Volume Of Reciprocal Space Research Articles

Stability of the Fe3O4 (√2 x √2)R 45° Surface in 0.1 M NaOH Investigated by High-Energy Surface X-Ray Diffraction

Transition metal oxides, especially Fe, Co, and Ni oxides, are of great interest as electrocatalysts for the oxygen evolution reaction (OER) in alkaline solution. However, detailed data on the atomic-scale oxide-electrolyte interface structure of these systems are rare. We present studies of a model oxide electrocatalyst, -reconstructed Fe3O4(001). This oxide surface has been extensively investigated under ultrahigh vacuum (UHV) conditions, leading to a detailed understanding of its atomic structure [2]. In previous in situ surface X-ray diffraction studies, we demonstrated that the reconstructed surface can survive transfer into electrochemical environment and determined the stability of the reconstruction as a function of potential [2]. Specifically, we showed that the ()R45° reconstructed Fe3O4(001) surface can be transferred into 0.1 M NaOH at 0.2 V vs. Ag/AgCl while maintaining surface structure and that the reconstruction is irreversibly lifted at sufficiently negative potentials.Here, we present more detailed in situ studies of this system, using the novel technique of High-Energy Surface X-Ray Diffraction (HESXRD) [3,4]. This technique enabled us to measure rapidly a huge reciprocal space volume, which allows to obtain very large sets of crystal truncation rods (CTRs) that can be analysed by surface crystallographic methods. These data provide detailed insights into the temporal stability of the surface at fixed potentials as well as potential-dependent changes in surface structure.In the experiments the Fe3O4(001) single crystal samples were prepared by sputtering and annealing in UHV, followed by sample transfer into the hanging-meniscus cell employed for the HESXRD studies. A new experimental procedure allowed to reduce the time of sample transfer and establishment of potential control to below one minute.The in situ HESXRD measurements were performed at beamline P21.2 of PETRA III at DESY. 7 symmetrically independent CTRs and 2 ()R45° fractional order rods could be measured. These data enabled detailed comparison of the oxide-electrolyte interface with the surface structure under UHV conditions [1]. The potential-dependent data indicate clear structural changes when applying more positive or more negative potentials than 0.2 V vs. Ag/AgCl, as illustrated in part A and B of Fig. 1. However, all surface structures were stable at constant potential over several hours, as indicated in part C of Fig. 1. The quality of the obtained results allows to determine quantitative analysis of the interface structure. First results of this analysis will be presented.We gratefully acknowledge financial support by the German ministry of Science and Education (BMBF) via projects 05K19FK3 and 05K22FK1.

Water layer and radiation damage effects on the orientation recovery of proteins in single-particle imaging at an X-ray free-electron laser

The noise caused by sample heterogeneity (including sample solvent) has been identified as one of the determinant factors for a successful X-ray single-particle imaging experiment. It influences both the radiation damage process that occurs during illumination as well as the scattering patterns captured by the detector. Here, we investigate the impact of water layer thickness and radiation damage on orientation recovery from diffraction patterns of the nitrogenase iron protein. Orientation recovery is a critical step for single-particle imaging. It enables to sort a set of diffraction patterns scattered by identical particles placed at unknown orientations and assemble them into a 3D reciprocal space volume. The recovery quality is characterized by a “disconcurrence” metric. Our results show that while a water layer mitigates protein damage, the noise generated by the scattering from it can introduce challenges for orientation recovery and is anticipated to cause problems in the phase retrieval process to extract the desired protein structure. Compared to these disadvantageous effects due to the thick water layer, the effects of radiation damage on the orientation recovery are relatively small. Therefore, minimizing the amount of residual sample solvent should be considered a crucial step in improving the fidelity and resolution of X-ray single-particle imaging experiments.

Oxidation and Reduction of Ir(100) Studied by High-Energy Surface X-ray Diffraction

The oxidation and reduction of an Ir(100) surface using 2.5, 5, and 10 mbar O2 partial pressure and a sample temperature of 775 K have been studied by using high-energy surface X-ray diffraction (HESXRD) which allowed to record large volumes of reciprocal space in short time periods. The complex 3D diffraction patterns could be disentangled in a stepwise procedure. For the 2.5 mbar experiment the measurements indicate the formation of an Ir(100)-O c(2 × 2) oxygen superstructure along with the onset of epitaxial IrO2(110) bulk oxide formation. For the 5 and 10 mbar O2 partial pressures the formation of additional IrO2 bulk oxide epitaxies with (100) and (101) orientations as well as of polycrystalline IrO2 was observed. Upon CO reduction, we found the IrO2 islands to be reduced into epitaxial and metallic Ir(111) and (221) oriented islands.

Soft-mode anisotropy in the negative thermal expansion material ReO3

We use a symmetry-motivated approach to analyse neutron pair distribution function data to investigate the mechanism of negative thermal expansion (NTE) in ReO$_3$. This analysis shows that the local structure of ReO$_3$ is dominated by an in-phase octahedral tilting mode and that the octahedral units are far less flexible to scissoring type deformations than the octahedra in the related compound ScF$_3$. These results support the idea that structural flexibility is an important factor in NTE materials, allowing the phonon modes that drive a volume contraction of the lattice to occupy a greater volume in reciprocal space. The lack of flexibility in ReO$_3$ restricts the NTE-driving phonons to a smaller region of reciprocal space, limiting the magnitude and temperature range of NTE. In addition, we investigate the thermal expansion properties of the material at high temperature and do not find the reported second NTE region. Finally, we show that the local fluctuations, even at elevated temperatures, respect the symmetry and order parameter direction of the observed $P4/mbm$ high pressure phase of ReO$_3$. The result indicates that the motions associated with rigid unit modes are highly anisotropic in these systems.

Anharmonic Eigenvectors and Acoustic Phonon Disappearance in Quantum Paraelectric SrTiO_{3}.

Pronounced anomalies in the SrTiO_{3} dynamical structure factor, S(Q,E), including the disappearance of acoustic phonon branches at low temperatures, were uncovered with inelastic neutron scattering (INS) and simulations. The striking effect reflects anharmonic couplings between acoustic and optic phonons and the incipient ferroelectric instability near the quantum critical point. It is rationalized using a first-principles renormalized anharmonic phonon approach, pointing to nonlinear Ti-O hybridization causing unusual changes in real-space phonon eigenvectors, frequencies, group velocities, and scattering phase space. Our method is general and establishes how T dependences beyond the harmonic regime, assessed by INS mapping of large reciprocal-space volumes, provide real-space insights into anharmonic atomic dynamics near phase transitions.

FORTE - a multipurpose high-vacuum diffractometer for tender X-ray diffraction and spectroscopy at the SIRIUS beamline of Synchrotron SOLEIL.

A new high-vacuum multipurpose diffractometer (called FORTE from the French acronyms of the project) has recently been installed at the tender/hard X-ray SIRIUS beamline of Synchrotron SOLEIL, France. The geometry chosen allows one to work either in the classical Eulerian four-circle geometry for bulk X-ray diffraction (XRD) or in the z-axis geometry for surface XRD. The diffractometer nicely fits the characteristics of the SIRIUS beamline, optimized to work in the 1.1-4.5 keV range, and allows one to perform unprecedented diffraction anomalous fine structure (DAFS) experiments in the tender X-ray region, also around non-specular reflections, covering a large reciprocal-space volume. Installation of an X-ray fluorescence detector on a dedicated flange allows simultaneous DAFS and X-ray absorption (XAS) measurements. The access to the tender X-ray region paves the way to resonant investigations around the L-edges of second-row transition elements which are constituents of functional oxide materials. It also enables access to several edges of interest for semiconductors. Finally, the control architecture based on synchronized Delta Tau units opens up exciting perspectives for improvement of the mechanical sphere of confusion.

Probing orientation information using 3-dimensional reciprocal space volume analysis.

The crystallographic texture of polycrystalline materials is the result of how these materials are processed and what external forces materials have experienced. Neutron and X-ray diffraction are standard methods to characterize global crystallographic textures. However, conventional neutron and X-ray texture analyses rely on pole figure inversion routines derived from intensity analysis of individual reflections or powder Rietveld analysis to reconstruct and model the orientation distribution from slices through reciprocal space. In this work, we describe an original approach to directly probe the crystallographic texture information of rolled aluminum from the intensity distribution in 3-dimensional reciprocal space volumes measured simultaneously. Using the TOPAZ time-of-flight Laue neutron diffractometer, reciprocal space analysis allowed determination of "pole spheres" with <1° angular resolution. These pole spheres are compared with reconstructed pole figures from classic texture analysis.

Implementation of cross correlation for energy discrimination on the time-of-flight spectrometer CORELLI.

The CORELLI instrument at Oak Ridge National Laboratory is a statistical chopper spectrometer designed and optimized to probe complex disorder in crystalline materials through diffuse scattering experiments. On CORELLI, the high efficiency of white-beam Laue diffraction combined with elastic discrimination have enabled an unprecedented data collection rate to obtain both the total and the elastic-only scattering over a large volume of reciprocal space from a single measurement. To achieve this, CORELLI is equipped with a statistical chopper to modulate the incoming neutron beam quasi-randomly, and then the cross-correlation method is applied to reconstruct the elastic component from the scattering data. Details of the implementation of the cross-correlation method on CORELLI are given and its performance is discussed.

A microcontroller for in situ single-crystal diffraction measurements with a PILATUS-2M detector under an alternating electric field

A new data acquisition system for in situ time-resolved three-dimensional reciprocal space mapping is reported. The system is based on a programmable microcontroller for generating a functional low-voltage signal, a pixel area detector serving as a master clock and a high-voltage amplifier. Both Bragg and diffuse scattering can be mapped in a large volume of reciprocal space under an alternating electric field of a pre-programmed shape. The system has been tested at the Swiss–Norwegian Beamline BM01 of the European Synchrotron by measuring the electric field dependence of diffuse X-ray scattering from a functional perovskite-based ferroelectric single crystal.

A rapid two-dimensional data collection system for the study of ferroelectric materials under external applied electric fields

Synchrotron X-rays on the Swiss Norwegian Beamline and BM28 (XMaS) at the ESRF have been used to record the diffraction response of the PMN-PT relaxor piezoelectric 67% Pb(Mg1/3Nb2/3)O3-33% PbTiO3 as a function of externally applied electric field. A DC field in the range 0-18 kV cm-1 was applied along the [001] pseudo-cubic direction using a specially designed sample cell for in situ single-crystal diffraction experiments. The cell allowed data to be collected on a Pilatus 2M area detector in a large volume of reciprocal space using transmission geometry. The data showed good agreement with a twinned single-phase monoclinic structure model. The results from the area detector were compared with previous Bragg peak mapping using variable electric fields and a single detector where the structural model was ambiguous. The coverage of a significantly larger section of reciprocal space facilitated by the area detector allowed precise phase analysis.

Expanding Lorentz and spectrum corrections to large volumes of reciprocal space for single-crystal time-of-flight neutron diffraction.

Evidence is mounting that potentially exploitable properties of technologically and chemically interesting crystalline materials are often attributable to local structure effects, which can be observed as modulated diffuse scattering (mDS) next to Bragg diffraction (BD). BD forms a regular sparse grid of intense discrete points in reciprocal space. Traditionally, the intensity of each Bragg peak is extracted by integration of each individual reflection first, followed by application of the required corrections. In contrast, mDS is weak and covers expansive volumes of reciprocal space close to, or between, Bragg reflections. For a representative measurement of the diffuse scattering, multiple sample orientations are generally required, where many points in reciprocal space are measured multiple times and the resulting data are combined. The common post-integration data reduction method is not optimal with regard to counting statistics. A general and inclusive data processing method is needed. In this contribution, a comprehensive data analysis approach is introduced to correct and merge the full volume of scattering data in a single step, while correctly accounting for the statistical weight of the individual measurements. Development of this new approach required the exploration of a data treatment and correction protocol that includes the entire collected reciprocal space volume, using neutron time-of-flight or wavelength-resolved data collected at TOPAZ at the Spallation Neutron Source at Oak Ridge National Laboratory.

Application of a pnCCD for energy-dispersive Laue diffraction with ultra-hard X-rays

In this work the spectroscopic performance of a pnCCD detector in the ultra-hard energy range between 40 and 140 keV is tested by means of an energy-dispersive Laue diffraction experiment on a GaAs crystal. About 100 Bragg peaks were collected in a single-shot exposure of the arbitrarily oriented sample to white synchrotron radiation provided by a wiggler at BESSY II and resolved in a large reciprocal-space volume. The positions and energies of individual Laue spots could be determined with a spatial accuracy of less than one pixel and a relative energy resolution better than 1%. In this way the unit-cell parameters of GaAs were extracted with an accuracy of 0.5%, allowing for a complete indexing of the recorded Laue pattern. Despite the low quantum efficiency of the pnCCD (below 7%), experimental structure factors could be obtained from the three-dimensional data sets, taking into account photoelectric absorption as well as Compton scattering processes inside the detector. The agreement between measured and theoretical kinematical structure factors calculated from the known crystal structure is of the order of 10%. The results of this experiment demonstrate the potential of pnCCD detectors for applications in X-ray structure analysis using the complete energy spectrum of synchrotron radiation.

Nebula: reconstruction and visualization of scattering data in reciprocal space.

Two-dimensional solid-state X-ray detectors can now operate at considerable data throughput rates that allow full three-dimensional sampling of scattering data from extended volumes of reciprocal space within second to minute time-scales. For such experiments, simultaneous analysis and visualization allows for remeasurements and a more dynamic measurement strategy. A new software, Nebula, is presented. It efficiently reconstructs X-ray scattering data, generates three-dimensional reciprocal space data sets that can be visualized interactively, and aims to enable real-time processing in high-throughput measurements by employing parallel computing on commodity hardware.

Surveying the higher dimensions of the aperiodic composite nonadecane/urea

We recently observed for the first time that there exist phase transitions where the structural changes correspond just to degrees of freedom hidden in the internal (super)space of an aperiodic material, here the composite nonadecane/urea [1]. A key factor in the discovery of this type of transition [2] was the examination of the diffraction pattern in 3D, only possible at the time on a four-circle triple-axis neutron spectrometer, the analyzer used in zero-energy transfer to reduce the background and improve resolution. Despite the greater accessibility in reciprocal space, the weak intensity of the superlattice reflections limited the volume of reciprocal space that could be explored. Modern neutron Laue diffractometers with large image-plate detectors permit rapid and extensive exploration of reciprocal space with high resolution in the two-dimensional projection and a wide dynamic range with negligible bleeding of intense diffraction spots [3]. Surveying nonadecane/urea with neutron Laue diffraction from 300K to 4K reveals further detail of the superspace-driven phase transition, notably an increase in misorientation in the plane perpendicular to the composite misfit axis, as well as a first-order transition to a new phase at lower temperature. These new observations shed further light on how nature can use the degrees of freedom hidden in the internal superspace to form states that cannot be envisaged in the usual 3D real space.

Yell: a computer program for diffuse scattering analysisviathree-dimensional delta pair distribution function refinement

Yell, a program for routine refinement of disorder models against single-crystal diffuse scattering data, is presented. The analysis is based on the three-dimensional delta pair distribution function (3D-ΔPDF) method, which provides direct access to interatomic correlations in real crystal structures. Substitutional, displacive and size-effect disorder models are covered. The input file format supports flexible usage of arithmetic expressions for constraining dependent parameter values. The program is designed to be run on desktop computers. By using an efficient fast-Fourier-transform-based diffuse scattering calculation algorithm, full least-square refinements of medium complexity disorder models may be performed within minutes or hours, even if the experimental diffuse scattering is represented by large and fine-sampled reciprocal space volumes. The program is written in C++ and the source code is distributed under the GPL licence. Binary distributions are currently available for Mac and Windows operating systems.

On the application of a single-crystal κ-diffractometer and a CCD area detector for studies of thin films

A multipurpose six-axis κ-diffractometer, together with the brilliance of the ESRF light source and a CCD area detector, has been explored for studying epitaxial relations and crystallinity in thin film systems. The geometrical flexibility of the six-axis goniometer allows measurement of a large volume in reciprocal space, providing an in-depth understanding of sample crystal relationships. By a set of examples of LaAlO3 thin films deposited by the atomic layer deposition technique, the possibilities of the set-up are presented. A fast panoramic scan provides determination of the crystal orientation matrices, prior to more thorough inspection of single Bragg nodes. Such information, in addition to a broadening analysis of families of single reflections, is shown to correlate well with the crystallinity, crystallite size, strain and epitaxial relationships in the thin films. The proposed set-up offers fast and easy sample mounting and alignment, along with crucial information on key features of the thin film structures.

Three dimensional reciprocal space measurement by x-ray diffraction using linear and area detectors: Applications to texture and defects determination in oriented thin films and nanoprecipitates

The authors present a method for the fast and efficient measurement of volumes of reciprocal space by x-ray diffraction using linear and area detectors. The goal of this technique is to obtain a complete overview of the reciprocal space to detect and characterize the nature and orientation of all the phases present. They first explain the detailed procedures and scan strategies required for transforming raw scattering data into three-dimensional maps of reciprocal space and present a complete open-source software package for advanced data processing, analysis, and visualization. Several case studies, chosen to highlight the overall capabilities of the technique, are then introduced. First, thermal diffuse scattering from a monocrystalline Si substrate is characterized by the presence of lines linking diffraction peaks in reciprocal space. Second, a detailed investigation of texture in multiphase thin layers permits us to reveal the unambiguous presence of fiber, axiotaxial, and epitaxial components in oriented films. The visualization of a significant fraction of reciprocal space has allowed us to identify an unexpected metastable phase, which could not be deduced from measurements carried out in the Bragg–Brentano geometry. The technique is then used to study planar defects in nickel silicides formed by solid-state reactions and micro twins in a GaP matrix containing coherent MnP precipitates. Overall, the authors show that the systematic acquisition of significant volumes of reciprocal space permits us to observe behaviors that might otherwise remain undetected when analyses are restricted to typical measurement scans.

Characterization of InGaN and InAlN Epilayers by Microdiffraction X-Ray Reciprocal Space Mapping

ABSTRACTWe report a study of InGaN and InAlN epilayers grown on GaN/Sapphire substrates by microfocused three-dimensional X-ray Reciprocal Space Mapping (RSM). The analysis of the full volume of reciprocal space, while probing samples on the microscale with a focused X-ray beam, allows us to gain uniquely valuable information about the microstructure of III-N alloy epilayers. It is found that “seed” InGaN mosaic nanocrystallites are twisted with respect to the ensemble average and strain free. This indicates that the growth of InGaN epilayers follows the Volmer-Weber mechanism with nucleation of “seeds” on strain fields generated by thea-type dislocations which are responsible for the twist of underlying GaN mosaic blocks. In the case of InAlN epilayer formation of composition gradient was observed at the beginning of the epitaxial growth.

InGaN epilayer characterization by microfocused x-ray reciprocal space mapping

We report the use of microfocused three-dimensional x-ray reciprocal space mapping to study InGaN epilayers with average InN content ∼20%-22%. Analysis of the full volume of reciprocal space, while probing samples on the microscale with a focused x-ray beam, allowed us to gain valuable information about the nanostructure of InN-rich InGaN epilayers. It is found that “seed” InGaN mosaic nanocrystallites are twisted with respect to the ensemble average and strain-free. The initial stages of InGaN-on-GaN epitaxial growth, therefore, conform to the Volmer-Weber growth mechanism with “seeds” nucleated on strain fields generated by the a-type edge dislocations.

Analysis of phases in the structure determination of an icosahedral virus.

The constraints imposed on structure-factor phases by noncrystallographic symmetry (NCS) allow phase improvement, phase extension to higher resolution and hence ab initio phase determination. The more numerous the NCS redundancy and the greater the volume used for solvent flattening, the greater the power for phase determination. In a case analyzed here the icosahedral NCS phasing appeared to have broken down, although later successful phase extension was possible when the envelope around the NCS region was tightened. The phases from the failed phase-determination attempt fell into four classes, all of which satisfied the NCS constraints. These four classes corresponded to the correct solution, opposite enantiomorph, Babinet inversion and opposite enantiomorph with Babinet inversion. These incorrect solutions can be seeded from structure factors belonging to reciprocal-space volumes that lie close to icosahedral NCS axes where the structure amplitudes tend to be large and the phases tend to be 0 or π. Furthermore, the false solutions can spread more easily if there are large errors in defining the envelope designating the region in which NCS averaging is performed.