Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfests theorem

The electron-diffraction pattern for two slits with magnetic flux confined to an inaccessible region between them is calculated. The Aharonov-Bohm effect gives a diffraction pattern that is asymmetric but has a symmetric envelope. In general, both the expected displacement and the kinetic momentum of the electron are nonzero as a consequence of the asymmetry. Nevertheless, Ehrenfests theorems and the conservation of momentum are satisfied. © 1992 The American Physical Society.

Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at a relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ""equation of state"" of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ""Mach number"" is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ""optical ship waves"" (the wave pattern formed by a two-dimensional packet of linear waves) is situated. Analytical theory of the ""optical ship waves"" is developed and two-dimensional dark soliton solutions of the generalized two-dimensional nonlinear Schrodinger equation describing the light beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.

X-ray diffraction data of tibolone Delta(4) isomer (isotibolone)

Tibolone is used for hormone reposition of postmenopause women and isotibolone is considered the major degradation product of tibolone. Isotibolone can also be present in tibolone API raw materials due to some inadequate synthesis. Its presence is then necessary to be identified and quantified in the quality control of both API and drug products. In this work we present the indexing of an isotibolone X-ray diffraction pattern measured with synchrotron light (lambda=1.2407 angstrom) in the transmission mode. The characterization of the isotibolone sample by IR spectroscopy, elemental analysis, and thermal analysis are also presented. The isotibolone crystallographic data are a=6.8066 angstrom, b=20.7350 angstrom, c=6.4489 angstrom, beta=76.428 degrees, V=884.75 angstrom(3), and space group P2(1), rho(o)= 1.187 g cm(-3), Z=2. (C) 2009 International Centre for Diffraction Data. [DOI: 10.1154/1.3257612]

Dehydration converts DsbG crystal diffraction from low to high resolution

Diffraction quality crystals are essential for crystallographic studies of protein structure, and the production of poorly diffracting crystals is often regarded as a dead end in the process. Here we show a dramatic improvement of poorly diffracting DsbG crystals allowing high-resolution diffraction data measurement. Before dehydration, the crystals are fragile and the diffraction pattern is streaky, extending to 10 Angstrom resolution. After dehydration, there is a spectacular improvement, with the diffraction pattern extending to 2 Angstrom resolution. This and other recent results show that dehydration is a simple, rapid, and inexpensive approach to convert poor quality crystals into diffraction quality crystals.

Precession electron diffraction in the transmission electron Microscope: electron crystallography and orientational mapping

Precession electron diffraction (PED) is a hollow cone non-stationary illumination technique for electron diffraction pattern collection under quasikinematicalconditions (as in X-ray Diffraction), which enables “ab-initio” solving of crystalline structures of nanocrystals. The PED technique is recently used in TEMinstruments of voltages 100 to 300 kV to turn them into true electron iffractometers, thus enabling electron crystallography. The PED technique, when combined with fast electron diffraction acquisition and pattern matching software techniques, may also be used for the high magnification ultra-fast mapping of variable crystal orientations and phases, similarly to what is achieved with the Electron Backscatter Diffraction (EBSD) technique in Scanning ElectronMicroscopes (SEM) at lower magnifications and longer acquisition times.

Particle shape and orientation in laser diffraction and static image analysis size distribution analysis of micrometer sized rectangular particles

Laser diffraction (LD) and static image analysis (SIA) of rectangular particles [United States Pharmacopeia, USP30-NF25, General Chapter <776>, Optical Miroscopy.] have been systematically studied. To rule out sample dispersion and particle orientation as the root cause of differences in size distribution profiles, we immobilize powder samples on a glass plate by means of a dry disperser. For a defined region of the glass plate, we measure the diffraction pattern as induced by the dispersed particles, and the 2D dimensions of the individual particles using LD and optical microscopy, respectively. We demonstrate a correlation between LD and SIA, with the scattering intensity of the individual particles as the dominant factor. In theory, the scattering intensity is related to the square of the projected area of both spherical and rectangular particles. In traditional LD the size distribution profile is dominated by the maximum projected area of the particles (A). The diffraction diameters of a rectangular particle with length L and breadth B as measured by the LD instrument approximately correspond to spheres of diameter ØL and ØB respectively. Differences in the scattering intensity between spherical and rectangular particles suggest that the contribution made to the overall LD volume probability distribution by each rectangular particle is proportional to A2/L and A2/B. Accordingly, for rectangular particles the scattering intensity weighted diffraction diameter (SIWDD) explains an overestimation of their shortest dimension and an underestimation of their longest dimension. This study analyzes various samples of particles whose length ranges from approximately 10 to 1000 μm. The correlation we demonstrate between LD and SIA can be used to improve validation of LD methods based on SIA data for a variety of pharmaceutical powders all with a different rectangular particle size and shape.

X-ray diffraction studies of muscle : observations on the anterior byssus retractor muscle of Mytilus edulis and the insect flight muscle from Sarcophaga bullata

The interfilament spacing of the anterior byssus retractor muscle from Mytilus edulis was studied as the muscle was extended. It was found that variations in this spacing were very small and consistent with the hypothesis that the interfilament spacing was independent of the extension of the muscle. It was observed that the interfilament spacing was dependent on the osmolarity of the bathing medium. In concentrated solutions of the artificial seawater, the interfilament spacing decreased; while in dilute solutions of artificial seawater, it was observed that the interfilament spacing was increasing. X-ray diffraction patterns were obtained from fresh, and glutaraldehyde fixed, specimens of insect flight muscle from Sarcophaga bullata. There patterns were in general agreement with previous X-ray diffraction studies of insect flight muscle. A reflexion G at 93A was observed and interpreted as arising from diffraction in the mitochondria. Specimens of dried insect flight muscle produced a diffraction pattern consisting of arc and ring reflexions. This was interpreted as suggesting an ordered arrangement of cristae, in the mitochondria from these muscles.

X-ray diffraction from Al powder using energy dispersive technique

Using the energy dispersive x ...ray diffraction (EDXD) technique, the room temperature diffraction pattern of Al powder was obtained at diffraction angles ~ 30° and 50°. From the small angle diffraction pattern the average relative intensities (IR) of the (111), (200), and (220) lines were measured to be equal to 100, 62, and 32 respectively. From the large diffraction angle IR for the (220), (311+222), (400), (331+420), and (422) lines were measured to be 100,201,17,90, and 19.5 respectively. The diffraction pattern at those two angles were obtained at several higher temperatures to measure the change in the intensities of the Al lines. From the intensity changes the increase of the Debye- Waller temperature factor, i.e ~B(T), with respect to the value at room temperature was determined to be 0.6+0.1 at 250°C, 1.10+0.15 at 350°C, 1.45+0.20 at 450°C, and 2.20±0.35 at 550°C.

X-ray diffraction study of the influence of temperature on the structural correlations of poly(2-hydroxypropyl ether of bisphenol A)

The X-ray diffraction pattern of glassy poly(2-hydroxypropyl ether of bisphenol A) is studied at room temperature on oriented samples in order to associate its different peaks to different structural correlations. On the other hand, X-ray diffraction patterns have been obtained at different temperatures from Tg − 50 K up to Tg + 50 K for the above-mentioned polymer. Attention has been paid to the evolution with temperature of the position of the wide diffraction maximum corresponding to interchain correlations in the polymer. The temperature evolution of this parameter shows a marked discontinuity just at the glass transition temperature.

Diffraction from thermotropic copolyester molecules

Analytical expressions for the meridional scattering from highly oriented random copolyesters are presented. These procedures are utilised in developing the relationship of the features in the diffraction pattern to compositions and relative lengths of the constituent monomer units. The difference between the scattering patterns for random and block copolymers are discussed. The theory is applied to an example of a liquid crystal froming random copolyester.

X-ray diffraction data of tibolone Delta(4) isomer (isotibolone)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Grazing incidence X-ray diffraction and atomic force microscopy analysis of BaBi2Ta2O9 thin films

Thin films of BaBi2Ta2O9 (BBT) composition were prepared through the metal organic decomposition method. The crystallinity, phase formation, crystallite size and morphology of the thin films were measured as a function of the type of substrate, stoichiometry of solution and process variables such as thickness and temperature. The thin films were investigated by grazing incidence X-ray diffractometry and atomic force microscopy (AFM) techniques. For the sample without excess of bismuth, diffraction peaks other than that of the BBT phase were observed. A well crystallized BBT single phase was observed for films prepared from a solution with 10% excess of bismuth, deposited on Si/Pt substrate, with a thickness up to 150 nm and sintered at temperatures of 700 degreesC. The thin BBT phase films heat-treated at 600 degreesC presented a diffraction pattern characteristic of samples with lower degree of crystallinity whereas for the thin films heat-treated at 800 degreesC, we observed the presence of other phases than the BBT. For the thin film deposited on the Sin+ substrate, we observe that the peaks corresponding to the BBT phase are broader than that observed on the samples deposited on the Pt and Si/Pt substrates. No variation of average crystallite size was observed as the excess of Bi increased from 10 to 20%. AFM images for the samples showed that the increasing the amount of bismuth promotes grain growth. The average surface roughness measured was in the range of 16-22 nm showing that the bismuth amount had no or little effect on the roughness of films. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Crystallization and preliminary X-ray diffraction analysis of a novel Arg49 phospholipase A(2) homologue from Zhaoermia mangshanensis venom

Zhaoermiatoxin, an Arg49 phospholipase A(2) homologue from Zhaoermia mangshanensis (formerly Trimeresurus mangshanensis, Ermia mangshanensis) venom is a novel member of the PLA(2)-homologue family that possesses an arginine residue at position 49, probably arising from a secondary Lys49 -> Arg substitution that does not alter the catalytic inactivity towards phospholipids. Like other Lys49 PLA(2) homologues, zhaoermiatoxin induces oedema and strong myonecrosis without detectable PLA(2) catalytic activity. A single crystal with maximum dimensions of 0.2 x 0.2 x 0.5 mm was used for X-ray diffraction data collection to a resolution of 2.05 angstrom using synchrotron radiation and the diffraction pattern was indexed in the hexagonal space group P6(4), with unit-cell parameters a = 72.9, b = 72.9, c = 93.9 angstrom.

An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images

We describe an approach to the high-resolution three-dimensional structural determination of macromolecules that utilizes ultrashort, intense x-ray pulses to record diffraction data in combination with direct phase retrieval by the oversampling technique. It is shown that a simulated molecular diffraction pattern at 2.5-Å resolution accumulated from multiple copies of single rubisco biomolecules, each generated by a femtosecond-level x-ray free electron laser pulse, can be successfully phased and transformed into an accurate electron density map comparable to that obtained by more conventional methods. The phase problem is solved by using an iterative algorithm with a random phase set as an initial input. The convergence speed of the algorithm is reasonably fast, typically around a few hundred iterations. This approach and phasing method do not require any ab initio information about the molecule, do not require an extended ordered lattice array, and can tolerate high noise and some missing intensity data at the center of the diffraction pattern. With the prospects of the x-ray free electron lasers, this approach could provide a major new opportunity for the high-resolution three-dimensional structure determination of single biomolecules.

Experiments and analysis of combined diffraction and self diffraction effects in a nematic liquid crystal cell

The potential for nonlinear optical processes in nematic-liquid-crystal cells is great due to the large phase changes resulting from reorientation of the nematic-liquid-crystal director. Here the combination of diffraction and self-diffraction effects are studied simultaneously by the use of a pair of focused laser beams which are coincident on a homeotropically aligned liquid-crystal cell. The result is a complicated diffraction pattern in the far field. This is analyzed in terms of the continuum theory for liquid crystals, using a one-elastic-constant approximation to solve the reorientation profile. Very good comparison between theory and experiment is obtained. An interesting transient grating, existing due to the viscosity of the liquid-crystal material, is observed in theory and practice for large cell-tilt angles.