Single Diffraction Pattern Research Articles

The strong phase object approximation may allow extending crystallographic phases of dynamical electron diffraction patterns of 3D protein nano-crystals

Abstract Simulations suggest that the strong phase object approximation of dynamical scattering may allow extracting crystallographic phase information from single 2D electron diffraction patterns of 3D protein crystals using probabilitistic procedures. Unlike other phasing methods, the procedure does not requires any additional knowledge – like real space images, atomicity, non-crystallographic symmetry, the presence or location of disordered solvent or the availability of a support with a known structure. In specific cases, the availability of precession electron diffraction data can further improve the phases.

High quality single shot diffraction patterns using ultrashort megaelectron volt electron beams from a radio frequency photoinjector

Single shot diffraction patterns using a 250-fs-long electron beam have been obtained at the UCLA Pegasus laboratory. High quality images with spatial resolution sufficient to distinguish closely spaced peaks in the Debye-Scherrer ring pattern have been recorded by scattering the 1.6 pC 3.5 MeV electron beam generated in the rf photoinjector off a 100-nm-thick Au foil. Dark current and high emittance particles are removed from the beam before sending it onto the diffraction target using a 1 mm diameter collimating hole. These results open the door to the study of irreversible phase transformations by single shot MeV electron diffraction.

Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method

We develop an efficient numerical method to compute single slit or double slit diffraction patterns from high frequency wave in inhomogeneous media. We approximate the high frequency asymptotic solution to the Helmholtz equation using the Eulerian Gaussian beam summation proposed in [20, 21]. The emitted rays from a slit are embedded in the phase space using an open segment. The evolution of this open curve is accurately computed using the recently developed Grid Based Particle Method [24] which results in a very efficient computational algorithm. Following the grid based particle method we proposed in [23, 24], we represent the open curve or the open surface by meshless Lagrangian particles sampled according to an underlying fixed Eulerian mesh. The end-points of the open curve are tracked explicitly and consistently with interior particles. To construct the overall wavefield, each of these sampling particles also carry necessary quantities that are obtained by solving advection-reaction equations. Numerical experiments show that the resulting method can model diffraction patterns in inhomogeneous media accurately, even in the occurrence of caustics. AMS subject classifications: 34E05, 78A05, 78A45

Three-dimensional structure determination from a single view

The ability to determine the structure of matter in three dimensions has profoundly advanced our understanding of nature. Traditionally, the most widely used schemes for three-dimensional (3D) structure determination of an object are implemented by acquiring multiple measurements over various sample orientations, as in the case of crystallography and tomography, or by scanning a series of thin sections through the sample, as in confocal microscopy. Here we present a 3D imaging modality, termed ankylography (derived from the Greek words ankylos meaning 'curved' and graphein meaning 'writing'), which under certain circumstances enables complete 3D structure determination from a single exposure using a monochromatic incident beam. We demonstrate that when the diffraction pattern of a finite object is sampled at a sufficiently fine scale on the Ewald sphere, the 3D structure of the object is in principle determined by the 2D spherical pattern. We confirm the theoretical analysis by performing 3D numerical reconstructions of a sodium silicate glass structure at 2 A resolution, and a single poliovirus at 2-3 nm resolution, from 2D spherical diffraction patterns alone. Using diffraction data from a soft X-ray laser, we also provide a preliminary demonstration that ankylography is experimentally feasible by obtaining a 3D image of a test object from a single 2D diffraction pattern. With further development, this approach of obtaining complete 3D structure information from a single view could find broad applications in the physical and life sciences.

Reconstruction from a single diffraction pattern of azimuthally projected electron density of molecules aligned parallel to a single axis

Diffraction from the individual molecules of a molecular beam, aligned parallel to a single axis by a strong electric field or other means, has been proposed as a means of structure determination of individual molecules. As in fiber diffraction, all the information extractable is contained in a diffraction pattern from incidence of the diffracting beam normal to the molecular alignment axis. The limited size of the object results in continuous diffraction patterns characterized by neither Bragg spots nor layer lines. Equations relating the scattered amplitudes to the molecular electron density may be conveniently formulated in terms of cylindrical harmonics. For simulated diffraction patterns from short C nanotubes aligned along their axes, iterative solution of the equation for the zeroth-order cylindrical harmonic and its inverse with appropriate constraints in real and reciprocal space enables the phasing of the measured amplitudes, and hence a reconstruction of the azimuthal projection of the molecule.

Crystal growth and comparative studies of XRD, spectral studies on new NLO crystals: l-Valine and l-valinium succinate

Nonlinear optical single crystals of l-valine and l-valinium succinate were grown by slow evaporation solution growth method using water as the solvent. Purity of crystals was increased by the method of recrystallization. The grown crystals were analyzed by the single crystals X-ray diffraction pattern which proved that LVS belongs to orthorhombic crystals system. The presence of functional groups and modes of vibrations were identified by FT-IR spectroscopy. The chemical structure of crystals was established by FT-NMR technique. The transmission range of grown crystals was identified by UV–vis–NIR. The transmission region of LVS was more effective than LV which could be used for NLO applications. The nonlinear optical property of the grown crystals was confirmed by second harmonic generation test which shows the suitability of NLO applications.

Evaluation of imaging plates as recording medium for images of negatively stained single particles and electron diffraction patterns of two-dimensional crystals

We evaluated imaging plates (IPs) and the DITABIS Micron scanner for their use in recording images of negatively stained single-particle specimens and electron diffraction patterns of two-dimensional crystals. We first established the optimal imaging and read-out conditions for images of negatively stained single-particle specimens using the signal-to-noise ratio of the images as the evaluation criterion. We found that images were best recorded on IPs at a magnification of 67,000x, read out with a gain setting of 20,000 and a laser power setting of 30% with subsequent binning over 2 x 2 pixels. Our results show that for images of negatively stained specimens, for which the resolution is limited to approximately 20 A, IPs are a good alternative to EM film. We also compared IPs with a 2K x 2K Gatan charge-coupled device (CCD) camera for their use in recording electron diffraction patterns of sugar-embedded two-dimensional crystals. Diffraction patterns of aquaporin-0 recorded on IPs and with the CCD camera showed reflections beyond 3 A and had similar R(Friedel) as well as R(merge) values. IPs can thus be used to collect diffraction patterns, but CCD cameras are more convenient and remain the best option for recording electron diffraction patterns.

Unit-cell determination from randomly oriented electron-diffraction patterns

Unit-cell determination is the first step towards the structure solution of an unknown crystal form. Standard procedures for unit-cell determination cannot cope with data collections that consist of single diffraction patterns of multiple crystals, each with an unknown orientation. However, for beam-sensitive nanocrystals these are often the only data that can be obtained. An algorithm for unit-cell determination that uses randomly oriented electron-diffraction patterns with unknown angular relationships is presented here. The algorithm determined the unit cells of mineral, pharmaceutical and protein nanocrystals in orthorhombic high- and low-symmetry space groups, allowing (well oriented) patterns to be indexed.

Phosphonate supported assembly of nanoscale lotus-leaf-shaped nonanuclear lanthanide clusters

Abstract Two discrete nonanuclear Ln(III) phosphonate clusters, formulated as, [Ln9(OH)(Hpmp)12(ClO4)(H2O)26](ClO4)13 · 18H2O (Ln = Nd for 1 and Pr for 2), were synthesized via the assembly of Ln(ClO4)3 with N-piperidinomethane-1-phosphonic acid (H2pmp) at a pH of 6.2 in aqueous solution. Single crystal X-ray diffraction and powder XRD patterns revealed that they are isostructural. In the crystal structure, the shape of arrangement of the nine Ln(III) ions can be described as a lotus-leaf. Furthermore, temperature-dependent magnetic susceptibilities of 1 and 2 have been investigated.

High-performance compact-multi-crystal analyzer for X-ray diffractometer scans

A new high-performance diffracted-beam analyzer consisting of multiple pieces of a perfect crystal is proposed. The pieces of Ge(111) crystal are set so that their crystal lattice planes coincide with tangent planes of a logarithmic spiral function. Each piece of the crystal works in the same manner as a single-crystal analyzer. An X-ray beam diffracted from a specimen is diffracted successively by individual crystals of the analyzer, and these diffracted beams are detected separately by a one-dimensional position-sensitive detector. If the analyzer consists of, for example, ten pieces of crystal, ten diffraction patterns can be observed in a single diffractometer scan, and they can be integrated into a single diffraction pattern. Thus the resulting intensity becomes greater by one order of magnitude, while the angular resolution is the same as that of a single-crystal analyzer. The geometrical aspects of the analyzer are described, and some experimental results are given.

Formation of x-ray vortex dipoles using a single diffraction pattern and direct phase measurement using interferometry

We have devised a method for generating x-ray vortices by using a diffraction pattern from a simple aperture with illumination wave fronts with spherical curvatures. The interferometry visualized the x-ray vortex dipoles by the direct phase measurement. Our interference technique enabled us to sensitively detect and quantitatively measure various phase dislocations on the x-ray wave fronts, providing useful methodologies for beam diagnostics and materials science.

Classification and averaging of random orientation single macromolecular diffraction patterns at atomic resolution

Single molecule imaging experiments at future X-ray free electron laser sources will provide large number of random 3D oriented diffraction patterns with low counting statistics. Grouping of this vast amount of data into classes of similar orientations and averaging must be performed before their orientation and structure reconstruction can take place. Classification algorithms performing all-pair pattern comparisons scale badly with the number of patterns in terms of their computing requirements, which presents a problem in case of improving resolution and decreasing signal to noise ratios. We describe an algorithm performing significantly less pattern comparisons and render classification possible in such cases. The invariance of patterns against rotation of the object about the primary beam axis is also exploited to decrease the number of classes and improve the quality of class averages. This work is the first, which demonstrates that it is possible to classify a dataset with realistic target parameters: 10 keV photon energy, 10(12) photons/pulse, 100 x 100 nm2 focusing, 538 kDa protein, 2.4 A resolution, 10(6) patterns, approximately 3 x 10(4) classes, <1 degree misorientation within classes. The effects of molecular symmetry and its consequences on classification are also analyzed.

Phase retrieval from a single near-field diffraction pattern with a large Fresnel number

A new method of phase retrieval from a single near-field diffraction image with a large Fresnel number is presented and discussed. This method requires only the oversampled diffraction pattern without any other information such as the object envelope. Moreover, we show that the combination with a fast computational method is possible when the linear oversampling ratio is an integer. Numerical simulations are also presented, showing that the method works well with noisy data.

Hydrothermal Synthesis of PbS Hollow Spheres with Single Crystal-Like Electron Diffraction Patterns

PbS hollow spheres were successfully prepared by a sodium citrate-assisted hydrothermal process at 120 degrees C for 12 h, employing lead acetate trihydrate, thiourea and sodium citrate as precursors. The diameter of PbS hollow spheres is 200-400 nm, which is composed of about 50-80 nm nanoparticles. The synthesized product was characterized by powder X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), electron diffraction (ED), Fourier transform-infrared (FT-IR) spectroscopy, ultraviolet-visible spectrometer (UV-vis) and near-infrared absorption spectrometer (NIR). The effects of the reaction conditions on morphologies of PbS structures were investigated. Star-shaped and flat PbS crystals were obtained by changing some experiment conditions. The results show that temperature, sodium citrate concentration, sulfur sources and solvent play key roles on the final morphologies formation of PbS crystals. Especially, ED result indicates that PbS hollow spheres hold single crystal-like electron diffraction patterns. And the possible formation mechanism of hollow spheres was proposed.

Studies on the growth aspects of semi-organic cadmium zinc thiourea acetate: A promising new NLO crystal

Single crystals of a new nonlinear optical material, cadmium zinc thiourea acetate (CZTA), were successfully grown by slow evaporation of the aqueous solution at room temperature. Single crystal X-ray diffraction pattern and FTIR spectrum analysis have confirmed the formation of the new crystal. The optical transmission studies and second harmonic generation (SHG) efficiency studies justified the device quality of the grown crystals.

Local epitaxy of YBa2Cu3Ox on polycrystalline Ni measured by x-ray microdiffraction

Polychromatic synchrotron x-ray microdiffraction is used to determine the epitaxy of YBa2Cu3Ox (YBCO) films grown on polycrystalline Y.15Zr.85O1.925/CeO2/Y2O3/Ni95W5(Ni) rolling-assisted, biaxially textured substrates (RABiTS). A novel analysis technique is introduced in which the orientation of mosaic films is measured by using a Hough transform to recognize arcs in Laue microdiffraction patterns that correspond to low-index zone axes. While the overall epitaxy is cube-on-cube, grain-by-grain analysis reveals a systematic misorientation of YBCO with respect to Ni: the YBCO [001] rotates toward the direction of the surface normal. The crystal mosaic (for rotation about the rolling direction) measured by a single diffraction pattern sampling a 0.5-μm2 surface area is 0.7° full width at half-maximum for YBCO grown on Ni grains with a low tilt; for more highly tilted grains, the YBCO patterns can no longer be measured, presumably due to the large mosaic. The YBCO mosaic over the entire area of a Ni grain is ∼2.5° and varies with grain size; the mosaic is smaller for larger grains.

Quasicrystal approximant Ho13Zn58 + δ (δ ≈ 0.6): an incommensurate modulated tunnel structure

In a systematic study of the binary quasicrystal approximants RE 13Zn∼58 (RE = rare earth elements) system, single crystals of Ho13Zn58 + δ have been prepared. It is unique among family members of the RE 13Zn∼58 system in that it shows a modulated superstructure ordering. Satellite reflections observed in single crystal X-ray diffraction pattern indicate the presence of a one-dimensional lattice distortion. The modulated structure has been solved and refined from X-ray data using the superspace group approach. The Ho13Zn58 +δ structure can be described in the (3 + 1)-dimensional superspace group Pc21 n(0β0)s0s with lattice parameters a = 24.6481(7) Å, b = 14.2484(4) Å, c = 14.0153(3) Å and a modulation vector q = (0, 0.741, 0). The crystal structure is closely related to those of other RE 13Zn∼58 compounds, comprising hexagon-shaped tunnels made up of rare earth-centred Zn polyhedra. All atoms in the structure are affected by a displacive modulation, but one set of Zn atoms are very strongly affected and display an almost composite behaviour with regard to the rest of the structure.

Lateral Phase Separation Gives Multiple Lamellar Phases in a “Binary” Surfactant/Water System: The Phase Behavior of Sodium Alkyl Benzene Sulfonate/Water Mixtures

We have examined the structure of the lamellar phase (Lalpha) that coexists with a micellar solution (L1) for a commercial sodium alkyl benzene sulfonate (LAS) mixed with water. The surfactant is a mixture containing C10-C13 alkyl chains, having all positional isomers of the benzene sulfonate group present except the 1-isomer. Unusually for ionic surfactants, the difference in compositions between the coexisting L1 and Lalpha phases is large (L1 = approximately 20 wt % LAS; Lalpha = approximately 65 wt %). The main technique employed was X-ray diffraction, supplemented by optical microscopy and differential scanning calorimetry (DSC). At ambient temperatures, the lamellar phase gives a single diffraction pattern with the main reflection (d) at approximately 32.5 A, whatever the composition. However, above 40 degrees C, the diffraction peak becomes broader and moves to higher d values. At higher temperatures still, several distinct and different diffraction peaks are observed, differing in detail according to composition. The largest d values (approximately 42-4 A) are observed for the lowest LAS concentrations, while the largest number of separate reflections (five) occurs for samples with approximately 44-50% LAS, both at the highest temperatures. Although there are some differences in the data between heating and cooling cycles, the d values return to the original value at low temperature. There are no observable transitions in DSC, nor is there any heterogeneity in the lamellar phase observable by microscopy. The data clearly indicate that there is some lateral separation of the different LAS isomers within the bilayers, which results in the formation of local lamellar regions having different surfactant compositions. This lateral phase separation may arise from the presence of an (electrostatic) attractive interaction, which gives rise to an upper consolute loop within the lamellar phase region of a pure LAS isomer. Similar mechanisms may occur in biological membranes and could be responsible for the occurrence of membrane lipid patches.

Femtosecond diffractive imaging with a soft-X-ray free-electron laser

Theory predicts that with an ultrashort and extremely bright coherent X-ray pulse, a single diffraction pattern may be recorded from a large macromolecule, a virus, or a cell before the sample explodes and turns into a plasma. Here we report the first experimental demonstration of this principle using the FLASH soft X-ray free-electron laser. An intense 25 fs, 4 x 10{sup 13} W/cm{sup 2} pulse, containing 10{sup 12} photons at 32 nm wavelength, produced a coherent diffraction pattern from a nano-structured non-periodic object, before destroying it at 60,000 K. A novel X-ray camera assured single photon detection sensitivity by filtering out parasitic scattering and plasma radiation. The reconstructed image, obtained directly from the coherent pattern by phase retrieval through oversampling, shows no measurable damage, and extends to diffraction-limited resolution. A three-dimensional data set may be assembled from such images when copies of a reproducible sample are exposed to the beam one by one.

Speckle Patterns with Atomic and Molecular de Broglie Waves

We have developed a nozzle source that delivers a continuous beam of atomic helium or molecular hydrogen having a high degree of transverse coherence and with adequate optical brightness to enable new kinds of experiments. Using this source we have measured single slit diffraction patterns and the first ever speckle-diffraction patterns using atomic and molecular de Broglie waves. Our results suggest fruitful application of coherent matter beams in dynamic scattering and diffractive imaging at short wavelength and with extreme surface sensitivity.