debye-Waller factors for indium and antimony as B(In) = 1.432(0.003) A ̊ 2 and B(Sb) = 0.865(0.002) A ̊ 2 with the residual index R = 2.24%. A search for anharmonic thermal vibrations was made for the present experimental data. On including the individual anharmonic thermal factors in the refinement process we obtain the anharmonic thermal parameters for indium and antimony as β(In) = −0.57(0.34) 10 −16 J A ̊ −3 and β(Sb)= −2.21(1.18) 10 −16 J A ̊ −3 , the Debye-Waller factors for the anharmonic model being B(In) = 1.333(0.003) A ̊ 2 and B(Sb) = 0.886(0.002) A ̊ 2 with R = 2.22%. The present work reveals excellent agreement, both in sign and magnitude, with the Bijvoet inequalities for a large number of reflections. In the ZnS structure, the weak quasi-forbidden reflections ( h + k + l = 4 n + 2) contain information about the covalent bond charges which was also deduced using a few 4 n + 2 type reflections. A net transfer of charge from In to Sb is observed in the present work.

Finite size effects in crystalline/amorphous multilayers

Extended X-ray diffraction experiments have been used to investigate the structure of Pb/Ge multilayers with a small (<15) number of bilayers. The detailed finite size structure in the X-ray diffraction profiles indicates that the multilayers are of very high quality. The authors present a one-dimensional kinematical calculation for these diffraction profiles, including continuous and discrete random fluctuations in layer thickness. The introduction of both continuous and discrete fluctuations causes a decrease in the number of secondary single-layer 'finite size' maxima in the high angle region, in agreement with the experimental results. No quantitative agreement is reached for the low angle region, which shows more finite size structure than predicted by the fluctuations deduced from the high angle region.

Radar sea-clutter at low grazing angles

An analysis of sea-clutter data obtained in conditions typical of sea state 2 at X-, S-, L- bands, UHF and VHF is presented. Results show that sea-clutter exhibits very different spectral characteristics at higher frequencies compared to those at low frequencies. Experimental sea-clutter coefficients as a function of grazing angle at various frequency bands were obtained for upswell and cross-swell conditions. Most sea-clutter models use the radar look direction relative to the wind direction as an input parameter (e.g. upwind, crosswind, etc.). Hence a direct comparison of sea-clutter magnitude with values calculated from models under different wind conditions was not made. Instead, these results were contrasted with those calculated from two sea-clutter (the GIT and Sittrop) models, assuming an upwind and a crosswind condition. The data were quite dissimilar in the low-grazing-angle regions to those predicted by the two models. Further research on sea-clutter in the low-grazing-angle regions is needed to ascertain and explain the observed differences. Sea-clutter amplitude statistics were found to fit the K-distribution best in the important low probability of false alarm region. The distribution approached that of a Rayleigh model for vertical polarisation and low-resolution waveforms. Non-Rayleigh statistics were frequently observed even for relatively low resolution and vertical polarisation waveforms. For horizontal polarisation and/or high resolution waveforms, the statistics approached those of a lognormal model. The statistical results provided further evidence that the K-distribution can serve as a limiting distribution for sea-clutter. The results of this paper are pertinent to shipboard radar applications where the grazing angle is low. They also provide additional information for sea-clutter modelling in the low-angle region, particu larly at the lower frequency bands.

A Monte Carlo calculation of the interparticle interference in small-angle X-ray scattering

In solution small-angle X-ray scattering data, the lowest-angle region is affected by interparticle correlations and potentially provides information concerning particle-particle interactions in solution, such as overall electrostatic interaction– attractive or repulsive – and tendency to form aggregates. A method is presented, based on a Monte Carlo approach, to calculate the interparticle interference for a solution of particles of arbitrary shape interacting through a simple two-particle hard-core potential. The method provides a basis for a quantitative analysis of the concentration-dependent scattering in the low-angle region. It has been used to study the relative effects of interparticle interference and particle dimerization in the scattering profiles for the proteins troponin C and lysozyme. The calculation may be generalized to include a more physically realistic potential.

Investigations on the phase formations, properties and single crystal growth in the high-Tc superconducting Ca-Sr-Bi-Cu-O system

We have performed investigations on the Ca-Sr-Bi-Cu-O system with respect to high-Tc superconductivity and structural properties. It is shown that there are two high-Tc superconducting phases in the system, i.e. a 110 K and an 85 K phase. The 85 K phase has a body-centred tetragonal structure with a stoichiometry of CaSr2Bi2Cu2O8. The 110 K phase is closely related to the 85 K phase. It is formed only in a very narrow temperature range and easily deteriorates to the phase with the lower Tc by quenching. Although some samples show a large diamagnetic signal at 110 K in ac-susceptibility measurements, there is still evidence of the presence of the 85 K phase. X-ray diffraction studies, especially in the low-angle region, show a structural relation between these two superconducting phases. The procedures of the preparation and the characterization of the 85 K and 110 K polycrystalline superconducting phases as well as the single crystal growth of the 85 K superconducting phase are described.

Glauber amplitude for scattering of electrons by hydrogen atoms: 1s-->2s,2p excitations.

The method proposed by Yates [Chem. Phys. Lett. 25, 480 (1974)] has been extended to the case of 1s\ensuremath{\rightarrow}2s,2p excitation of a hydrogen atom by electron impact. An alternative analytical procedure used by Berestetskii, Lifshitz, and Pitaevskii [Quantum Electrodynamics (Pergamon, Oxford, 1982), p. 539] has, however, been adopted for the evaluation of the third term of the Glauber series. In the process Yates's expression for the third Glauber term for electron--hydrogen-atom elastic scattering has been reproduced. The differential scattering cross section for the excitation process has been calculated as suggested by Yates. This cross section is found to be in reasonable agreement in the low-angle region with the exact Glauber results reported by Tai et al. [Phys. Rev. A 1, 1819 (1970)] and by Gien [Phys. Rev. A 20, 1457 (1979)].

The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum

The validity of the Kirchhoff approximation for rough surface scattering is examined by comparison with exact results obtained by solving an integral equation. The pressure release boundary condition is assumed. The field quantity calculated is the bistatic scattering cross section, which is obtained with a Monte Carlo technique. The accuracy of correcting the Kirchhoff scattering cross section for shadowing is also addressed. The surface realizations used are randomly rough with a Gaussian roughness spectrum and have height variations in only one direction. The surface correlation length is found to be the most important parameter in defining the valid region of the Kirchhoff approximation away from the low grazing angle region. A procedure is given that provides a quantitative measure of the accuracy of the shadow-corrected approximation when the root-mean-square (rms) slope angle of the surface γ is ≲20° and when the incident grazing angle θ is ≳2γ. Examples with θ≲2γ are also discussed.

Microstructure and Magnetic Behavior of Fe/Ti Multilayered Films

ABSTRACTFe/Ti multilayered films composed of Fe and Ti layers with various thickness ( dFe of 10 ∼ 1000 A and dTi of 10 ∼ 200 A ) have been prepared at Ar gas pressure of 2 mTorr by two pairs of Facing Targets Sputtering apparatus which can deposit very thin and continuous films on plasma-free substrates. The total thickness of Fe layers was 1000 A in all of the specimen films.The periodic microstructure due to compositional modulation was clearly observed not only in the low angle region of X-ray diffraction diagrams but also in the Auger electron spectroscopic depth profile.With decreasing dFe from 1000 to 20 A, the diffraction intensity of (110) plane in the Fe bcc phase lowered for dTi of 10∼200 A and its interplanar spacing ( d-spacing ) increased for dTi above 50A. This diffraction peak disappeared with further decreasing d below 15 A. At dFe around 25 A, a different peak appeared at the angle slightly lower than that of Fe(110) peak. The diffraction intensity of (002) plane in the Ti hcp phase increased with decreasing dFe. However, its d-spacing depended little on the dFe and took the same value as that of bulk Ti except for very small dTi.The net saturation magnetization of Fe layers in all of the specimen films decreased gradually with decreasing dFe from 1000 to 50 A, decreased abruptly with further decreasing dFe and became nearly zero at dFe below 15A.The films annealed at 200 and 400 °C showed obscure periodic microstructure and had larger d-spacing of ∝ −Fe(110) and smaller saturation magnetization than those of the as-deposited ones.

Solid Particle Erosion of Brittle Materials (Part 5)

The erosion tests were performed for nine kinds of ceramics such as SiC, Si3N4 and Al2O3 and window glass using SiC, Al2O3 and glass powders as abrasive at the impingement angle (θ) of 90-20 degrees. The erosive wear (V) for many target and abrasive particle pairs is almost proportional to the square of the impingement angle as proposed by Bitter. However, there were several pairs for which the exponent n in V∝(sinθ)n deviates greatly from two. The pair of Si3N4 (9S) target and Al2O3 abrasive has a small n, 0.8. The small n value is explained by the fact that the erosive wear by brittle erosion mechanism in the high impingement angle region is suppressed because of large toughness of the target and that the erosive wear by scratching in the low impingement angle region is significant. The n's large than two were observed in glass abrasives. This is caused by a large change of effective stress with changing the impingement angle, and the larger change in stress resulted from the slip of abrasive particle on the surface of target which is caused by the melting of glass by the rubbing heat at the instant of impingement. The melting phenomenon of particles and/or targets was observed also for Al2O3. The exponent n for SiC particles are always larger than that for Al2O3 particles for the same target. Changing the impingement angle in the erosion test is considered to be effective for finding some clue to understand the erosion mechanism and mechanical or chemical phenomena occurring at a minute area of impingement.

Phase properties of binary mixtures of monogalactosyldiacylglycerols differing in hydrocarbon chain substituents dispersed in aqueous systems

Monogalactosyldiacylglycerols isolated from spinach leaves contain a high proportion of polyunsaturated fatty acyl substituents and form hexagonal-II structures when dispersed in excess water. Catalytic hydrogenation of the lipid in the presence of Adam's catalyst completely saturates the hydrocarbon chains and the lipid forms typical open sheet bilayer structures in water at 20°C. Binary mixtures of the native and hydrogenated lipid tend to phase separate at 20°C. Freeze-fracture electron microscopy reveals lamellar phase lipid indispersed with regions of hexagonal-II structure and the proportions of each reflect the composition of the mixture. X-ray diffraction in both wide- and low-angle regions show that the saturated lipid forms the typical stable gel-phase structure in mixtures that are allowed to equilibrate over three days at 20°C. The phase transition behaviour of binary mixtures of the two galactolipids was investigated by differential scanning calorimetry and fluorescence probe methods. Thermal studies indicate that the phase-separated gel structure undergoes an anomalous transition compared with the saturated pure lipid in that the transition temperature is reduced from about 57°C to 41°C and the enthalpy of the transition is also somewhat reduced. Furthermore, the transition appears to involve the conversion of the completely phase-separated system into bilayer coexisting with phases intermediate between bilayer and hexagonal-II. A homogeneous hexagonal-II phase is presumably formed at higher temperatures. The thermal and structural studies were consistent with fluorescence polarization measurements of 1,6-diphenyl-1,3,5-hexatriene interpolated into the hydrocarbon domain of the structure.

Global characteristics of magnetic flux ropes in the Venus ionosphere

In this paper we examine the global characteristics of the magnetic flux ropes in the Venus ionosphere. These structures are the most common magnetic feature of the ionosphere, being observed on more than 70% of the orbits of the Pioneer Venus orbiter passing through the dayside ionosphere. The spatial occurrence of flux ropes maximizes at altitudes near 165 km; they may occupy more than 50% of the ionospheric volume at this altitude. At higher altitudes the fractional volume occupied by ropes decreases below 20%. Characteristic radii of the ropes vary between 6 km at 160 km altitude and 15 km at 500 km altitude, and scale roughly with both the local ion gyroradius and ion inertial length. Ropes above 200 km altitude in the low zenith angle regions (χ &lt; 45°) appear to have quasi‐horizontal orientations, while those below 200 km tend to be quasi‐vertical. The high zenith angle cases (χ &gt; 45°) tend to be horizontal above 300 km and randomly oriented below 300 km. Ropes may tend to be more tightly ‘twisted’ at low altitudes than at high, and more so in the χ &lt; 45° regions than nearer the terminator. Rope field strengths are highest near the altitudes where their occurrence maximizes, i.e., near 165 km, and scale with the square root of the ambient thermal pressure. Finally, the global polarities of flux rope field‐aligned currents appear to be random and do not clearly support a steady, nonturbulent global formation mechanism.

Triethylgermyllithium association in solutions studied by the method of x-ray diffraction in liquids

X-ray diffraction patterns for Et 3GeLi solutions in benzene, hexane and tetrahydrofuran (THF) are measured and radial distribution functions (RDF's) are calculated. Narrow peaks are detected in the RDF's pertaining to the distances between atoms of coupled Et 3GeLi molecules. This shows directly that these molecules exist in solution in associated forms. The associate structures are different in hydrocarbon and electron-donor solvents. It is found that the nearest neighbour distance between germanium atoms of coupled molecules is 4.5 Å in benzene and hexane and 4.0 Å in THF solutions. Packing of large associates produces the diffraction peak seen in scattering curves of solutions in the low angle region. The associate dimensions (diameters) are estimated from these peak positions as 12.5–14 Å in hydrocarbons and 10 Å in THF.

Solution structure of ionic polymers and their catalysis

Recent X-ray and neutron scattering studies of dilute solutions of polyelectrolytes show distinct peak in low angle regions. The peak position depends on the degree of polymerization. When two fractions are mixed, not two but a single peak appears, suggesting strongly that the peak is due to inter-molecular ordering of macroions. The Bragg distance (intermacro-ion distance) , 2Dexp, decreases with increasing polymer concentration. With increasing concentration of added salt, the 2Dexp increases (not decreases). The 2Dexp values obtained from the X-ray data and also from the neutron scattering are always smaller than (about one half of) .2Do, an intermacroion distance calculated with the assumption of simple cubic distribution, for fractionated polyacrylates, polystyrenesulfonate (Mw/MN < 1.2) , polymethacrylate and poly-L-lysine. This suggests the presence of a two-state structure in solutions, which is a consequence of unusually intense macroion-gegenion interaction. On the basis of this interaction, polyelectrolytes are known to show remarkable catalytic influence on various interionic reactions. Our explanation of the polyelectrolyte catalysis is based on the Brönsted-Bjerrum equation, k/k* = fA. fB/fX (k, k* : rate constants with and without polyelectrolyte, f's: activity coefficients of the reactants A and B and of the activated complex X). Besides the electrostatic stabilization or destabilization of the reactants and/or the activated complex, which was pointed out earlier, a new factor responsible for variation of the activity coefficient term is found to be important, namely solvent. The high pressure study indicates clearly that the solvation-desolvation factor is of a substantial importance. The volume of activation (ΔV≠) shows that acceleration caused by polystyrenesulfonate for the Ag+-induced aquation reaction of Co (NH3)5Br2+ is largely due to dehydration of the activated complex by the macroions. Correspondingly the entropy of activation (ΔS≠) is increased so that the free energy of activation (ΔG≠) and hence the fX is lowered. On the other hand, deceleration of the OH−-hydrolysis of the Co complex is found to be due to dehydration of the reactants. In this case, addition of macroions lowers ΔV≠, ΔS≠, and accordingly the reactant activity and hence increases ΔG≠.

Time resolved small angle scattering during isothermal crystallization of unoriented poly(ethylene terephthalate) using synchrotron radiation

AbstractThe time course of the small angle scattering pattern of amorphous poly(ethylene terephthalate), (PET), was measured during isothermal crystallization using synchrotron radiation. The samples were heated to temperatures between 117 and 145°C in an oven placed in the path of the X‐ray beam. The scattering curves were measured within 10 s at intervals of 1 s so as to follow the kinetics of the process continuously. It appears that the distance between the centres of mass of the crystallites decreases with increasing crystallization time as in oriented PET. The integrated small angle scattering follows approximately the same time course as the increase in the degree of crystallinity during an isothermal crystallization yielding Avrami exponents between 5 and 7. Guinier plots of the low angle region show that the scattering can be attributed to rod‐like particles.

Changed Lyotropic Liquid Crystalline Structure Due to Polymerization of the Amphiphilic Component

Optical patterns in polarized light and x-ray reflections in the low-angle region were used to detect a shift from one liquid crystalline structure to another during polymerization. The polymerization took place in a Iotropic liquid crystal of water and sodium undecenoate, with a structure consisting of cylinders in a two-dimensional hexagonal close packing. After polymerization, a lamellar liquid crystalline structure was obtained.

Effects of density gradients on bottom reflection loss for a class of marine sediments

The sensitivity of bottom reflection loss to a density gradient is examined within the context of a physically meaningful model consisting of a fluid sediment layer having depth-dependent density and sound speed overlying a substrate having solid properties. The bottom grazing-angle range is divided into two regions, the low-angle and the high-angle regions. In the low-angle region sediment sound-speed gradients refract incident energy upward before it encounters the substrate. In the high-grazing-angle region, energy impinges on the substrate. Through the use of a numerical plane-wave reflection coefficient model it is shown that the effect of a density gradient on low-angle bottom loss is small. An expression indicating this effect is derived and is shown to agree with numerical bottom-loss calculations. The high-angle bottom loss is more influenced by a density gradient because of the impedance changes at the sediment–substrate interface which accompany a density gradient. It is shown that introduction of density gradient of 0.002 g/cm3/m can cause the high-angle bottom loss to change on the average by 12.5%, 7%, and 3% in 100-m clay, silt, and sand layers, respectively.

Röntgenkleinstwinkelstreuung an Erythrocyten

The operational range of X-ray small-angle scattering was extended to particles and structures in the μm-range by the construction of a 50 m long scattering device. Erythrocytes were selected as a suitable object for study. They were found to have a radius of gyration of 2.3 ± 0.2 μm, corresponding to a particle diameter of 6.0 ± 0.5 μm. The volume was calculated from Perod's invariant and found to be 67 ± 10 μm3. For the first time, absolute measurements could be done without weakening the primary beam, which allowed the direct determination of the mass of the particle. The mass of the erythrocyte was calculated to be 78 ± 20 pg. In all experiments a slit collimation was used. The divergence of the incident beam was smaller than the halfwidth of the scattering curve by a factor of 2.5. Therefore, the low-angle region of the scattering profile was hardly influenced by distortions due to collimation disregarding the normalization factor.

Inelastic scattering of gamma rays by K-shell electrons in heavy atoms

The differential cross sections for the inelastic scattering of 279 keV gamma rays by K-shell electrons of bismuth are determined experimentally at six scattering angles. Two NaI(Tl) scintillation spectrometers and a fast-slow coincidence circuit are used, and the final coincidence counts are collected on a 20-channel pulse-height analyser. The bound-to-free electron differential cross section ratios are compared with those calculated using different non-relativistic theories. The experimental differential K-shell electron cross sections are compared directly with those of the free electron and with the average bound electron differential cross sections obtained on the basis of the Hartree-Fock and Thomas-Fermi atomic models. In the low-angle region the trend of the experimental differential cross section ratios agrees with that of the incoherent scattering function values based on the Thomas-Fermi model. The total cross section is also estimated and found to be a little less than 60% of that due to free electrons.

Influence of intrachain double bonds on the properties of solution grown single crystals of polyethylene

The influence of intrachain trans double bonds, statistically distributed along a polyethylene chain, on the structure and behaviour of chain-folded single crystals has been studied. The dependence upon the percentage of double bonds of dissolution and thermal properties, external crystal habit, X-ray diffraction in the wide- and low-angle regions, of solution grown single crystals of ethylene-butadiene copolymers may be interpreted by assuming that a certain amount of CH 2CHCHCH 2 units are incorporated in the lattice as defects. The results of the bromination of single crystals of a sample of ethylene-butadiene copolymers show that about the 56% of double bonds, not accessible to bromine, are situated not on the fold surface but in the inner part of the crystals.

A comparison of mode match, geometrical theory of diffraction, and Kirchhoff radiation

Using as a model a parallel-plate flanged waveguide excited by a uniform magnetic line source, the techniques of mode match, geometrical theory of diffraction, and Kirchhoff radiation are compared. In all cases the aperture fields are analyzed in terms of waveguide modes; the far-field results are Fourier transforms of the aperture fields. To within normalization, the Kirchhoff results compare surprisingly well with the two other methods except near resonance and in the low observation angle regions where the diffracted components of the field are dominant.