BornAgain: software for simulating and fitting grazing-incidence small-angle scattering

Illuminating the nanostructure of diffuse interfaces: Recent advances and future directions in reflectometry techniques

Diffuse soft matter interfaces take many forms, from end-tethered polymer brushes or adsorbed surfactants to self-assembled layers of lipids. These interfaces play crucial roles across a multitude of fields, including materials science, biophysics, and nanotechnology. Understanding the nanostructure and properties of these interfaces is fundamental for optimising their performance and designing novel functional materials. In recent years, reflectometry techniques, in particular neutron reflectometry, have emerged as powerful tools for elucidating the intricate nanostructure of soft matter interfaces with remarkable precision and depth. This review provides an overview of selected recent developments in reflectometry and their applications for illuminating the nanostructure of diffuse interfaces. We explore various principles and methods of neutron and X-ray reflectometry, as well as ellipsometry, and discuss advances in their experimental setups and data analysis approaches. Improvements to experimental neutron reflectometry methods have enabled greater time resolution in kinetic measurements and elucidation of diffuse structure under shear or confinement, while innovation in analysis protocols has significantly reduced data processing times, facilitated co-refinement of reflectometry data from multiple instruments and provided greater-than-ever confidence in proposed structural models. Furthermore, we highlight some significant research findings enabled by these techniques, revealing the organisation, dynamics, and interfacial phenomena at the nanoscale. We also discuss future directions and potential advancements in reflectometry techniques. By shedding light on the nanostructure of diffuse interfaces, reflectometry techniques enable the rational design and tailoring of interfaces with enhanced properties and functionalities.

(Sub-)Picosecond Surface Correlations of Femtosecond Laser Excited Al-Coated Multilayers Observed by Grazing-Incidence X-ray Scattering

Femtosecond high-intensity laser pulses at intensities surpassing 1014 W/cm2 can generate a diverse range of functional surface nanostructures. Achieving precise control over the production of these functional structures necessitates a thorough understanding of the surface morphology dynamics with nanometer-scale spatial resolution and picosecond-scale temporal resolution. In this study, we show that single XFEL pulses can elucidate structural changes on surfaces induced by laser-generated plasmas using grazing-incidence small-angle X-ray scattering (GISAXS). Using aluminium-coated multilayer samples we distinguish between sub-picosecond (ps) surface morphology dynamics and subsequent multi-ps subsurface density dynamics with nanometer-depth sensitivity. The observed subsurface density dynamics serve to validate advanced simulation models representing matter under extreme conditions. Our findings promise to open new avenues for laser material-nanoprocessing and high-energy-density science.

INSIGHT: in situ heuristic tool for the efficient reduction of grazing-incidence X-ray scattering data

INSIGHT is a Python-based software tool for processing and reducing 2D grazing-incidence wide- and small-angle X-ray scattering (GIWAXS/GISAXS) data. It offers the geometric transformation of the 2D GIWAXS/GISAXS detector image to reciprocal space, including vectorized and parallelized pixel-wise intensity correction calculations. An explicit focus on efficient data management and batch processing enables full control of large time-resolved synchrotron and laboratory data sets for a detailed analysis of kinetic GIWAXS/GISAXS studies of thin films. It processes data acquired with arbitrarily rotated detectors and performs vertical, horizontal, azimuthal and radial cuts in reciprocal space. It further allows crystallographic indexing and GIWAXS pattern simulation, and provides various plotting and export functionalities. Customized scripting offers a one-step solution to reduce, process, analyze and export findings of large in situ and operando data sets.

Structure of liquid-vapor interfaces: Perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence x-ray diffraction

Grazing-incidence x-ray diffraction (GIXRD) is a scattering technique that allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of surface tension and interface roughness. However, the corresponding standard data analysis at nonzero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here, we overcome this ambiguity by proposing a physically consistent model of the bulk contribution based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we extend the model to account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the x-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid-vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision computer simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid-vapor coexistence line. A sensitivity analysis shows that our findings are robust with respect to the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.

Epitaxial graphene growth on cubic silicon carbide on silicon with high temperature neutron reflectometry: an operando study

The growth of graphene on silicon carbide on silicon offers a very attractive route towards novel wafer-scale photonic and electronic devices that are easy to fabricate and can be integrated in silicon manufacturing. Using a Ni/Cu catalyst for the epitaxial growth of graphene has been successful in the mitigation of the very defective nature of the underlying silicon carbide on silicon, leading to a consistent graphene coverage over large scales. A more detailed understanding of this growth mechanism is warranted in order to further optimise the catalyst composition, preferably via the use of operando characterization measurements. Here, we report in situ neutron reflectometry measurements of (Ni, Cu)/SiC films on silicon wafers, annealed from room temperature to 1100 °C, which initiates graphene formation at the buried (Ni, Cu)/SiC interface. Detailed modelling of the high temperature neutron reflectometry and corresponding scattering length density profiles yield insights into the distinct physical mechanisms within the different temperature regimes. The initially smooth solid metallic layers undergo intermixing and roughening transitions at relatively low temperatures below 500 °C, and then metal silicides begin to form above 600 °C from interfacial reactions with the SiC, releasing atomic carbon. At the highest temperature range of 600-1100 °C, the low neutron scattering length density at high temperature is consistent with a silicon-rich, liquid surface phase corresponding to molten nickel silicides and copper. This liquid catalyst layer promotes the liquid-phase epitaxial growth of a graphene layer by precipitating the excess carbon available at the SiC/metal interface.

Highly Ordered Monolayers of μm-Sized Polystyrene Spheres Studied by Grazing-Incidence Small-Angle X-ray Scattering, Simulations, and Geometrical Calculations

Unraveling the two-dimensional (2D) structural ordering of colloidal particles assembled at a flat surface is essential for understanding and optimizing their physical properties. So far, grazing-incidence small-angle X-ray scattering (GISAXS) has been widely used to determine crystallographic information on 2D self-assembled structures of nanosize objects. However, solving the structure of 2D lattices consisting of micrometer (μm)-sized objects still remains a challenge using scattering methods. Here, a model 2D SCALMS (supported catalytically active liquid metal solution) template is fabricated from μm-sized polystyrene (PS) spheres that form a monolayer on top of the flat solid support. GISAXS patterns of the sample were collected for rotation angles around its surface normal in steps of 3°. For every rotation angle, different Bragg-type interference maxima along the out-of-plane (qz) direction were observed. On the basis of simulations of GISXAS patterns of single domains of ordered particle arrangements using the distorted wave Born approximation (DWBA) and validation against a simple geometrical scattering model, the interference maxima could nicely be interpreted to originate from a monolayer of the μm-sized spherical particles which are arranged in domains of hexagonal 2D paracrystalline order. This novel GISAXS evaluation technique serves as a proof of principle for determining the μm-size periodicity of 2D crystalline domains and demonstrates its potential to spatially resolve the relative orientations of such domains with respect to a reference direction.

Hybrid Metrology for Nanostructured Optical Metasurfaces

Metasurfaces have garnered increasing research interest in recent years due to their remarkable advantages, such as efficient miniaturization and novel functionalities compared to traditional optical elements such as lenses and filters. These advantages have facilitated their rapid commercial deployment. Recent advancements in nanofabrication have enabled the reduction of optical metasurface dimensions to the nanometer scale, expanding their capabilities to cover visible wavelengths. However, the pursuit of large-scale manufacturing of metasurfaces with customizable functions presents challenges in controlling the dimensions and composition of the constituent dielectric materials. To address these challenges, the combination of block copolymer (BCP) self-assembly and sequential infiltration synthesis (SIS), offers an alternative for fabrication of high-resolution dielectric nanostructures with tailored composition and optical functionalities. However, the absence of metrological techniques capable of providing precise and reliable characterization of the refractive index of dielectric nanostructures persists. This study introduces a hybrid metrology strategy that integrates complementary synchrotron-based traceable X-ray techniques to achieve comprehensive material characterization for the determination of the refractive index on the nanoscale. To establish correlations between material functionality and their underlying chemical, compositional and dimensional properties, TiO2 nanostructures model systems were fabricated by SIS of BCPs. The results from synchrotron-based analyses were integrated into physical models, serving as a validation scheme for laboratory-scale measurements to determine effective refractive indices of the nanoscale dielectric materials.

Decoding the Self-Assembly Plasmonic Interface Structure in a PbS Colloidal Quantum Dot Solid for a Photodetector

Hybrid plasmonic nanostructures have gained enormous attention in a variety of optoelectronic devices due to their surface plasmon resonance properties. Self-assembled hybrid metal/quantum dot (QD) architectures offer a means of coupling the properties of plasmonics and QDs to photodetectors, thereby modifying their functionality. The arrangement and localization of hybrid nanostructures have an impact on exciton trapping and light harvesting. Here, we present a hybrid structure consisting of self-assembled gold nanospheres (Au NSs) embedded in a solid matrix of PbS QDs for mapping the interface structures and the motion of charge carriers. Grazing-incidence small-angle X-ray scattering is utilized to analyze the localization and spacing of the Au NSs within the hybrid structure. Furthermore, by correlating the morphology of the Au NSs in the hybrid structure with the corresponding differences observed in the performance of photodetectors, we are able to determine the impact of interface charge carrier dynamics in the coupling structure. From the perspective of architecture, our study provides insights into the performance improvement of optoelectronic devices.

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.

Extraction of interaction parameters from specular neutron reflectivity in thin films of diblock copolymers: an "inverse problem"

Diblock copolymers have been shown to undergo microphase separation due to an interplay of repulsive interactions between dissimilar monomers, which leads to the stretching of chains and entropic loss due to the stretching. In thin films, additional effects due to confinement and monomer-surface interactions make microphase separation much more complicated than in that in bulks (i.e., without substrates). Previously, physics-based models have been used to interpret and extract various interaction parameters from the specular neutron reflectivities of annealed thin films containing diblock copolymers (J. P. Mahalik, J. W. Dugger, S. W. Sides, B. G. Sumpter, V. Lauter and R. Kumar, Interpreting neutron reflectivity profiles of diblock copolymer nanocomposite thin films using hybrid particle-field simulations, Macromolecules, 2018, 51(8), 3116; J. P. Mahalik, W. Li, A. T. Savici, S. Hahn, H. Lauter, H. Ambaye, B. G. Sumpter, V. Lauter and R. Kumar, Dispersity-driven stabilization of coexisting morphologies in asymmetric diblock copolymer thin films, Macromolecules, 2021, 54(1), 450). However, extracting Flory-Huggins χ parameters characterizing monomer-monomer, monomer-substrate, and monomer-air interactions has been labor-intensive and prone to errors, requiring the use of alternative methods for practical purposes. In this work, we have developed such an alternative method by employing a multi-layer perceptron, an autoencoder, and a variational autoencoder. These neural networks are used to extract interaction parameters not only from neutron scattering length density profiles constructed using self-consistent field theory-based simulations, but also from a noisy ad hoc model constructed previously. In particular, the variational autoencoder is shown to be the most promising tool when it comes to the reconstruction and extraction of parameters from an ad hoc neutron scattering length density profile of a thin film containing a symmetric di-block copolymer (poly(deuterated styrene-b-n-butyl methacrylate)). This work paves the way for automated analysis of specular neutron reflectivities from thin films of copolymers using machine learning tools.

Mixed Small-Molecule Matrices Improve Nanoparticle Dispersibility in Organic Semiconductor-Nanoparticle Films

Controlling the dispersibility of nanocrystalline inorganic quantum dots (QDs) within organic semiconductor (OSC):QD nanocomposite films is critical for a wide range of optoelectronic devices. This work demonstrates how small changes to the OSC host molecule can have a dramatic detrimental effect on QD dispersibility within the host organic semiconductor matrix as quantified by grazing incidence X-ray scattering. It is commonplace to modify QD surface chemistry to enhance QD dispersibility within an OSC host. Here, an alternative route toward optimizing QD dispersibilities is demonstrated, which dramatically improves QD dispersibilities through blending two different OSCs to form a fully mixed OSC matrix phase.

Extracting the morphology of gold bipyramids from small-angle X-ray scattering experiments via form factor modelling

Accurate shape description is a challenge in materials science. Small-angle X-ray scattering (SAXS) can provide the shape, size and polydispersity of nanoparticles by form factor modelling. However, simple geometric models such as the ellipsoid may not be enough to describe objects with complex shapes. This work shows that the form factor of gold nanobipyramids is accurately described by a truncated bicone model, which is validated by comparison with transmission electron microscopy (TEM) data for nine different synthesis batches; the average shape parameters (width, height and truncation) and the sample polydispersity are obtained. In contrast, the ellipsoid model yields worse fits of the SAXS data and exhibits systematic discrepancies with the TEM results.

Structural Characterization of Nanoparticle-Supported Lipid Bilayer Arrays by Grazing Incidence X-ray and Neutron Scattering

Arrays of nanoparticle-supported lipid bilayers (nanoSLB) are lipid-coated nanopatterned interfaces that provide a platform to study curved model biological membranes using surface-sensitive techniques. We combined scattering techniques with direct imaging, to gain access to sub-nanometer scale structural information on stable nanoparticle monolayers assembled on silicon crystals in a noncovalent manner using a Langmuir-Schaefer deposition. The structure of supported lipid bilayers formed on the nanoparticle arrays via vesicle fusion was investigated using a combination of grazing incidence X-ray and neutron scattering techniques complemented by fluorescence microscopy imaging. Ordered nanoparticle assemblies were shown to be suitable and stable substrates for the formation of curved and fluid lipid bilayers that retained lateral mobility, as shown by fluorescence recovery after photobleaching and quartz crystal microbalance measurements. Neutron reflectometry revealed the formation of high-coverage lipid bilayers around the spherical particles together with a flat lipid bilayer on the substrate below the nanoparticles. The presence of coexisting flat and curved supported lipid bilayers on the same substrate, combined with the sub-nanometer accuracy and isotopic sensitivity of grazing incidence neutron scattering, provides a promising novel approach to investigate curvature-dependent membrane phenomena on supported lipid bilayers.

Protein Cage-Stabilized Emulsions: Formulation and Characterization

The formulation of Pickering emulsions using protein cages is gaining interest for applications in molecular delivery. Despite the growing interest, methods to investigate the at the liquid-liquid interface are limited. This chapter describes standard methods to formulate and protocols to characterize protein cage-stabilized emulsions. The characterization methods are dynamic light scattering (DLS), intrinsic fluorescence spectroscopy (TF), circular dichroism (CD), and small angle X-ray scattering (SAXS). Combining these methods allows understanding of the protein cage nanostructure at the oil/water interface.

Light propagation in layered media in a total reflection geometry: a transfer matrix method using virtually linear basis functions to handle critical conditions

For light propagation in a layered refractive index profile, critical conditions occur when the wave vector perpendicular to the layering becomes zero. Such conditions can occur in a total reflection geometry. Conventional transfer matrix methods become singular, and geometrical optics concepts break down at critical conditions. We introduce two new, to the best of our knowledge, basis systems using virtual linear functions that obey the Helmholtz equation and turn to linear functions required for critical conditions.

GenX 3: the latest generation of an established tool

Improvements to the GenX program are discussed, including performance, model building and error analysis.

Since its publication more than 15 years ago the GenX software has been continuously developed and has established itself as a standard package for analyzing X-ray and neutron reflectometry data. The evolution of the software during the last two major revisions is reported here. This includes a simplified model builder for beginners, simple samples, additional sample models, statistical error analysis and the use of just-in-time compilation modules for the reflectometry kernel to achieve higher performance. In addition, the influence of experimental errors on the reflectivity curve is discussed, and new features are described that allow the user to include these in the error statistics to improve the fitting and uncertainty estimation.

Real-Time Observation of Temperature-Induced Surface Nanofaceting in M-Plane α-Al2O3

The spontaneous crystal surface reconstruction of M-plane α-Al₂O₃ is employed for nanopatterning and nanofabrication in various fields of research including, among others, magnetism, superconductivity, and optoelectronics. In this reconstruction process the crystalline surface transforms from a planar morphology to one with a nanoscale ripple patterning. However, the high sample temperature required to induce surface reconstruction made in situ studies of the process seem unfeasible. The kinetics of ripple pattern formation therefore remained uncertain, and thus production of templates for nanofabrication could not advance beyond a trial-and-error stage. We present an approach combining in situ real-time grazing incidence small-angle X-ray scattering experiments (GISAXS) with model-based analysis and with ex situ atomic force microscopy (AFM) to observe this morphological transition in great detail. Our approach provides time-resolved information about all relevant morphological parameters required to trace the surface topography on the nanometer scale during reconstruction, i.e., the time dependence of the pattern wavelength, the ripple length, width, and height, and thus their facet angles. It offers a comprehensive picture of this process exemplified by a M-plane α-Al₂O₃ surface annealed at 1325 °C for 930 min. Fitting the model parameters to the experimental GISAXS data revealed a Johnson-Mehl-Avrami-Kolmogorov type of behavior for the pattern wavelength and a predominantly linear time dependence of the other parameters. In this case the reconstruction resulted in a crystalline surface fully patterned with asymmetric ripple-shaped nanostructures of 75 nm periodicity, 15 nm in height, and 630 nm in length. By elucidating the time dependence of these morphological parameters, this study shows a powerful way to significantly advance the predictability of annealing outcome and thus to efficiently customize nanopatterned α-Al₂O₃ templates for improved nanofabrication routines.

State of the art of ultra-thin gold layers: formation fundamentals and applications

Fabrication of ultra-thin gold (Au) layers (UTGLs) has been regarded as the key technique to achieve applications with tunable optical response, flexible sensors and electronic devices. Various strategies have been developed to optimize the wetting process of Au, resulting in the formation of UTGLs at a minimum thickness. The related studies on UTGLs attracted huge attention in recent years. On the one hand, the growth processes of UTGLs on different substrates were in-depth probed by advanced in situ characterization techniques and the effects of optimization strategies on the growth of UTGLs were also revealed. On the other hand, based on the understanding of the growth behavior and the assistance of optimization strategies, various applications of UTGLs were realized based on optical/plasmon responses, surface-enhanced Raman scattering and as electrodes for various sensors and electronic devices, as well as being seed layers for thin film growth. In this focused review, both the fundamental and practical studies on UTGLs in the most recent years are elaborated in detail. The growth processes of UTGLs revealed by in situ characterization techniques, such as grazing-incidence small-angle X-ray scattering (GISAXS), as well as the state of the art of UTGL-based applications, are reviewed.

Evolution of surface and sub-surface morphology and chemical state of exsolved Ni nanoparticles

Nanoparticle formation by dopant exsolution (migration) from bulk host lattices is a promising approach to generate highly stable nanoparticles with tunable size, shape, and distribution. We investigated Ni dopant migration from strontium titanate (STO) lattices, forming metallic Ni nanoparticles at STO surfaces. Ex situ scanning probe measurements confirmed the presence of nanoparticles at the H₂ treated surface. In situ ambient pressure X-ray photoelectron spectroscopy (AP-XPS) revealed reduction from Ni²⁺ to Ni⁰ as Ni dopants migrated to the surface during heating treatments in H₂. During Ni migration and reduction, the Sr and Ti chemical states were mostly unchanged, indicating the selective reduction of Ni during treatment. At the same time, we used in situ ambient pressure grazing incidence X-ray scattering (GIXS) to monitor the particle morphology. As Ni migrated to the surface, it nucleated and grew into compressed spheroidal nanoparticles partially embedded in the STO perovskite surface. These findings provide a detailed picture of the evolution of the nanoparticle surface and subsurface chemical state and morphology as the nanoparticles grow beyond the initial nucleation and growth stages.

Compact Peptoid Molecular Brushes for Nanoparticle Stabilization

Controlling the interfaces and interactions of colloidal nanoparticles (NPs) via tethered molecular moieties is crucial for NP applications in engineered nanomaterials, optics, catalysis, and nanomedicine. Despite a broad range of molecular types explored, there is a need for a flexible approach to rationally vary the chemistry and structure of these interfacial molecules for controlling NP stability in diverse environments, while maintaining a small size of the NP molecular shell. Here, we demonstrate that low-molecular-weight, bifunctional comb-shaped, and sequence-defined peptoids can effectively stabilize gold NPs (AuNPs). The generality of this robust functionalization strategy was also demonstrated by coating of silver, platinum, and iron oxide NPs with designed peptoids. Each peptoid (PE) is designed with varied arrangements of a multivalent AuNP-binding domain and a solvation domain consisting of oligo-ethylene glycol (EG) branches. Among designs, a peptoid (PE5) with a diblock structure is demonstrated to provide a superior nanocolloidal stability in diverse aqueous solutions while forming a compact shell (∼1.5 nm) on the AuNP surface. We demonstrate by experiments and molecular dynamics simulations that PE5-coated AuNPs (PE5/AuNPs) are stable in select organic solvents owing to the strong PE5 (amine)-Au binding and solubility of the oligo-EG motifs. At the vapor-aqueous interface, we show that PE5/AuNPs remain stable and can self-assemble into ordered 2D lattices. The NP films exhibit strong near-field plasmonic coupling when transferred to solid substrates.

Efficient solution of particle shape functions for the analysis of powder total scattering data

Structural characterization of powder samples via total scattering methods, in either real or reciprocal space, must take into account the effect of particle shape. Here, the shape contribution of a set of ideally isolated particles to the small-angle scattering (SAS) component of the intensity profile is modelled using the shape function [Svergun & Koch (2003). Rep. Prog. Phys. 66, 1735-1782]. The shape function is obtained by orientational averaging of common volume functions (CVFs) for a discrete set of directions. The effects of particle size and size dispersity are accounted for via scaling of the CVFs and their convolution with the underlying probability distribution. The method is applied to shapes with CVFs expressed analytically or by using discrete tables. The accurate calculation of SAS particle shape contributions up to large momentum transfer demonstrates the reliability and flexibility of modelling shape functions from sets of CVFs. The algorithm presented here is computationally efficient and can be directly incorporated into existing routines for analysis of powder total scattering data.

Guidelines for collaborative development of sustainable data treatment software

Software development for data reduction and analysis at large research facilities is increasingly professionalized, and internationally coordinated. To foster software quality and sustainability, and to facilitate collaboration, representatives from software groups of European neutron and muon facilities have agreed on a set of guidelines for development practices, infrastructure, and functional and non-functional product properties. These guidelines have been derived from actual practices in software projects from the EU funded consortium ‘Science and Innovation with Neutrons in Europe in 2020’ (SINE2020), and have been enriched through extensive literature review. Besides guiding the work of the professional software engineers in our computing groups, we hope to influence scientists who are willing to contribute their own data treatment software to our community. Moreover, this work may also provide inspiration to scientific software development beyond the neutron and muon field.

Using small-angle scattering to guide functional magnetic nanoparticle design

Magnetic nanoparticles offer unique potential for various technological, biomedical, or environmental applications thanks to the size-, shape- and material-dependent tunability of their magnetic properties. To optimize particles for a specific application, it is crucial to interrelate their performance with their structural and magnetic properties. This review presents the advantages of small-angle X-ray and neutron scattering techniques for achieving a detailed multiscale characterization of magnetic nanoparticles and their ensembles in a mesoscopic size range from 1 to a few hundred nanometers with nanometer resolution. Both X-rays and neutrons allow the ensemble-averaged determination of structural properties, such as particle morphology or particle arrangement in multilayers and 3D assemblies. Additionally, the magnetic scattering contributions enable retrieving the internal magnetization profile of the nanoparticles as well as the inter-particle moment correlations caused by interactions within dense assemblies. Most measurements are used to determine the time-averaged ensemble properties, in addition advanced small-angle scattering techniques exist that allow accessing particle and spin dynamics on various timescales. In this review, we focus on conventional small-angle X-ray and neutron scattering (SAXS and SANS), X-ray and neutron reflectometry, gracing-incidence SAXS and SANS, X-ray resonant magnetic scattering, and neutron spin-echo spectroscopy techniques. For each technique, we provide a general overview, present the latest scientific results, and discuss its strengths as well as sample requirements. Finally, we give our perspectives on how future small-angle scattering experiments, especially in combination with micromagnetic simulations, could help to optimize the performance of magnetic nanoparticles for specific applications.

SGTools: a suite of tools for processing and analyzing large data sets from in situ X-ray scattering experiments

In situ synchrotron small-angle X-ray scattering (SAXS) is a powerful tool for studying dynamic processes during material preparation and application. The processing and analysis of large data sets generated from in situ X-ray scattering experiments are often tedious and time consuming. However, data processing software for in situ experiments is relatively rare, especially for grazing-incidence small-angle X-ray scattering (GISAXS). This article presents an open-source software suite (SGTools) to perform data processing and analysis for SAXS and GISAXS experiments. The processing modules in this software include (i) raw data calibration and background correction; (ii) data reduction by multiple methods; (iii) animation generation and intensity mapping for in situ X-ray scattering experiments; and (iv) further data analysis for the sample with an order degree and interface correlation. This article provides the main features and framework of SGTools. The workflow of the software is also elucidated to allow users to develop new features. Three examples are demonstrated to illustrate the use of SGTools for dealing with SAXS and GISAXS data. Finally, the limitations and future features of the software are also discussed.

Using refnx to Model Neutron Reflectometry Data from Phospholipid Bilayers

Neutron reflectometry has emerged as a powerful method for studying the structure of thin films in contact with solution at sub-molecular spatial resolution (Penfold and Thomas, J Phys Condens Matter 2:1369-1412, 1990). This type of experiment is undertaken at large international central facilities and experience in data analysis and interpretation is not always available "locally". Here, we describe the application of the refnx software suite (Nelson and Prescott, J Appl Crystallogr 52:193-200, 2019) to the analysis of a single phospholipid bilayer deposited at a silicon/buffer interface. The data is modeled such that the fitted parameters are readily interpretable by researchers working with lipid bilayers.

State of the Art and Prospects for Halide Perovskite Nanocrystals

Metal-halide perovskites have rapidly emerged as one of the most promising materials of the 21st century, with many exciting properties and great potential for a broad range of applications, from photovoltaics to optoelectronics and photocatalysis. The ease with which metal-halide perovskites can be synthesized in the form of brightly luminescent colloidal nanocrystals, as well as their tunable and intriguing optical and electronic properties, has attracted researchers from different disciplines of science and technology. In the last few years, there has been a significant progress in the shape-controlled synthesis of perovskite nanocrystals and understanding of their properties and applications. In this comprehensive review, researchers having expertise in different fields (chemistry, physics, and device engineering) of metal-halide perovskite nanocrystals have joined together to provide a state of the art overview and future prospects of metal-halide perovskite nanocrystal research.

Mutually Beneficial Combination of Molecular Dynamics Computer Simulations and Scattering Experiments

We showcase the combination of experimental neutron scattering data and molecular dynamics (MD) simulations for exemplary phospholipid membrane systems. Neutron and X-ray reflectometry and small-angle scattering measurements are determined by the scattering length density profile in real space, but it is not usually possible to retrieve this profile unambiguously from the data alone. MD simulations predict these density profiles, but they require experimental control. Both issues can be addressed simultaneously by cross-validating scattering data and MD results. The strengths and weaknesses of each technique are discussed in detail with the aim of optimizing the opportunities provided by this combination.

Probing morphology and chemistry in complex soft materials within situresonant soft x-ray scattering

Small angle scattering methodologies have been evolving at fast pace over the past few decades due to the ever-increasing demands for more details on the complex nanostructures of multiphase and multicomponent soft materials like polymer assemblies and biomaterials. Currently, element-specific and contrast variation techniques such as resonant (elastic) soft/tender x-ray scattering, anomalous small angle x-ray scattering, and contrast-matching small angle neutron scattering, or combinations of above are routinely used to extract the chemical composition and spatial arrangement of constituent elements at multiple length scales and examine electronic ordering phenomena. Here we present some recent advances in selectively characterizing structural architectures of complex soft materials, which often contain multi-components with a wide range of length scales and multiple functionalities, where novel resonant scattering approaches have been demonstrated to decipher a higher level of structural complexity that correlates to functionality. With the advancement of machine learning and artificial intelligence assisted correlative analysis, high-throughput and autonomous experiments would open a new paradigm of material research. Further development of resonant x-ray scattering instrumentation with crossplatform sample environments will enable multimodalin situ/operando characterization of the system dynamics with much improved spatial and temporal resolution.

Direct observation of spin correlations in an artificial triangular lattice Ising spin system with grazing-incidence small-angle neutron scattering

The triangular lattice with Ising magnetic moments is an archetypical example of geometric frustration. In the case of dipolar-coupled out-of-plane moments, the geometric frustration results in a disordered classical spin-liquid state at higher temperatures while the system is predicted to transition to an anti-ferromagnetic stripe ground state at low temperatures. In this work we fabricate artificial triangular Ising spin systems without and with uniaxial in-plane compression to tune the nature and temperature of the correlations. We probe the energy scale and nature of magnetic correlations by grazing-incidence small-angle neutron scattering. In particular, we apply a newly-developed empirical structure-factor model to describe the measured short-range correlated spin-liquid state, and find good agreement with theoretical predictions. We demonstrate that grazing-incidence neutron scattering on our high-quality samples, in conjunction with detailed modeling of the scattering using the Distorted Wave Born Approximation, can be used to experimentally quantify the spin-liquid-like correlations in highly-frustrated artificial spin systems.

Towards reflectivity profile inversion through artificial neural networks

The goal of specular neutron and x-ray reflectometry is to infer a material’s scattering length density (SLD) profile from its experimental reflectivity curves. This paper focuses on the investigation of an original approach to the ill-posed non-invertible problem which involves the use of artificial neural networks (ANNs). In particular, the numerical experiments described here deal with large data sets of simulated reflectivity curves and SLD profiles, and aim to assess the applicability of data science and machine learning technology to the analysis of data generated at large-scale neutron scattering facilities. It is demonstrated that, under certain circumstances, properly trained deep neural networks are capable of correctly recovering plausible SLD profiles when presented with previously unseen simulated reflectivity curves. When the necessary conditions are met, a proper implementation of the described approach would offer two main advantages over traditional fitting methods when dealing with real experiments, namely (1) sample physical models are described under a new paradigm: detailed layer-by-layer descriptions (SLDs, thicknesses, roughnesses) are replaced by parameter-free curves ρ(z), allowing a priori assumptions to be used in terms of the sample family to which a given sample belongs (e.g. ‘thin film,’ ‘lamellar structure’,etc.); (2) the time required to reach a solution is shrunk by orders of magnitude, enabling faster batch analysis for large datasets.

Improved thermal stability of antireflective moth-eye topography imprinted on PMMA/TiO2surface nanocomposites

The thermal stability of antireflective moth-eye topographical features fabricated by nanoimprint lithography on poly (methyl methacrylate) (PMMA) incorporating TiO₂nanoparticles is explored. The effect of nanoparticle load on the relaxation dynamics of the moth-eye nanostructure is evaluated via grazing incidence small angle x-ray scattering measurements byin situmonitoring the structural decay of the nanopatterns upon thermal annealing. It is demonstrated that the incorporation of TiO₂nanoparticles to the imprinted surface nanocomposite films delays greatly the pattern relaxation which, in turn, enhances the stability of the patterned topography even at temperatures well above the polymer glass transition (T_g). The improved thermal behavior of the antireflective films will significantly enhance their functionality and performance in light-trapping applications where temperatures typically rise, such as solar devices or solar glass panels.

Numerically stable form factor of any polygon and polyhedron

Coordinate-free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes's theorem. Apparent singularities, all removable, are discussed in detail. Cancellation near the singularities causes a loss of precision that can be avoided by using series expansions. An important application domain is small-angle scattering by nanocrystals.

Stress-Assisted Thermal Diffusion Barrier Breakdown in Ion Beam Deposited Cu/W Nano-Multilayers on Si Substrate Observed by in Situ GISAXS and Transmission EDX

The thermal stability of Cu/W nano-multilayers deposited on a Si substrate using ion beam deposition was analyzed in situ by GISAXS and transmission EDX-a combination of methods permitting the observation of diffusion processes within buried layers. Further supporting techniques such as XRR, TEM, WAXS, and AFM were employed to develop an extensive microstructural understanding of the multilayer before and during heating. It was found that the pronounced in-plane compressive residual stress and defect population induced by ion beam deposition result in low thermal stability driven by thermally activated self-interstitial and vacancy diffusion, ultimately leading to complete degradation of the layered structure at moderate temperatures. The formation of Cu protrusions was observed, and a model was formulated for stress-assisted Cu diffusion driven by Coble creep along W grain boundaries, along with the interaction with Si substrate, which showed excellent agreement with the observed experimental data. The model provided the explanation for the experimentally observed strong correlation between thin film deposition conditions, microstructural properties, and low thermal stability that can be applied to other multilayer systems.

Understanding near-surface polymer dynamics by a combination of grazing-incidence neutron scattering and virtual experiments

Neutron spin-echo spectroscopy is a unique experimental method for the investigation of polymer dynamics. The combination of neutron spin-echo spectroscopy with grazing-incidence geometry (GINSES) opens the possibility to probe the dynamics of soft-matter materials in the vicinity of the solid substrate in the time range up to 100 ns. However, the usage of the GINSES technique has some peculiarities and, due to the novelty of the method and complexity of the scattering geometry, difficulties in further data analysis occur. The current work discusses how virtual experiments within the distorted-wave Born approximation using the BornAgain software can improve GINSES data treatment and aid the understanding of polymer dynamics in the vicinity of the solid surface. With two examples, poly(N-isopropyl acrylamide) brushes and poly(ethylene glycol) microgels on Si surfaces, the simulation as well as the application of the simulation to the GINSES data analysis are presented. The approach allowed a deeper insight to be gained of the background effect and scattering contribution of different layers.

Small-angle X-ray scattering from GaN nanowires on Si(111): facet truncation rods, facet roughness and Porod's law

Small-angle X-ray scattering from GaN nanowires grown on Si(111) is measured in the grazing-incidence geometry and modelled by means of a Monte Carlo simulation that takes into account the orientational distribution of the faceted nanowires and the roughness of their side facets. It is found that the scattering intensity at large wavevectors does not follow Porod's law I(q) ∝ q-4. The intensity depends on the orientation of the side facets with respect to the incident X-ray beam. It is maximum when the scattering vector is directed along a facet normal, reminiscent of surface truncation rod scattering. At large wavevectors q, the scattering intensity is reduced by surface roughness. A root-mean-square roughness of 0.9 nm, which is the height of just 3-4 atomic steps per micrometre-long facet, already gives rise to a strong intensity reduction.

Electric-field-intensity-modulated scattering as a thin-film depth probe

Grazing-incidence X-ray scattering is a common technique to elucidate nanostructural information for thin-film samples, but depth-resolving this nanostructure is difficult using a single or few images. An in situ method to extract film thickness, the index of refraction and depth information using scattering images taken across a range of incident angles is presented here. The technique is described within the multilayer distorted-wave Born approximation and validated using two sets of polymer thin films. Angular divergence and energy resolution effects are considered, and implementation of the technique as a general beamline procedure is discussed. Electric-field-intensity-modulated scattering is a general technique applicable to myriad materials and enables the acquisition of depth-sensitive information in situ at any grazing-incidence-capable beamline.

In situ Grazing-Incidence Small-Angle X-ray Scattering Observation of Gold Sputter Deposition on a PbS Quantum Dot Solid

For PbS quantum dot (QD)-based optoelectronic devices, gold is the most frequently used electrode material. In most device architectures, gold is in direct contact with the QD solid. To better understand the formation of the interface between gold and a close-packed QD layer at an early stage, in situ grazing-incidence small-angle X-ray scattering is used to observe the gold sputter deposition on a 1,2-ethanedithiol (EDT)-treated PbS QD solid. In the kinetics of gold layer growth, the forming and merging of small gold clusters (radius less than 1.6 nm) are observed at the early stages. The thereby formed medium gold clusters (radius between 1.9-2.4 nm) are influenced by the QDs' templating effect. Furthermore, simulations suggest that the medium gold clusters grow preferably along the QDs' boundaries rather than as a top coating of the QDs. When the thickness of the sputtered gold layer reaches 6.25 nm, larger gold clusters with a radius of 5.3 nm form. Simultaneously, a percolation layer with a thickness of 2.5 nm is established underneath the gold clusters. This fundamental understanding of the QD-gold interface formation will help to control the implementation of sputtered gold electrodes on close-packed QD solids in device manufacturing processes.

Generalizing small-angle scattering form factors with linear transformations

Nanostructure characterization using small-angle scattering is often performed by iteratively fitting a scattering model to experimental data. These scattering models are usually derived in part from the form factors of the expected shapes of the particles. Most small-angle-scattering pattern-fitting software is well equipped with form factor libraries for high-symmetry models, yet there is more limited support for distortions to these ideals that are more typically found in nature. Here, a means of generalizing high-symmetry form factors to these lower-symmetry cases via linear transformations is introduced, significantly expanding the range of form factors available to researchers. These linear transformations are composed of a series of scaling, shear, rotation and inversion operations, enabling particle distortions to be understood in a straightforward and intuitive way. This approach is expected to be especially useful for in situ studies of nanostructure growth where anisotropic structures change continuously and large data sets must be analysed.

Carbon Deposition on Hematite (α-Fe2O3) Nanocubes by Annealing in the Air: Morphology Study with Grazing Incidence Small Angle X-ray Scattering (GISAXS)

GISAXS has been used to study morphology change of α-Fe2O3 nanocubes after annealing processes. A submonolayer of the nanocubes was deposited on a Si(100) substrate. While an annealing at 400 °C in vacuum does not change a GISAXS pattern from as-prepared nanocubes submonolayer, subsequent annealing in air at the same temperature altered the GISAXS pattern significantly. SEM images showed that the air-annealed nanocubes were coated with thin layers which were identified as amorphous carbon layers based on Raman measurements. GISAXS simulations from morphologies of nanocube with 38 nm side-length and core-shell (nanocube-core and 7 nm thick carbon-shell) reproduced measured patterns from the vacuum- and the air-annealed nanocubes, respectively. The current study provides new approach for in-situ characterization of carbon deposition on a uniform shape nanoparticle through monitoring of deposited carbon thickness.

Oriented thick films of block copolymer made by multiple successive coatings: perforated lamellae versus oriented lamellae

Building 3D ordered nanostructures by copolymer deposition on a substrate implies a full control beyond the thin film regime. We have used here block copolymers (BCPs) forming bulk lamellar phases to form thick, i.e. much thicker than the lamellar period, structured films on a substrate. Films are formed by a simple method of multiple successive coatings. The film structure is controlled using the combined action of surface templating and annealing time. Sections of the thick layers were characterized by scanning electron microscopy (SEM) after etching of one of the BCP moieties. We show that perfect hexagonally perforated films (HPL) with lamellae parallel to the substrate are formed for a wide thickness range up to 300 nm. Grazing incidence small angle X-ray scattering (GISAXS) confirms such an organization by revealing that perforations sit on a hexagonal lattice. A lamellar organization perpendicular to the substrate is shown to take over for thicker films. A scenario consistent with our observations is proposed, where the sequence of phases results from the balance between surface and stretching energy effects.

Self assembled monolayer of silica nanoparticles with improved order by drop casting

This paper reports on the formation of large area, self assembled, highly ordered monolayers of stearyl alcohol grafted silica nanospheres of ≈50 nm diameter on a silicon substrate based on the drop-casting method. Our novel approach to achieve improved order uses stearyl alcohol as an assistant by adding it to the colloidal NanoParticle (NP) dispersion from which the monolayers are formed. Additionally, a heat treatment step is added, to melt the stearyl alcohol in the monolayer and thereby give the particles more time to further self-assemble, leading to additional improvement in the monolayer quality. The formation of the monolayers is significantly affected by the concentration of the NPs and the stearyl alcohol, the volume of the drop as well as the time of the heat treatment. A high surface coverage and uniform monolayer film of SiO2 NPs is achieved by appropriate control of the above-mentioned preparation parameters. Structural characterization of the obtained SiO2 NP monolayer was done locally by Scanning Electron Microscopy (SEM), and globally by X-ray reflectivity (XRR) and grazing incidence small-angle X-ray scattering (GISAXS), where the data was reproduced by simulation within the Distorted Wave Born Approximation (DWBA). In conclusion, our modified drop-casting method is a simple, inexpensive method, which provides highly ordered self-assembled monolayers of silica particles, if combined with a compatible additive and a heat treatment step. This method might be more general and also applicable to different particles after finding an appropriate additive.

Colloidal PbS quantum dot stacking kinetics during deposition via printing

Colloidal PbS quantum dots (QDs) are attractive for solution-processed thin-film optoelectronic applications. In particular, directly achieving QD thin-films by printing is a very promising method for low-cost and large-scale fabrication. The kinetics of QD particles during the deposition process play an important role in the QD film quality and their respective optoelectronic performance. In this work, the particle self-organization behavior of small-sized QDs with an average diameter of 2.88 ± 0.36 nm is investigated for the first time in situ during printing by grazing-incidence small-angle X-ray scattering (GISAXS). The time-dependent changes in peak intensities suggest that the structure formation and phase transition of QD films happen within 30 seconds. The stacking of QDs is initialized by a templating effect, and a face-centered cubic (FCC) film forms in which a superlattice distortion is also found. A body-centered cubic nested FCC stacking is the final QD assembly layout. The small size of the inorganic QDs and the ligand collapse during the solvent evaporation can well explain this stacking behavior. These results provide important fundamental understanding of structure formation of small-sized QD based films prepared via large-scale deposition with printing with a slot die coater.