Series Of Diffraction Patterns Research Articles

Actinic patterned mask imaging using extreme ultraviolet ptychography microscope with high harmonic generation source

Extreme ultraviolet (EUV) lithography is expected to be used for 3 nm technology nodes and beyond, yet the need for actinic mask metrology and inspection remains a critical challenge. In this study, we demonstrate an EUV ptychography microscope as a high-harmonic generation-based actinic mask imaging tool. A series of diffraction patterns on an EUV mask is used to reconstruct both the amplitude and phase information of the periodic patterns using ptychographic algorithms. The results show that the EUV ptychography microscope has the potential for determining the actinic metrology of EUV masks and providing phase information for EUV mask development.

Emergence of anomalous dynamics in soft matter probed at the European XFEL

Dynamics and kinetics in soft matter physics, biology, and nanoscience frequently occur on fast (sub)microsecond but not ultrafast timescales which are difficult to probe experimentally. The European X-ray Free-Electron Laser (European XFEL), a megahertz hard X-ray Free-Electron Laser source, enables such experiments via taking series of diffraction patterns at repetition rates of up to 4.5 MHz. Here, we demonstrate X-ray photon correlation spectroscopy (XPCS) with submicrosecond time resolution of soft matter samples at the European XFEL. We show that the XFEL driven by a superconducting accelerator provides unprecedented beam stability within a pulse train. We performed microsecond sequential XPCS experiments probing equilibrium and nonequilibrium diffusion dynamics in water. We find nonlinear heating on microsecond timescales with dynamics beyond hot Brownian motion and superheated water states persisting up to 100 μs at high fluences. At short times up to 20 μs we observe that the dynamics do not obey the Stokes-Einstein predictions.

Further improvements to the ptychographical iterative engine

Ptychography is a form of phase imaging that uses iterative algorithms to reconstruct an image of a specimen from a series of diffraction patterns. It is swiftly developing into a mainstream technique, with a growing list of applications across a range of imaging modalities. As the field has advanced, numerous reconstruction algorithms have been proposed, yet the early approaches have not seen major improvement and remain popular. In this paper, we revisit the first such algorithm, the ptychographical iterative engine (PIE), and show how a simple revision and powerful extension can deliver an order of magnitude speed increase and handle difficult data sets where the original version fails completely.

PyNX.Ptycho: a computing library for X-ray coherent diffraction imaging of nanostructures

X-ray imaging techniques have undergone a remarkable development during the past decade, taking advantage of coherent X-ray sources. Among these techniques, ptychography allows reconstruction of the specimen and the illumination probe from a series of diffraction patterns without any prior knowledge about the sample. However, the reconstruction of the ptychographic data remains challenging and the reconstruction software is often not publicly available. Presented here is an open-source library for the reconstruction of two-dimensional ptychographic data, written in Python. This library implements existing algorithms, with examples of data reconstruction on both simulated and experimental (Bragg ptychography on heterogeneous strained InAs/GaAs nanowires) data sets. It can be used for educational (simulation) purposes or experimental data analysis, and also features an OpenCL version of the ptychography algorithm for high-performance computing.

Neutron diffraction on functional materials under electric field or mech. load

In this contribution neutron diffraction studies on functional materials under special environmenal conditions will be presented. In particular, studies of ferroelectric ceramics under high electric fields as well as shape memory alloys under mechanical load will be highlighted. The investigations were carried out at the high-resolution neutron powder diffractometer SPODI (FRM II / Garching n. Munich) which offers special sample environmenal tools for electric fields, mechanical load etc. In-situ studies on ferroelectrics under the influence of high electric fields enable to establish correlations between the macroscopic poling behaviour and corresponding structural changes. The investigations were carried out on technologically applied lead zirconate titanate based samples and on a bismuth sodium titanate based system. A self-designed device allows the investigation of large bulk samples under different orientations of the electric field. This method allows to analyze the poling mechanisms in technical ferroelectrics, such as piezoelectric effect, domain reorientation and phase transformations. In the system Bi0.5Na0.5TiO3 - BaTiO3 – K0.5Na0.5NbO3 the large recoverable field-induced strain could be attributed to a reversible field-induced phase transition from an almost non-polar, pseudocubic tetragonal phase to a distorted, ferroelectric active phase [1]. Polycristalline monoclinic nickel-titanium shape memory alloys have been investigated under mechanical load to analyze their stress-strain behaviour and to derive the elastic constants. A novel tensile rig allows to orient the load axis in a Eulerian cradle like manner. The elastic constants tensor could be calculated based on a series of diffraction patterns under different sample orientations in the initial state and under 0.6 % strain. Furthermore the contributions of elastic deformation (lattice dilatation) and inelastic deformation (orentation of twins) to the total strain could be separated.

Structured-illumination-based lensless diffractive imaging and its application to optical image encryption

In this paper, we propose a new method in the structured-illumination-based lensless diffractive imaging using variable grating pitches. When a phase grating pitch is sequentially changed, a series of diffraction patterns can be recorded by a charge-coupled device (CCD) camera. Subsequently, a phase retrieval algorithm with a rapid convergence rate is developed to recover a high-quality object from the recorded diffraction patterns. The proposed method is further applied to optical image encryption, and simulation results are presented to demonstrate validity of the proposed method.

Experimental study of annular bright field (ABF) imaging using aberration-corrected scanning transmission electron microscopy (STEM)

Experimental parameters used in the annular bright field (ABF) imaging method were tested using images simulated with the multislice method. Images simulated under identical conditions were found to agree well with experimental images. The ABF technique was shown to be relatively insensitive to the sample thickness and the defocus. In experimental ABF images, atomic columns exhibited dark contrast over a wide range of specimen thickness and defocus values, from 10 to 70nm and −20 to +20nm, respectively. A series of diffraction patterns at atomic columns, obtained using the diffraction imaging method, exhibited higher intensities in their central regions (0–11mrad) for light elements and in their peripheral regions (11–22mrad) for heavy elements. The results indicated that the contrast of light elements is enhanced by subtraction of the central region of the transmitted beam, since this is blocked by a circular mask in the ABF-STEM technique. Thus, the overall contrast of light elements is greatly improved, allowing them to be clearly visualized.

Astigmatic electron diffraction imaging: a novel mode for structure determination

In a conventional transmission electron microscope, stigmators are used to correct for the effects of axial astigmatism in the diffraction lens. It seems feasible that these same stigmators could also be used to form a series of 'astigmatic' diffraction patterns. It is shown how this series of diffraction patterns could then be used to perform exit-surface wavefunction reconstruction. This has the advantage that the diffraction patterns are not resolution limited by the objective aperture as are images when performing exit-surface wavefunction reconstruction from a focal series. A scheme for carrying out phase reconstruction from a series of astigmatic diffraction patterns in an electron microscope is presented.

Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm.

We propose an iterative phase retrieval method that uses a series of diffraction patterns, measured only in intensity, to solve for both amplitude and phase of the image wave function over a wide field of view and at wavelength-limited resolution. The new technique requires an aperture that is scanned to two or more positions over the object wave function. A simple implementation of the method is modeled and demonstrated, showing how the algorithm uses overlapping data in real space to resolve ambiguities in the solution. The technique opens up the possibility of practical transmission lensless microscopy at subatomic resolution using electrons, x rays, or nuclear particles.

Temperature resolved X-ray diffraction as a tool of thermal analysis

Time and temperature resolved X-ray diffraction was used for thermal analysis. Series of diffraction patterns were measured, while the samples are heated/cooled stepwise or isothermally with freely selectable temperature programs.

Transmission electron microscopy of Cd3As2 and eutectoid Cd3As2-As crystals

Cadmium arsenide, Cd3As2, is a narrow band-gap semiconductor with forbidden energy gap of 0.14 eV. The electron density in as-grown n-type crystals is as high as 2 3 10 my3 [1] and electron mobilities have been reported from 0.3 to 2.0 m Vy1 sy1 at 300 K, while approaching 28 m Vy1 sy1 at 4.2 K [2, 3] making them suitable for photo detectors, thermal detectors, ultrasonic multipliers, and Hall generators [4, 5]. Hence, crystal and band structures remain of interest [6]. Its accepted crystal structure is tetragonal with a ˆ 1:267 nm, c ˆ 2:548 nm and space group I41cd [7]. This work examined the crystal structure of Cd3As2 and lattice defects using transmission electron microscopy (not reported on bulk material). Crystals were grown by sublimation under two sets of conditions, by transport within an evacuated silica ampoule in a temperature gradient with condensation occurring above the solid-solid phase transition of 578 8C [8], and in an argon gas ow with recondensation in a temperature region of 335 8C to 385 8C as described by Lovett [9]. Specimens for electron microscopy were prepared by grinding and polishing followed by argon ion etching. Intensities and d-values of diffraction peaks for Cd3As2 obtained by powder X-ray diffractometry are as reported by Steigmann and Goodyear [7], supporting a body-centred tetragonal with a unit cell of 16 cubes. In each cube, the As ions are arranged approximately cubic close-packed (f.c.c.), and the Cd ions are tetrahedrally co-ordinated. Certain of the cadmium ions are shifted from their idealized positions by approximately 0.02 nm, and others by 0.025 nm. The arsenic ions are also displaced and As±As bond lengths vary from 0.448 to 0.47 nm. These ionic displacements lead to violation of extinction conditions in this structure. A series of electron diffraction patterns of Cd3As2 were obtained using a JEM-200CX transmission electron microscope (TEM). A reciprocal lattice cell, as shown in Fig. 1, was reconstructed using these electron diffraction patterns. The lattice parameters thus derived are a  1:26(7) nm, and c  2:54(8) nm. Part of the series of diffraction patterns is shown in Fig. 2. These diffraction patterns can be indexed unambiguously based on the lattice parameters obtained above. The zone axes for each diffraction pattern are [0 0 1], [2 0 1], [1 0 0], [2 1 0], and [1 1 1], respectively. However, there are additional diffractions which are not observed in the X-ray powder diffraction spectrum. These diffractions are forbidden re ections. Their occurrence in electron diffraction patterns is because of the displacements of cadmium and arsenic ions from their exact positions in the unit cell, and because of double diffraction. For example, in the pattern of Fig. 2c, there is a column of diffraction spots between 0 0 0 and 0 4 0 and three rows of diffraction spots between 0 0 0 and 0 0 8, and all the alternative columns and rows which are parallel to these. These are forbidden re ections in this structure. The faint diffraction spot of (0 0 4) in Fig. 2c becomes a strong re ection in Fig. 2d due to double diffraction of (1 2 1)‡ (1 2 3) ˆ (0 0 4). All the faint spots in Fig. 2e are forbidden diffractions, but their occurrences are due to ionic displacements, and not because of double re ections. The appearances of forbidden re ections due to ionic displacements depend also on the specimen thickness. Fig. 2f is a diffraction pattern with the electron beam parallel to [1 1 1], but is taken from a thinner specimen and is more populated with forbidden diffractions such as (h h 0) or (0 k k). Certain patterns from samples prepared under the second set of growth conditions exhibited different symmetry. Energy dispersive X-ray analysis of these distinguishable crystalline regions showed them to be arsenic. A eutectoid mixture of Cd3As2 and As with up to ,5 at % As was observed by Carpenter et al. [10] in ®lms of evaporated Cd3As2 as prepared using a pulsed-laser technique. In the present work, the proportion of As in the (Cd3As2 ±As) eutectoid was less than ,0.1 at %. Electron diffraction patterns of these arsenic phases indicated that their structure is orthorhombic with parameters a ˆ 0:71(3) nm, b ˆ 0:73(3) nm, c ˆ 1:25(1) nm and with space group Pnnn, rather than hexagonal. Electron diffraction patterns with zone axes [1 0 0] and [1 3 0] are shown in Fig. 3. The new arsenic unit cell is possibly due to the presence in solution of low levels of cadmium below the detection level of EDS X-ray analyser (Link Systems, 860 series II). Using bright-®eld and dark-®eld imaging, structural defects were observed within the Cd3As2 crystals and within the new phase of arsenic.

Electron radiation damage to protein crystals of bacteriorhodopsin at different temperatures

A series of diffraction patterns from two-dimensional protein crystals of bacteriorhodopsin (purple membrane) at different temperatures (294 K, 98 K and 4 K) were recorded as the diffraction spots faded due to radiation damage. The patterns were then computationally evaluated in order to obtain a quantitative measurement of the structural preservation while irradiating the specimen. To provide statistically significant results, diffraction spots corresponding to spacings of 3Å(1200 spots) and 7Å(600 spots) were measured. A substantial increase of the lifetime of high resolution spots was found using liquid nitrogen as a coolant, whereas further structural preservation at liquid helium temperature was significant but smaller. It appears likely therefore that high resolution images are accessible even at liquid nitrogen temperature. Mechanical stability and the absence of thermal specimen drift are certainly of equivalent importance for successful high resolution imaging.

Simplified analysis of helium scattering: supernumerary rainbows from a soft, corrugated potential

This paper presents a simple, but quantitative approach to the analysis of helium diffraction from surfaces. Instead of calculating the intensities of helium diffraction beams, we analyze the locations of the supernumerary rainbows, or oscillations in the intensity envelope of the diffraction beams. Within a semiclassical framework, we interpret the supernumerary rainbows in terms of the phase integrals associated with the different classical scattering trajectories. Using a perturbation theory to calculate the classical trajectories, we obtain a simple, closed formula which predicts the locations of the supernumerary rainbows as a function of the scattering angle. This formula includes a correction for the softness of the scattering potential. Since the soft-potential effect depends strongly on the angle between the incoming and outgoing trajectories, our scattering formula can be used to extract both the corrugation and the decay length of the scattering potential from a series of diffraction patterns taken at various angles of incidence. The results of our perturbative semiclassical analysis are in good agreement with those of exact quantum-mechanical calculations.

Application of time and temperature resolved x-ray diffraction (TRXRD) to thermal analysis

The application of TRXRD for thermal analysis is demonstrated using examples of phase transitions, solid-state reactions and high-temperature corrosion. The measuring system produces a series of diffraction patterns, which are evaluated by a difference procedure that a reduces the data to curves comparable to DSC and TG curves and thus suited to kinetic evaluation.

Electron diffraction simulation on Micro-VAX II computers with the aid of an array processor

A computer program for 2-d electron diffraction pattern simulation has been developed under the DEC Micro-VAX II/Micro-VMS environment. Diffraction patterns or images formed by focusing an electron beam of arbitrary energy on a sample can be simulated. The 3-d sample structure can be either pre-calculated or on-line generated based on the symmetry and other necessary information provided by the user. The output is a series of diffraction patterns or images, at the user's choice, from equal intervaled thicknesses of the sample. By using the multi-slice method, the effect of multiple scattering of electrons by a crystal is taken into account. An array processor is utilized to speed up the calculations which involves mostly 2-d arrays.

Quasicrystal structures in submicron spheres of pure nickel and nickel-chromium alloys

The icosahedral quasicrystal with a fivefold rotation symmetry was first reported in Al-M (M = Cr, Mn, Fe) alloys. Later, quasicrystals with eightfold, tenfold, and twelvefold rotation symmetries were also reported. A twelvefold symmetry has been found in a Ni-70.6 at%Cr alloy and an eightfold symmetry has been found in a Cr-Ni-Si alloy. This indicates a potential for nickel-chromium alloys to form the quasicrystal phase.An intermediate state between crystalline and quasicrystalline states is also discussed by Li, Teng, et. al. in an Al-Cu-Mg alloy due to the coexistence of micro-quasicrystal and micro-crystal grains. When regions larger than 1 nm are measured, a coherent boundary is found between micro-quasicrystal and micro-crystal grains.A diffraction pattern with seemingly twelvefold symmetry is found in pure nickel and Ni-20at%Cr sphere of about 25 nm diameter as shown in Figure 1. The diffraction patterns do not have true twelvefold symmetry but the first diffraction ring is found to have twelve diffracted spots. Similar structures are found in Ni-10at%Cr and shown in Figure 2 with a series of diffraction patterns.

Microdiffraction in Dedicated STEM

Microdiffraction in dedicated STEM instruments has shown considerable promise as a source of microanalytical information. A major problem has been the relatively inefficient sequential methods used to obtain the diffraction pattern. The apparatus shown schematically in Fig. 1 has facilitated parallel viewing and recording of diffraction patterns in the HB5 STEM. The equipment is robust, low cost and can be installed with no modifications to the microscope.A series of diffraction patterns were recorded under identical conditions at a (110) zone axis in an Al-4% Cu foil shown in Fig. 2(a) to allow direct comparison of sequential and parallel recording methods. The thickness in this part of the foil was ∼220 nm as measured from the projected widths of θ' plates. The selected area “rocking beam” images in Figs. 2(b) and (d) are clearly noisy, suffer from scan distortions and their usefulness for phase identification and crystal orientation is severely limited.

Use of the Culgoora Radioheliograph for the Generation of Diffraction Patterns

A series of diffraction patterns produced with the electronic imaging system of the Culgoora radioheliograph is presented. These patterns serve both to illustrate the quality of this type of imaging system and to demonstrate the advantage, in special circumstances, of constructing a radio-frequency simulation of an optical imaging device.

Disappearance Voltage Determinations Using a Convergent Beam

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Surface Structures Formed during the Interaction of Sulphur Compounds with the (111) Face of Nickel

The interaction of hydrogen sulphide, n-propyl mercaptan, and dimethyl disulphide with the (111) and (100) faces of nickel has been studied by LEED at temperatures up to 700 K. During interaction and subsequent annealing, in vacuo below 10−9 Torr at temperatures up to 1200 K, series of diffraction patterns were observed. Four of the patterns on (111) have been attributed to coincidence nets arising from structures which involve rearrangement and reorientation to (100) type layers. The patterns are described and the interpretations discussed.