Experimental Diffraction Patterns Research Articles

Charge mobility calculation of organic semiconductors without use of experimental single-crystal data

Prediction of material properties of newly designed molecules is a long-term goal in organic electronics. In general, it is a difficult problem, because the material properties are dominated by the unknown packing structure. We present a practical method to obtain charge transport properties of organic single crystals, without use of experimental single-crystal data. As a demonstration, we employ the promising molecule C10–DNBDT. We succeeded in quantitative evaluation of charge mobility of the single crystal using our quantum wave-packet dynamical simulation method. Here, the single-crystal data is computationally obtained by searching possible packing structures from structural formula of the molecule. We increase accuracy in identifying the actual crystal structure from suggested ones by using not only crystal energy but also similarity between calculated and experimental powder X-ray diffraction patterns. The proposed methodology can be a theoretical design technique for efficiently developing new high-performance organic semiconductors, since it can estimate the charge transport properties at early stage in the process of material development.

Preliminary exploration of hard X-ray coherent diffraction imaging method at SSRF

Coherent X-ray diffraction imaging (CDI) method is a powerful X-ray imaging technique with high resolution up to nanometer scale. Most of the synchrotron radiation facilities and free electron laser facilities are equipped with this state-of-the-art imaging technique and have made many outstanding achievements in multiple scientific areas. Up to now, although scanning CDI (ptychography) method based on a soft X-ray source has been opened to users, the hard X-ray CDI experimental platform has not been built at Shanghai Synchrotron Radiation Facility (SSRF) which can research some relatively thick specimens and easily extend to three-dimensional imaging. As some new beamlines with undulator source were put into operation recently, it is possible and feasible to build up the CDI experimental platform with hard X-ray. In this article, we report the hard X-ray CDI experimental platform development process and preliminary experimental results of coherent diffraction pattern and image reconstruction at SSRF. Based on the operating BL19U2 biological small-angle X-ray scattering (SAXS) beamline at SSRF, the hard X-ray coherent beam is obtained through effective optical path designation at 12 keV and 13.5 keV. The hard X-ray optimization includes tuning several slits, double crystal monochromator (DCM), horizontal deflection mirror, focusing mirror system and pinhole, etc. Furthermore, hard X-ray CDI experiments are conducted. The spatial coherent length of the incident beam is also measured from the pinhole diffraction pattern. This platform can provide both conventional mode and scanning mode (ptychography) for the coherent diffraction imaging method, and the correct image reconstruction from the experimental diffraction patterns proves that the platform has the experimental capability for hard X-ray CDI. In the conventional forward scattering CDI mode, coherent diffraction patterns of pinhole are collected and used to analyse the coherence property of the optimized X-ray beam. The structure of pinhole is also reconstructed from the diffraction pattern. In the scanning CDI mode, a zone plate is used as a sample. The central area of zone plate is reconstructed correctly. About 90 nm/pixel resolution of reconstruction is achieved which is extremely dependent on the X-ray flux density from the undulator source emission. Hard X-ray CDI experimental platform based on the synchrotron radiation facility is first built in China. It will provide effective software and hardware supporting for the development and application of hard X-ray CDI experiments in China in the future.

Refinement for single-nanoparticle structure determination from low-quality single-shot coherent diffraction data.

With the emergence of X-ray free-electron lasers, it is possible to investigate the structure of nanoscale samples by employing coherent diffractive imaging in the X-ray spectral regime. In this work, we developed a refinement method for structure reconstruction applicable to low-quality coherent diffraction data. The method is based on the gradient search method and considers the missing region of a diffraction pattern and the small number of detected photons. We introduced an initial estimate of the structure in the method to improve the convergence. The present method is applied to an experimental diffraction pattern of an Xe cluster obtained in an X-ray scattering experiment at the SPring-8 Angstrom Compact free-electron LAser (SACLA) facility. It is found that the electron density is successfully reconstructed from the diffraction pattern with a large missing region, with a good initial estimate of the structure. The diffraction pattern calculated from the reconstructed electron density reproduced the observed diffraction pattern well, including the characteristic intensity modulation in each ring. Our refinement method enables structure reconstruction from diffraction patterns under difficulties such as missing areas and low diffraction intensity, and it is potentially applicable to the structure determination of samples that have low scattering power.

Features of the Real Structure of Metallic Silver Nanoparticles Located in Channels of Mesoporous Silicate SBA-15

The features of diffraction on silver nanoparticles located in channels of mesoporous silicate SBA-15 are analyzed. A computer simulation of diffraction patterns is performed for crystallites with different sizes, the cubic structure, and stacking faults. The experimental diffraction patterns are compared with simulated ones. Together with the stacking fault concentration, the average crystallite sizes are determined in the direction normal to the close packed layers and along the layers in the crystal structure.

Orientation Relationships and Lattice Misfit between a Nb Matrix and γ-Silicide in a Nb–Si Composite

Orientation relationships {110}Nb||{100}γ and 〈111〉Nb||〈001〉γ between the crystal lattices of the Nb solid solution and particles of γ-silicide Nb5Si3 were determined by transmission electron microscopy. The following two types of matching planes were found: {110}Nb||{100}γ and {111}Nb||{001}γ. The former planes form steps at an angle of 120°. The correctness of the calculated orientation relationships was confirmed and these relationships were compared with experimental electron diffraction patterns using methods of mathematical modeling, which enable one to obtain superimposed electron diffraction patterns of several phases and tilt the model crystal. An interface model in two sections was constructed. The morphology of the interface between the particle and the matrix was explained in terms of structural features. The lattice misfit between the matrix and γ-silicide was calculated.

Optical microscopy for measuring tapered fibers beyond the diffraction limit.

We describe a technique that allows the improvement of the resolution of optical microscopes for nanofiber measurements beyond the diffraction limit. It can be readily implemented on any microscope. We demonstrated it by measuring tapered fibers radii from 0.4 to 4 µm with a resolution below the diffraction limit, from a few nanometers up to 50 nm in the worst case, depending on the radii. This technique is a non-contact measurement with the microscope objective placed a few centimeters from the nanofiber. We acquire the experimental diffraction pattern by scanning the object plane of the microscope system, upstream and downstream the nanofiber. We compare this experimental diffraction pattern to a bank of all the simulated patterns for all the radii. The radius of the simulated diffraction pattern that best matches to the experimental one is the sought radius.

Determination of the phase composition of partially dehydroxylated kaolinites by modelling their X-ray diffraction patterns

AbstractModelling of experimental X-ray diffraction (XRD) patterns is used to determine the phase composition of partially dehydroxylated kaolinite samples. To identify unambiguously the presence of two or three phases in the heated kaolinite samples, the full range of their XRD patterns has to be analysed. Two different kaolinites, from Imerys (UK) and from Georgia (USA; KGa-21), were studied. The heating temperatures were selected to cover the entire range of dehydroxylation for both kaolinites (400–550°C for Imerys and 400–495°C for KGa-21). Two different dehydroxylation pathways were observed. At each stage of partial dehydroxylation, the kaolinite from Imerys consisted of the original, non-dehydroxylated kaolinite and of a fully dehydroxylated phase, metakaolinite. During partial dehydroxylation of kaolinite KGa-21, each product formed at a given heating temperature consisted of three phases: the original kaolinite; a dehydroxylated phase, metakaolinite; and a phase with diffraction features corresponding to a defective kaolinite-like structure. To determine the content of metakaolinite in a partially dehydroxylated specimen, its experimental XRD pattern was reproduced by the optimal summation of the diffraction patterns of the initial kaolinite and metakaolinite. A procedure that reveals the basic diffraction features of the third phase is suggested. The XRD patterns and thus the structures of the metakaolinites formed after dehydroxylation of the Imerys and KGa-21 samples differ substantially. The conventional determination of the initial kaolinite and metakaolinite contents in partially dehydroxylated kaolinite based on the analysis of basal reflections and weight losses may lead to overlooking the formation of the intermediate phases.

Cluster-based CaII, MgII and CdII coordination polymers based on amino-functionalized tri-phenyl tetra-carboxylate: Bi-functional photo-luminescent sensing for Fe3+ and antibiotics

Excess and deficiency of iron(III) and antibiotics from normal permissible limits will induce serious disorders, so their detection is important but challenging. In this work, the asymmetric amino-functionalized tetra-carboxylate H4L (2′-amino-1,1’:4′,1″-terphenyl-3,3″,5,5″-tetracarboxylic acid) containing large conjugated ter-phenyl aromatic backbones have been synthesized and employed. Through a one-pot powerful solvo-thermal synthetic strategy, a series of unique tri-nuclear cluster-based CaII, MgII and CdII coordination polymers, namely [Ca1.5(μ8-HL)(DMF)]n (1), {[Mg1.5(μ7-HL)·(H2O)2]·3H2O}n (2) and {[Cd1.5(μ10-L)0.75]n·H2O·DMF}n (3) have been successfully prepared. 1–3 exhibit excellent photo-luminescent properties and good fluorescence stability. Structural analyses reveal that tri-nuclear CaII secondary building blocks (SBUS) are linked via HL3−, forming the 2D clustered-based micro-porous coordination polymer 1. As for 2, three carboxylate groups of partly de-pronated HL3− also link these neighboring tri-nuclear MgII SBUS, which constructs the 2D MgII coordination framework 2. As for 3, fully de-pronated L4− also links these neighboring tri-nuclear CdII SBUS, which ultimately constructs the 3D micro-porous coordination framework 3. Experimental powder x-ray diffraction (PXRD) patterns coincide well with the theoretical patterns, which indicate that we have successfully synthesized the pure phase material 1–3. Photo-luminescent experiments demonstrate that coordination polymers 1–3 can be successfully applied towards bi-functional sensing for sensitive detection of Fe3+ and the antibiotics NZF (Nitrofurazone). To the best of our knowledge, this is the first example of the application of amino-functionalized tri-phenyl tetra-carboxylate based MOFs towards bi-functional discrimination of Fe3+ and NZF antibiotics with high efficiency Ksv values (For Fe3+: 7.28 × 104 M−1 for 1; 3.38 × 104 M−1 for 2 and 3.29 × 104 M−1 for 3 and for NZF antibiotics: 4.47 × 103 M−1 for 1; 4 × 103 M−1 for 2 and 5.6 × 103 M−1 for 3).

Structure of Hydrated Crystal (Lc), Tilted Gel (Lβ'), and Liquid Crystal (Lα) Phases of Linear Alkylbenzene Sulfonate (LAS) Studied by X-ray Diffraction and Molecular Dynamics Simulation.

Precipitation of crystals in aqueous surfactant solutions hampers their use as liquid detergents. Understanding the molecular structure that causes the crystal formation is of key importance in designing a new surfactant. In this study, we first identified the hydrated crystal (Lc) structure of linear alkylbenzene sulfonate (LAS) at ambient temperature by combining X-ray diffraction (XRD) with all-atom molecular dynamics (MD) simulation. It is known that the Lc domain involves only a stoichiometrically small number of water molecules, and the water number of existing interlamellar layers may change when the system shows the thermally induced phase transition. Therefore, we explored possible crystal structures with five different hydration levels of 0, 0.5, 1, 2, and 4 water per LAS using MD simulations with the d-spacing measured by XRD. Among them, only the diffraction pattern calculated for the monohydrate LAS well coincided with the experimental diffraction pattern at 300 K. A structural change of the monohydrate from the Lc phase to the tilted gel (Lβ') phase was also observed by heating from 300 to 360 K in the MD simulations, where a cross-sectional structure of the alkyl groups of LAS molecules changed from a face-centered rectangular lattice to a hexagonal one. Further heating to 400 K resulted in a disordered liquid crystal (Lα) phase. Thus, configurational changes of the detergent during thermally induced phase transitions were well explored and characterized by MD simulations with the aid of XRD data. This approach can be broadly applied where we explore the phase behavior of hydrated crystals of any surfactant species.

Role of the strained substrate in the x-ray diffraction of free-standing epitaxial nanostructures under grazing incidence conditions

Semiconductor heteronanostructures are of interest for a vast field of applications in optoelectronics. Fast and reliable characterization of their structural properties is of high importance for industry and science. By the example of free-standing ${\mathrm{In}}_{0.6}{\mathrm{Ga}}_{0.4}\mathrm{As}$ quantum dots (QDs), we discuss the contributions of the strained epitaxial surface nanostructures and the substrate to the scattered x-ray intensity under grazing incidence conditions. In the frame of the distorted wave Born approximation, we take into account multiple scattering and coherent interactions of the x-ray beams involved in the diffraction process. Employing the finite-element method, we give a detailed analysis of the strain distribution inside the nanostructure and the substrate. Further, analyzing the experimental and simulated x-ray diffraction patterns in x-ray grazing incidence diffraction, we demonstrate the importance of accounting for strain in the substrate and interference effects between the surface and the QDs for strain analysis of the nano-objects. The advantages of our approach are demonstrated by comparison with the standard isostrain approach that is commonly used for strain analysis of the nanostructures. We show that neglecting the substrate contribution to the x-ray scattering causes errors in the standard isostrain approach. Finally, the substrate contribution itself may yield information sufficient for a novel and fast approach for the structural characterization of strained semiconductor heteronanostructures.

Many-beam dynamical scattering simulations for scanning and transmission electron microscopy modalities for 2D and 3D quasicrystals

ABSTRACTWe present a general theory of electron scattering from both 2D and 3D quasicrystals, applicable to both transmission (forescatter) and scanning (backscatter) geometries. Specifically, simulations of conventional zone axis diffraction patterns, convergent beam diffraction patterns and electron backscatter diffraction for decagonal AlNiCo are presented. As expected, the geometry of the diffraction pattern is similar to kinematical patterns, but the intensity distributions show strong dynamical effects in all the modalities. Experimental electron backscatter diffraction patterns for AlNiCo are compared to simulated patterns for this 2D quasicrystalline structure as well as one of its crystalline monoclinic approximant phases, CoAl. While the simulated patterns from the quasicrystalline and approximant phases are very similar to the experimental patterns, direct comparison shows a better agreement with the decagonal phase.

Indexing grazing-incidence X-ray diffraction patterns of thin films: lattices of higher symmetry.

Grazing-incidence X-ray diffraction studies on organic thin films are often performed on systems showing fibre-textured growth. However, indexing their experimental diffraction patterns is generally challenging, especially if low-symmetry lattices are involved. Recently, analytical mathematical expressions for indexing experimental diffraction patterns of triclinic lattices were provided. In the present work, the corresponding formalism for crystal lattices of higher symmetry is given and procedures for applying these equations for indexing experimental data are described. Two examples are presented to demonstrate the feasibility of the indexing method. For layered crystals of the prototypical organic semiconductors di-indeno-perylene and (ortho-di-fluoro)-sexi-phenyl, as grown on highly oriented pyrolytic graphite, their yet unknown unit-cell parameters are determined and their crystallographic lattices are identified as monoclinic and orthorhombic, respectively.

Search for common minima in joint optimization of multiple cost functions

We present a novel optimization method, named the Combined Optimization Method (COM), for the joint optimization of two or more cost functions. Unlike the conventional joint optimization schemes, which try to find minima in a weighted sum of cost functions, the COM explores search space for common minima shared by all the cost functions. Given a set of multiple cost functions that have qualitatively different distributions of local minima with each other, the proposed method finds the common minima with a high success rate without the help of any metaheuristics. As a demonstration, we apply the COM to the crystal structure prediction in materials science. By introducing the concept of data assimilation, i.e., adopting the theoretical potential energy of the crystal and the crystallinity, which characterizes the agreement with the theoretical and experimental X-ray diffraction patterns, as cost functions, we show that the correct crystal structures of Si diamond, low quartz, and low cristobalite can be predicted with significantly higher success rates than the previous methods.

Analysis of theoretical and experimental X-ray diffraction patterns for distinct mordenite frameworks

Experimental and theoretical XRD patterns of mordenite frameworks were correlated in this work. The experimental XRD analysis showed that the incorporation of Ag and Fe ions in mordenite modified the intensity of peaks in the diffraction patterns. For theoretical studies, two framework models of mordenite (MOR6 and MOR7) were used. Theoretical results conducted through DFT computational simulations were able to predict correctly the angular positions of the experimental peaks observed in XRD patterns. These theoretical results showed that the ion exchange of $${\hbox {Na}^{+}}$$ by $${\hbox {Ag}^{+}}$$ cations in the zeolitic framework leads to a decrease in intensity of XRD peaks {2 0 0}, {0 2 0} and {1 5 0}, similar to observed experimentally. This is caused by local structural rearrangements produced by the ion exchange. For $${\hbox {Fe}}$$ incorporation in zeolite, two options were considered theoretically: ion exchange and isomorphous substitution of $${\hbox {Al}^{3+}}$$ in tetrahedral positions.

Moiré structures in twisted bilayer graphene studied by transmission electron microscopy

We investigate imaging of moiré structures in free-standing twisted bilayer graphene (TBG) carried out by transmission electron microscopy (TEM) in diffraction and in-line Gabor holography modes. Electron diffraction patterns of TBG acquired at typical TEM electron energies of 80–300 keV exhibit the diffraction peaks caused by diffraction on individual layers. However, diffraction peaks at the scattering angles related to the periodicity of the moiré structure have not been observed in such diffraction patterns. We show that diffraction on moiré structure can create intense diffraction peaks if the energy of the probing electrons is very low, in the range of a few tens of eV. Experimental diffraction patterns of TBG acquired with low-energy electrons of 236 eV exhibiting peaks attributed to the moiré structure periodicity are shown. In holography mode, the intensity of the wave transmitted through the sample and measured in the far-field can be enhanced or decreased depending on the atomic arrangement, as for example AA or AB stacking. Thus, a decrease of intensity in the far-field must not necessarily be associated with some absorption inside the sample but can simply be a result of a particular atomic arrangement. We believe that our findings can be important for exploiting graphene as a support in electron imaging.

Roles of Hydration and Magnetism on the Structure of Ferrihydrite from First Principles

We report density functional theory calculations aimed at predicting thermodynamically stable structures for ferrihydrite across a range of possible compositions determined by the amount of structural water. Based on an assumed formula unit of Fe5O8H + nH2O, we performed ab initio calculations with evolutionary searching to find the lowest enthalpy structures as a function of the water content up to n = 2. This is the most exhaustive search for the ferrihydrite structure conducted so far; more than 5000 unique configurations were generated and evaluated over five states of hydration. Among them, the Michel akdaliate model was generated, along with several energetically comparable new structures at higher states of hydration. However, a direct comparison between calculated and experimental pair distribution function and X-ray diffraction patterns for the 50 lowest energy structures shows that none beyond the Michel model could be associated with ferrihydrite. Nevertheless, this energetically comparable str...

Phase analysis of hydrated Portland cement

The paper studies the quantitative phase composition in cement paste using the Rietveld refinement method. Investigations are carried out within 0–67 h time period at 40, 50 and 70 °C. It is found that tobermorite, deliate and mCanH2O10Si2 are major phases in cement phase, where m = 5 or 3, and n = 3 or 1. The phase composition is determined by the contribution from estimated peak intensities to the integrated peak intensity which, in turn, is compared to the experimental diffraction patterns. The volume fractions of the studied phases are measured. It is found that the time and temperature of isothermal curing significantly affect the structure of the cement paste.

Single-particle imaging without symmetry constraints at an X-ray free-electron laser.

The analysis of a single-particle imaging (SPI) experiment performed at the AMO beamline at LCLS as part of the SPI initiative is presented here. A workflow for the three-dimensional virus reconstruction of the PR772 bacteriophage from measured single-particle data is developed. It consists of several well defined steps including single-hit diffraction data classification, refined filtering of the classified data, reconstruction of three-dimensional scattered intensity from the experimental diffraction patterns by orientation determination and a final three-dimensional reconstruction of the virus electron density without symmetry constraints. The analysis developed here revealed and quantified nanoscale features of the PR772 virus measured in this experiment, with the obtained resolution better than 10 nm, with a clear indication that the structure was compressed in one direction and, as such, deviates from ideal icosahedral symmetry.

Synthesis and Magnetic Properties of Solid Solutions of Ferromagnetic Layered Coordination Polymers Prepared from Solution and the Solid State

Reaction of mixtures of Co(NCS)2 and Ni(NCS)2 with ethylisonicotinate in EtOH in a ratio of 1:2 leads to the formation of solid solutions (mixed crystals) of the layered compound [CoxNi1–x(NCS)2(ethylisonicotinate)2]n that are always contaminated with an additional crystalline phase. Pure samples of the desired layer compound are accessible by using an excess of the metal salts, but in this case the Co content in the solid solutions, as determined by atomic absorption spectroscopy and energy dispersive X-ray spectroscopy, is always lower than that used in the synthesis. Therefore, solid solutions of CoxNi1–x(NCS)2(ethylisonicotinate)4 were synthesized that upon heating transform into solid solutions of the desired layered compound, and in this case the Co/Ni ratio exactly corresponds to that used in the synthesis. The formation of solid solutions of all compounds is already indicated by comparison of the experimental powder X-ray diffraction pattern of the solid solutions with that of physical mixtures wi...

Analysis of Fraunhofer diffraction patterns’ entropy based on apertures shaped as national borders

How aesthetically pleasing is your country’s diffraction pattern? This work summarizes the calculated and experimental Fraunhofer diffraction patterns obtained from using apertures lithographically formed into shapes of national borders. Calculations are made based on the fast Fourier transform of the aperture images. The entropy of a diffraction pattern image, based on its two-dimensional gradient, for each of 113 nations has also been computed. Results suggest that most nations’ diffraction patterns fall under one of two prominent trends forming as a function of geographical area, with one trend being less entropic than the other.