Grazing-incidence transmission X-ray scattering: surface scattering in the Born approximation

In Situ and Operando X-ray Scattering Methods in Electrochemistry and Electrocatalysis

Electrochemical and electrocatalytic processes are of key importance for the transition to a sustainable energy supply as well as for a wide variety of other technologically relevant fields. Further development of these processes requires in-depth understanding of the atomic, nano, and micro scale structure of the materials and interfaces in electrochemical devices under reaction conditions. We here provide a comprehensive review of in situ and operando studies by X-ray scattering methods, which are powerful and highly versatile tools to provide such understanding. We discuss the application of X-ray scattering to a wide variety of electrochemical systems, ranging from metal and oxide single crystals to nanoparticles and even full devices. We show how structural data on bulk phases, electrode-electrolyte interfaces, and nanoscale morphology can be obtained and describe recent developments that provide highly local information and insight into the composition and electronic structure. These X-ray scattering studies yield insights into the structure in the double layer potential range as well as into the structural evolution during electrocatalytic processes and phase formation reactions, such as nucleation and growth during electrodeposition and dissolution, the formation of passive films, corrosion processes, and the electrochemical intercalation into battery materials.

Molecular-weight effects of a homopolymer on the AB- and ABC-stacks of perforations in block copolymer/homopolymer films

We have demonstrated the molecular-weight effects of adding homopolystyrene (hPS) on the evolution of perforated layers and double gyroids in polystyrene-block-poly(methyl methacrylate)-based films during isothermal annealing. Two homopolystyrenes of 2.8 and 17 kg mol-1 were used. To prepare blend films, PS-b-PMMA and hPSx (x: 2.8 or 17) were mixed at a weight-fraction ratio of 75/25 in toluene and then spin-coated at SiOx/Si. Spin coating inevitably produced films with thick edges at the periphery of the substrate. The structural evolution of the spun films was in situ characterized by grazing incidence small-angle X-ray scattering (GISAXS). The annealed films were then characterized using a scanning electron microscope (SEM). We found that thin middle regions behaved differently from thick beads for the films. The middle of the blend films mainly formed perforated layers with different spatial orders and orientations, depending on the molecular weight of added hPS chains. Hexagonally perforated layers quickly formed at 205 °C for PS-b-PMMA/hPS2.8 films. However, when hPS17 was used instead of hPS2.8, perforated layers formed with defects in PS-b-PMMA/hPS17 films annealed at 205 °C. Annealing at 240 °C improved the spatial order and orientation of perforated layers for a PS-b-PMMA/hPS17 film. Nevertheless, annealing at 240 °C inversely depressed the in-plane spatial order of perforated layers for a PS-b-PMMA/hPS2.8 film. The depression in the in-plane spatial order is ascribed to a dilution effect of added short chains. Compared to the middle regions, the thick beads went through several metastable phases, such as perpendicularly oriented perforated layers and double gyroids.

Hydride formation and dynamic phase changes during template-assisted Pd electrodeposition

We investigated the structural evolution of electrochemically fabricated Pd nanowiresin situby means of grazing-incidence transmission small- and wide-angle x-ray scattering (GTSAXS and GTWAXS), x-ray fluorescence (XRF) and two-dimensional surface optical reflectance (2D-SOR). This shows how electrodeposition and the hydrogen evolution reaction (HER) compete and interact during Pd electrodepositon. During the bottom-up growth of the nanowires, we show thatβ-phase Pd hydride is formed. Suspending the electrodeposition then leads to a phase transition fromβ-phase Pd hydride toα-phase Pd. Additionally, we find that grain coalescence later hinders the incorporation of hydrogen in the Pd unit cell. GTSAXS and 2D-SOR provide complementary information on the volume fraction of the pores occupied by Pd, while XRF was used to monitor the amount of Pd electrodeposited.

Strategy to simulate and fit 2D grazing-incidence small-angle X-ray scattering patterns of nanostructured thin films

Grazing-incidence small-angle X-ray scattering (GISAXS) is a widely used method for the characterization of the nanostructure of supported thin films and enables time-resolved in situ measurements. The 2D scattering patterns contain detailed information about the nanostructures within the film and at its surface. However, this information is distorted not only by the reflection of the X-ray beam at the substrate-film interface and its refraction at the film surface but also by scattering of the substrate, the sample holder and other types of parasitic background scattering. In this work, a new, efficient strategy to simulate and fit 2D GISAXS patterns that explicitly includes these effects is introduced and demonstrated for (i) a model case nanostructured thin film on a substrate and (ii) experimental data from a microphase-separated block copolymer thin film. To make the protocol efficient, characteristic linecuts through the 2D GISAXS patterns, where the different contributions dominate, are analysed. The contributions of the substrate and the parasitic background scattering - which ideally are measured separately - are determined first and are used in the analysis of the 2D GISAXS patterns of the nanostructured, supported film. The nanostructures at the film surface and within the film are added step by step to the real-space model of the simulation, and their structural parameters are determined by minimizing the difference between simulated and experimental scattering patterns in the selected linecuts. Although in the present work the strategy is adapted for and tested with BornAgain, it can be easily used with other types of simulation software. The strategy is also applicable to grazing-incidence small-angle neutron scattering.

Symmetry-Breaking and Self-Sorting in Block Copolymer-Based Multicomponent Nanocomposites

Co-assembly of inorganic nanoparticles (NPs) and nanostructured polymer matrix represents an intricate interplay of enthalpic or entropic forces. Particle size largely affects the phase behavior of the nanocomposite. Theoretical studies indicate that new morphologies would emerge when the particles become comparable to the soft matrix's size, but this has rarely been supported experimentally. By designing a multicomponent blend composed of NPs, block copolymer-based supramolecules, and small molecules, a 3-D ordered lattice beyond the native BCP's morphology was recently reported when the particle is larger than the microdomain of BCP. The blend can accommodate various formulation variables. In this paper, when the particle size equals the microdomain size, a symmetry-broken phase appears in a narrow range of particle sizes and compositions, which we named the "train track" structure. In this phase, the NPs aligned into a 3-D hexagonal lattice and packed asymmetrically along the c axis, making the projection of the ac and the bc plane resemble train tracks. Computational studies show that the broken symmetry reduces the polymer chain deformation and stabilizes the metastable hexagonally perforated lamellar morphology. Given the mobility of the multicomponent blend, the system shows a self-sorting behavior: segregating into two macroscopic phases with different nanostructures based on only a few nanometers NP size differences. Smaller NPs form "train track" morphology, while larger NPs form a "simple hexagon" structure, where the NPs take a symmetric hexagonal arrangement. Detailed structural evolution and simulation studies confirm the systematic-wide cooperativity across different components, indicating the strong self-regulation of the multicomponent system.

Nanoparticle-induced morphological transformation in block copolymer-based nanocomposites

By controlling the chemical composition and the spatial organization of nanoparticles, hybrid nanocomposites incorporating ordered arrangements of nanoparticles could be endowed with exotic physical and chemical properties to fulfill demands in advanced electronics or energy-harvesting devices. However, a simple method to fabricate hybrid nanocomposites with precise control of nanoparticle distribution is still challenging. We demonstrate that block copolymer-based nanocomposites containing well-ordered nanoparticles with various morphologies can be readily obtained by adjusting the nanoparticle concentration. Moreover, the structural evolution of nanocomposite thin films as a function of nanoparticle loading is unveiled using grazing-incidence transmission small-angle X-ray scattering and atomic force microscopy. The morphological transformation proceeds through a phase transition from perforated lamellae to in-plane cylinder layout, followed by structural changes. The successful achievement of a variety of morphologies represents an effective and straightforward approach to producing functional hybrid nanocomposites for potential applications in various functional devices.

Uncovering the out-of-plane nanomorphology of organic photovoltaic bulk heterojunction by GTSAXS

The bulk morphology of the active layer of organic solar cells (OSCs) is known to be crucial to the device performance. The thin film device structure breaks the symmetry into the in-plane direction and out-of-plane direction with respect to the substrate, leading to an intrinsic anisotropy in the bulk morphology. However, the characterization of out-of-plane nanomorphology within the active layer remains a grand challenge. Here, we utilized an X-ray scattering technique, Grazing-incident Transmission Small-angle X-ray Scattering (GTSAXS), to uncover this new morphology dimension. This technique was implemented on the model systems based on fullerene derivative (P3HT:PC71BM) and non-fullerene systems (PBDBT:ITIC, PM6:Y6), which demonstrated the successful extraction of the quantitative out-of-plane acceptor domain size of OSC systems. The detected in-plane and out-of-plane domain sizes show strong correlations with the device performance, particularly in terms of exciton dissociation and charge transfer. With the help of GTSAXS, one could obtain a more fundamental perception about the three-dimensional nanomorphology and new angles for morphology control strategies towards highly efficient photovoltaic devices.

Uncertainties in the reconstruction of nanostructures in EUV scatterometry and grazing incidence small-angle X-ray scattering

Increasing miniaturization and complexity of nanostructures require innovative metrology solutions with high throughput that can assess complex 3D structures in a non-destructive manner. EUV scatterometry is investigated for the characterization of nanostructured surfaces and compared to grazing-incidence small-angle X-ray scattering (GISAXS). The reconstruction is based on a rigorous simulation using a Maxwell solver based on finite-elements and is statistically validated with a Markov-Chain-Monte-Carlo sampling method. It is shown that in comparison to GISAXS, EUV allows to probe smaller areas and to reduce the computation times obtaining comparable uncertainties.

Improving grazing-incidence small-angle X-ray scattering-computed tomography images by total variation minimization

Grazing-incidence small-angle X-ray scattering coupled with computed tomography (CT) has enabled the visualization of the spatial distribution of nanostructures in thin films. In this study, to optimize the CT image quality, total variation regularization is introduced to minimize sinogram image noise and artifacts.

Grazing-incidence small-angle X-ray scattering (GISAXS) coupled with computed tomography (CT) has enabled the visualization of the spatial distribution of nanostructures in thin films. 2D GISAXS images are obtained by scanning along the direction perpendicular to the X-ray beam at each rotation angle. Because the intensities at the q positions contain nanostructural information, the reconstructed CT images individually represent the spatial distributions of this information (e.g. size, shape, surface, characteristic length). These images are reconstructed from the intensities acquired at angular intervals over 180°, but the total measurement time is prolonged. This increase in the radiation dosage can cause damage to the sample. One way to reduce the overall measurement time is to perform a scanning GISAXS measurement along the direction perpendicular to the X-ray beam with a limited interval angle. Using filtered back-projection (FBP), CT images are reconstructed from sinograms with limited interval angles from 3 to 48° (FBP-CT images). However, these images are blurred and have a low image quality. In this study, to optimize the CT image quality, total variation (TV) regularization is introduced to minimize sinogram image noise and artifacts. It is proposed that the TV method can be applied to downsampling of sinograms in order to improve the CT images in comparison with the FBP-CT images.

Nanoscale viscosity of confined polyethylene oxide

Complex fluids near interfaces or confined within nanoscale volumes can exhibit substantial shifts in physical properties compared to bulk, including glass transition temperature, phase separation, and crystallization. Because studies of these effects typically use thin film samples with one dimension of confinement, it is generally unclear how more extreme spatial confinement may influence these properties. In this work, we used x-ray photon correlation spectroscopy and gold nanoprobes to characterize polyethylene oxide confined by nanostructured gratings (<100nm width) and measured the viscosity in this nanoconfinement regime to be ∼500 times the bulk viscosity. This enhanced viscosity occurs even when the scale of confinement is several times the polymer's radius of gyration, consistent with previous reports of polymer viscosity near flat interfaces.

Unwarping GISAXS data

Grazing-incidence small-angle X-ray scattering (GISAXS) is a powerful technique for measuring the nanostructure of coatings and thin films. However, GISAXS data are plagued by distortions that complicate data analysis. The detector image is a warped representation of reciprocal space because of refraction, and overlapping scattering patterns appear because of reflection. A method is presented to unwarp GISAXS data, recovering an estimate of the true undistorted scattering pattern. The method consists of first generating a guess for the structure of the reciprocal-space scattering by solving for a mutually consistent prediction from the transmission and reflection sub-components. This initial guess is then iteratively refined by fitting experimental GISAXS images at multiple incident angles, using the distorted-wave Born approximation (DWBA) to convert between reciprocal space and detector space. This method converges to a high-quality reconstruction for the undistorted scattering, as validated by comparing with grazing-transmission scattering data. This new method for unwarping GISAXS images will broaden the applicability of grazing-incidence techniques, allowing experimenters to inspect undistorted visualizations of their data and allowing a broader range of analysis methods to be applied to GI data.

A corrective prescription for GISAXS

A new 'unwarping' algorithm presented by Liu and Yager in this issue constructs SAXS data consistent with experimental GISAXS data, eliminating many of the complications arising in GISAXS that are commonly modeled within the framework of the distorted-wave Born approximation. The method promises to open new pathways for processing, modeling and analyzing GISAXS data using techniques developed for SAXS.

Unravelling the structural rearrangement of polymer colloidal crystals under dry sintering conditions

The structural rearrangement of polystyrene colloidal crystals under dry sintering conditions has been revealed by in situ grazing incidence X-ray scattering. The measured diffraction patterns were analysed using distorted wave Born approximation (DWBA) theory and the structural parameters of the as-grown colloidal crystals of three different particle sizes were determined for the in-plane and out-of-plane directions in a film. By analysing the temperature evolution of the diffraction peak positions, integrated intensities, and widths, the detailed scenario of the structural rearrangement of crystalline domains at the nanoscale has been revealed, including thermal expansion, particle shape transformation and crystal amorphisation. Based on DWBA analysis, we demonstrate that in the process of dry sintering, the shape of colloidal particles in a crystal transforms from a sphere to a polyhedron. Our results deepen the understanding of the thermal annealing of polymer colloidal crystals as an efficient route for the design of new nano-materials.

Self-organization of porous anodic alumina films studied in situ by grazing-incidence transmission small-angle X-ray scattering

Self-ordered porous anodic alumina (PAA) films are studied extensively due to a large number of possible applications in nanotechnology and low cost of production. Whereas empirical relationships between growth conditions and produced oxides have been established, fundamental aspects regarding pore formation and self-organization are still under debate. We present in situ structural studies of PAA films using grazing-incidence transmission small-angle X-ray scattering. We have considered the two most used recipes where the pores self-organize: 0.3 M H₂SO₄ at 25 V and 0.3 M C₂H₂O₄ at 40 V. During anodization we have followed the evolution of the structural parameters: average interpore distance, length of ordered pores domains, and thickness of the porous oxide layer. Compared to the extensively used ex situ investigations, our approach gives an unprecedented temporal accuracy in determination of the parameters. By using of Al(100), Al(110) and Al(111) surfaces, the influence of surface orientation on the structural evolution was studied, and no significant differences in the interpore distance and domain length could be observed. However, the rate of oxide growth in 0.3 M C₂H₂O₄ at 40 V was significantly influenced by the surface orientation, where the slowest growth occurs for Al(111). In 0.3 M H₂SO₄ at 25 V, the growth rates were higher, but the influence of surface orientation was not obvious. The structural evolution was also studied on pre-patterned aluminum surfaces. These studies show that although the initial structures of the oxides are governed by pre-patterning geometry, the final structures are dictated by the anodization conditions.

Growth of porous anodic alumina films studied in situ under electrochemical anodization conditions by grazing-incidence transmission small-angle X-ray scattering.

Fast X-ray reflectivity measurements using an X-ray pixel area detector at the DiffAbs beamline, Synchrotron SOLEIL

This paper describes a method for rapid measurements of the specular X-ray reflectivity signal using an area detector and a monochromatic, well collimated X-ray beam (divergence below 0.01°), combined with a continuous data acquisition mode during the angular movements of the sample and detector. In addition to the total integrated (and background-corrected) reflectivity signal, this approach yields a three-dimensional mapping of the reciprocal space in the vicinity of its origin. Grazing-incidence small-angle scattering signals are recorded simultaneously. Measurements up to high momentum transfer values (close to 0.1 nm^-1, also depending on the X-ray beam energy) can be performed in total time ranges as short as 10 s. The measurement time can be reduced by up to 100 times as compared with the classical method using monochromatic X-ray beams, a point detector and rocking scans (integrated reflectivity signal).

MINERVA: A facility to study Microstructure and INterface Evolution in Realtime under VAcuum

A sample environment to enable real-time X-ray scattering measurements to be recorded during the growth of materials by thermal evaporation in vacuum is presented. The in situ capabilities include studying microstructure development with time or during exposure to different environmental conditions, such as temperature and gas pressure. The chamber provides internal slits and a beam stop, to reduce the background scattering from the X-rays passing through the entrance and exit windows, together with highly controllable flux rates of the evaporants. Initial experiments demonstrate some of the possibilities by monitoring the growth of bathophenanthroline (BPhen), a common molecule used in organic solar cells and organic light emitting diodes, including the development of the microstructure with time and depth within the film. The results show how BPhen nanocrystal structures coarsen at room temperature under vacuum, highlighting the importance of using real time measurements to understand the as-deposited pristine film structure and its development with time. More generally, this sample environment is versatile and can be used for investigation of structure-property relationships in a wide range of vacuum deposited materials and their applications in, for example, optoelectronic devices and energy storage.

Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver

Laterally periodic nanostructures have been investigated with grazing-incidence small-angle X-ray scattering (GISAXS) by using the diffraction patterns to reconstruct the surface shape. To model visible light scattering, rigorous calculations of the near and far field by numerical solution of Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, owing to the discrepancy between the incident wavelength and the finite-element size. This drawback vanishes for GISAXS because of the small angles of incidence, the conical scattering geometry and the periodicity of the surface structures, which allows a rigorous computation of the diffraction efficiencies with sufficient numerical precision. To develop metrology tools based on GISAXS, lamellar gratings with line widths down to 55 nm were produced by state-of-the-art electron-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows the detailed reconstruction of the grating line shape for thick non-homogeneous substrates as well. The reconstructed geometric line-shape models are statistically validated by applying a Markov chain Monte Carlo sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nanometre uncertainty.

Healing X-ray scattering images

X-ray scattering images contain numerous gaps and defects arising from detector limitations and experimental configuration. We present a method to heal X-ray scattering images, filling gaps in the data and removing defects in a physically meaningful manner. Unlike generic inpainting methods, this method is closely tuned to the expected structure of reciprocal-space data. In particular, we exploit statistical tests and symmetry analysis to identify the structure of an image; we then copy, average and interpolate measured data into gaps in a way that respects the identified structure and symmetry. Importantly, the underlying analysis methods provide useful characterization of structures present in the image, including the identification of diffuse versus sharp features, anisotropy and symmetry. The presented method leverages known characteristics of reciprocal space, enabling physically reasonable reconstruction even with large image gaps. The method will correspondingly fail for images that violate these underlying assumptions. The method assumes point symmetry and is thus applicable to small-angle X-ray scattering (SAXS) data, but only to a subset of wide-angle data. Our method succeeds in filling gaps and healing defects in experimental images, including extending data beyond the original detector borders.

Rapid ordering of block copolymer thin films

Block-copolymers self-assemble into diverse morphologies, where nanoscale order can be finely tuned via block architecture and processing conditions. However, the ultimate usage of these materials in real-world applications may be hampered by the extremely long thermal annealing times-hours or days-required to achieve good order. Here, we provide an overview of the fundamentals of block-copolymer self-assembly kinetics, and review the techniques that have been demonstrated to influence, and enhance, these ordering kinetics. We discuss the inherent tradeoffs between oven annealing, solvent annealing, microwave annealing, zone annealing, and other directed self-assembly methods; including an assessment of spatial and temporal characteristics. We also review both real-space and reciprocal-space analysis techniques for quantifying order in these systems.

Characterization of the shape and line-edge roughness of polymer gratings with grazing incidence small-angle X-ray scattering and atomic force microscopy

Grazing-incidence small-angle X-ray scattering (GISAXS) is increasingly used for the metrology of substrate-supported nanoscale features and nanostructured films. In the case of line gratings, where long objects are arranged with a nanoscale periodicity perpendicular to the beam, a series of characteristic spots of high-intensity (grating truncation rods, GTRs) are recorded on a two-dimensional detector. The intensity of the GTRs is modulated by the three-dimensional shape and arrangement of the lines. Previous studies aimed to extract an average cross-sectional profile of the gratings, attributing intensity loss at GTRs to sample imperfections. Such imperfections are just as important as the average shape when employing soft polymer gratings which display significant line-edge roughness. Herein are reported a series of GISAXS measurements of polymer line gratings over a range of incident angles. Both an average shape and fluctuations contributing to the intensity in between the GTRs are extracted. The results are critically compared with atomic force microscopy (AFM) measurements, and it is found that the two methods are in good agreement if appropriate corrections for scattering from the substrate (GISAXS) and contributions from the probe shape (AFM) are accounted for.

Determining the shape and periodicity of nanostructures using small-angle X-ray scattering

The semiconductor industry is exploring new metrology techniques capable of meeting the future requirement to characterize three-dimensional structure where the critical dimensions are less than 10 nm. X-ray scattering techniques are one candidate owing to the sub-Å wavelengths which are sensitive to internal changes in electron density. Critical-dimension small-angle X-ray scattering (CDSAXS) has been shown to be capable of determining the average shape of a line grating. Here it is used to study a set of line gratings patternedviaa self-aligned multiple patterning process, which resulted in a set of mirrored lines, where the individual line shapes were asymmetric. The spacing between lines was systematically varied by sub-nm shifts. The model used to simulate the scattering was developed in stages of increasing complexity in order to justify the large number of parameters included. Comparisons between the models at different stages of development demonstrate that the measurement can determine differences in line shapes within the superlattice. The shape and spacing between lines within a given set were determined to sub-nm accuracy. This demonstrates the potential for CDSAXS as a high-resolution nanostructure metrology tool.

Metrics of graininess: robust quantification of grain count from the non-uniformity of scattering rings

The diffraction rings that arise in X-ray scattering experiments frequently exhibit non-uniformity or `spottiness' as a result of the finite number of grains within the probed volume. This article explores a variety of ways to assess this graininess and shows that scaling relationships can be used to quantitatively relate ring non-uniformity to the number of grains within the scattering volume. The applicability of the method is demonstrated for grain counts from 10 to 107, enabling measurement of the crystalline fraction or of the average grain size from 6 nm to 120 µm. This method enables quantification of grain size even in cases where the intrinsic peak width is much smaller than the instrumental broadening. The method is validated with experimental measurements on a variety of systems.

Performance of polycapillary X-ray optics for confocal energy-dispersive small-angle X-ray scattering

A confocal energy-dispersive small-angle X-ray scattering (EDSAXS) setup based on polycapillary optics was designed. In this confocal EDSAXS setup, a polycapillary slightly focusing X-ray lens (PSFXRL) and a polycapillary parallel X-ray lens (PPXRL) with a long input focal distance were placed confocally in the excitation channel and detection channel, respectively. This confocal configuration was helpful in improving the signal-to-noise ratio of the EDSAXS. The high gain in power density of the PSFXRL and PPXRL decreased the power requirement of the X-ray source for EDSAXS. The confocal EDSAXS technology could be used to perform nondestructive andin situanalysis of samples such as milk powder in its packaging.