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Diffuse scattering is a promising method to gain additional insight into protein dynamics from macromolecular crystallography experiments. Bragg intensities yield the average electron density, while the diffuse scattering can be processed to obtain a three-dimensional reciprocal-space map that is further analyzed to determine correlated motion. To make diffuse scattering techniques more accessible, software for data processing called mdx2 has been created that is both convenient to use and simple to extend and modify. mdx2 is written in Python, and it interfaces with DIALS to implement self-contained data-reduction workflows. Data are stored in NeXus format for software interchange and convenient visualization. mdx2 can be run on the command line or imported as a package, for instance to encapsulate a complete workflow in a Jupyter notebook for reproducible computing and education. Here, mdx2 version 1.0 is described, a new release incorporating state-of-the-art techniques for data reduction. The implementation of a complete multi-crystal scaling and merging workflow is described, and the methods are tested using a high-redundancy data set from cubic insulin. It is shown that redundancy can be leveraged during scaling to correct systematic errors and obtain accurate and reproducible measurements of weak diffuse signals.

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The suitability of point focus X-ray beam and area detector techniques for the determination of the uniaxial symmetry axis (fibre texture) of the natural mineral satin spar is demonstrated. Among the various diffraction techniques used in this report, including powder diffraction, 2D pole figures, rocking curves looped on φ and 2D X-ray diffraction, a single simple symmetric 2D scan collecting the reciprocal plane perpendicular to the apparent fibre axis provided sufficient information to determine the crystallographic orientation of the fibre axis. A geometrical explanation of the 'wing' feature formed by diffraction spots from the fibre-textured satin spar in 2D scans is provided. The technique of wide-range reciprocal space mapping restores the 'wing' featured diffraction spots on the 2D detector back to reciprocal space layers, revealing the nature of the fibre-textured samples.

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The structure and the chemical composition of individual layers as well as of interfaces belonging to the two heterostructures M1 (BaFe12O19/YbFeO3/YSZ) and M2 (YbFeO3/BaFe12O19/YSZ) grown by pulsed laser deposition on yttria-stabilized zirconia (YSZ) substrates are deeply characterized by using a combination of methods such as high-resolution X-ray diffraction, transmission electron microscopy (TEM), and atomic-resolution scanning TEM with energy-dispersive X-ray spectroscopy. The temperature-dependent magnetic properties demonstrate two distinct heterostructures with different coercivity, anisotropy fields, and first anisotropy constants, which are related to the defect concentrations within the individual layers and to the degree of intermixing at the interface. The heterostructure with the stacking order BaFe12O19/YbFeO3, i.e., M1, exhibits a distinctive interface without any chemical intermixture, while an Fe-rich crystalline phase is observed in M2 both in atomic-resolution EDX maps and in mass density profiles. Additionally, M1 shows high c-axis orientation, which induces a higher anisotropy constant K1 as well as a larger coercivity due to a high number of phase boundaries. Despite the existence of a canted antiferromagnetic/ferromagnetic combination (T < 140 K), both heterostructures M1 and M2 do not reveal any detectable exchange bias at T = 50 K. Additionally, compressive residual strain on the BaM layer is found to be suppressing the ferromagnetism, thus reducing the Curie temperature (Tc) in the case of M1. These findings suggest that M1 (BaFe12O19/YbFeO3/YSZ) is suitable for magnetic storage applications.

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Diffuse scattering is a promising method to gain additional insight into protein dynamics from macromolecular crystallography (MX) experiments. Bragg intensities yield the average electron density, while the diffuse scattering can be processed to obtain a three-dimensional reciprocal space map, that is further analyzed to determine correlated motion. To make diffuse scattering techniques more accessible, we have created software for data processing called mdx2 that is both convenient to use and simple to extend and modify. Mdx2 is written in Python, and it interfaces with DIALS to implement self-contained data reduction workflows. Data are stored in NeXus format for software interchange and convenient visualization. Mdx2 can be run on the command line or imported as a package, for instance to encapsulate a complete workflow in a Jupyter notebook for reproducible computing and education. Here, we describe mdx2 version 1.0, a new release incorporating state-of-the-art techniques for data reduction. We describe the implementation of a complete multi-crystal scaling and merging workflow, and test the methods using a high-redundancy dataset from cubic insulin. We show that redundancy can be leveraged during scaling to correct systematic errors, and obtain accurate and reproducible measurements of weak diffuse signals.

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Materials with strong spin-orbit coupling (SOC) have been continuously attracting intensive attention due to their promising application in energy-efficient, high-density, and nonvolatile spintronic devices. Particularly, transition-metal perovskite oxides with strong SOC have been demonstrated to exhibit efficient charge-spin interconversion. In this study, we systematically investigated the impact of epitaxial strain on the spin-orbit torque (SOT) efficiency in the SrIrO3(SIO)/Ni81Fe19(Py) bilayer. The results reveal that the SOT efficiency is strongly related to the octahedral rotation around the in-plane axes of the single-crystal SIO. By modulating the epitaxial strain using different substrates, the SOT efficiency can be remarkably improved from 0.15 to 1.45. This 10-fold enhancement of SOT efficiency suggests that modulating the epitaxial strain is an efficient approach to control the SOT efficiency in complex oxide-based heterostructures. Our work may have the potential to advance the application of complex oxides in energy-efficient spintronic devices.

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Diffuse scattering is a powerful technique to study disorder and dynamics of macromolecules at atomic resolution. Although diffuse scattering is always present in diffraction images from macromolecular crystals, the signal is weak compared with Bragg peaks and background, making it a challenge to visualize and measure accurately. Recently, this challenge has been addressed using the reciprocal space mapping technique, which leverages ideal properties of modern X-ray detectors to reconstruct the complete three-dimensional volume of continuous diffraction from diffraction images of a crystal (or crystals) in many different orientations. This chapter will review recent progress in reciprocal space mapping with a particular focus on the strategy implemented in the mdx-lib and mdx2 software packages. The chapter concludes with an introductory data processing tutorial using Python packages DIALS, NeXpy, and mdx2.

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A dynamical theory is developed of X-ray diffraction on a crystal with surface relief for the case of high-resolution triple-crystal X-ray diffractometry. Crystals with trapezoidal, sinusoidal and parabolic bar profile models are investigated in detail. Numerical simulations of the X-ray diffraction problem for concrete experimental conditions are performed. A simple new method to resolve the crystal relief reconstruction problem is proposed.

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This work introduces the high-energy surface X-ray diffraction analysis toolkit (HAT), an open-source cross-platform software package written in Python to allow the extraction and processing of high-energy surface X-ray diffraction (HESXRD) data sets. Thousands of large-area detector images are collected in a single HESXRD scan, corresponding to billions of pixels and hence reciprocal space positions. HAT is an optimized reciprocal space binner that implements a graphical user interface to allow the easy and interactive exploration of HESXRD data sets. Regions of reciprocal space can be selected with movable and resizable masks in multiple views and are projected onto different axes to allow the creation of reciprocal space maps and the extraction of crystal truncation rods. Current and future versions of HAT can be downloaded and used free of charge.

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This work presents a new approach suitable for mapping reciprocal space in three dimensions with standard laboratory equipment and a typical X-ray diffraction setup. The method is based on symmetric and coplanar high-resolution X-ray diffraction, ideally realized using 2D X-ray pixel detectors. The processing of experimental data exploits the Radon transform commonly used in medical and materials science. It is shown that this technique can also be used for diffraction mapping in reciprocal space even if a highly collimated beam is not available. The application of the method is demonstrated for various types of epitaxial microcrystals on Si substrates. These comprise partially fused SiGe microcrystals that are tens of micrometres high, multiple-quantum-well structures grown on SiGe microcrystals and pyramid-shaped GaAs/Ge microcrystals on top of Si micropillars.

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In this paper, the study of defects in InAs/GaSb type-II superlattices using high-resolution an x-ray diffraction method as well as scanning (SEM) and transmission (TEM) electron microscopy is presented. The investigated superlattices had 200 (#SL200), 300 (#SL300), and 400 (#SL400) periods and were grown using molecular beam epitaxy. The growth conditions differed only in growth temperature, which was 370 °C for #SL400 and #SL200, and 390 °C for #SL300. A wings-like diffuse scattering was observed in reciprocal space maps of symmetrical (004) GaSb reflection. The micrometer-sized defect conglomerates comprised of stacking faults, and linear dislocations were revealed by the analysis of diffuse scattering intensity in combination with SEM and TEM imaging. The following defect-related parameters were obtained: (1) integrated diffuse scattering intensity of 0.1480 for #SL400, 0.1208 for #SL300, and 0.0882 for #SL200; (2) defect size: (2.5-3) µm × (2.5-3) µm -#SL400 and #SL200, (3.2-3.4) µm × (3.7-3.9) µm -#SL300; (3) defect diameter: ~1.84 µm -#SL400, ~2.45 µm -#SL300 and ~2.01 µm -#SL200; (4) defect density: 1.42 × 106 cm-2 -#SL400, 1.01 × 106 cm-2 -#SL300, 0.51 × 106 cm-2 -#SL200; (5) diameter of stacking faults: 0.14 µm and 0.13 µm for #SL400 and #SL200, 0.30 µm for #SL300.

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Many polymorphic crystal structures of copper phthalocyanine (CuPc) have been reported over the past few decades, but despite its manifold applicability, the structure of the frequently mentioned α polymorph remained unclear. The base-centered unit cell (space group C2/c) suggested in 1966 was ruled out in 2003 and was replaced by a primitive triclinic unit cell (space group P 1). This study proves unequivocally that both α structures coexist in vacuum-deposited CuPc thin films on native silicon oxide by reciprocal space mapping using synchrotron radiation in grazing incidence. The unit-cell parameters and the space group were determined by kinematic scattering theory and provide possible molecular arrangements within the unit cell of the C2/c structure by excluded-volume considerations. In situ X-ray diffraction experiments and ex situ atomic force microscopy complement the experimental data further and provide insight into the formation of a smooth thin film by a temperature-driven downward diffusion of CuPc molecules during growth.

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In the present paper we discuss correlations between crystal structure and magnetic properties of epitaxial ε-Fe2O3 films grown on GaN. The large magnetocrystalline anisotropy and room temperature multiferroic properties of this exotic iron oxide polymorph, make it a perspective material for the development of low power consumption magnetic media storage devices. Extending our recent progress in PLD growth of ε-Fe2O3 on the surface of technologically important nitride semiconductors, we apply reciprocal space tomography by electron and x-ray diffraction to investigate the break of crystallographic symmetry occurring at the oxide-nitride interface resulting in the appearance of anisotropic crystallographic disorder in the sub-100 nm ε-Fe2O3 films. The orthorhombic-on-hexagonal nucleation scenario is shown responsible for the development of a peculiar columnar structure observed in ε-Fe2O3 by means of HRTEM and AFM. The complementary information on the direct and reciprocal space structure of the columnar ε-Fe2O3 films is obtained by various techniques and correlated to their magnetic properties. The peculiar temperature dependence of magnetization studied by the small-field magnetization derivative method and by neutron diffraction reveals the existence of a magnetic softening below 150 K, similar to the one observed earlier solely in nanoparticles. The magnetization reversal in ε-Fe2O3 films probed by X-ray magnetic circular dichroism is found different from the behavior of the bulk averaged magnetization measured by conventional magnetometry. The presented results fill the gap between the numerous studies performed on randomly oriented ε-Fe2O3 nanoparticles and much less frequent investigations of epitaxial epsilon ferrite films with lattice orientation fixed by the substrate.

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A furnace that covers the temperature range from room temperature up to 2000 K has been designed, built and implemented on the D2AM beamline at the ESRF. The QMAX furnace is devoted to the full exploration of the reciprocal hemispace located above the sample surface. It is well suited for symmetric and asymmetric 3D reciprocal space mapping. Owing to the hemispherical design of the furnace, 3D grazing-incidence small- and wide-angle scattering and diffraction measurements are possible. Inert and reactive experiments can be performed at atmospheric pressure under controlled gas flux. It is demonstrated that the QMAX furnace allows monitoring of structural phase transitions as well as microstructural evolution at the nanoscale, such as self-organization processes, crystal growth and strain relaxation. A time-resolved in situ oxidation experiment illustrates the capability to probe the high-temperature reactivity of materials.

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Strain-induced fast ion conduction has been a research area of interest for nanoscale energy conversion and storage systems. However, because of significant discrepancies in the interpretation of strain effects, there remains a lack of understanding of how fast ionic transport can be achieved by strain effects and how strain can be controlled in a nanoscale system. In this study, we investigated strain effects on the ionic conductivity of Gd0.2Ce0.8O1.9-δ (100) thin films under well controlled experimental conditions, in which errors due to the external environment could not intervene during the conductivity measurement. In order to avoid any interference from perpendicular-to-surface defects, such as grain boundaries, the ionic conductivity was measured in the out-of-plane direction by electrochemical impedance spectroscopy analysis. With varying film thickness, we found that a thicker film has a lower activation energy of ionic conduction. In addition, careful strain analysis using both reciprocal space mapping and strain mapping in transmission electron microscopy shows that a thicker film has a higher tensile strain than a thinner film. Furthermore, the tensile strain of thicker film was mostly developed near a grain boundary, which indicates that intrinsic strain is dominant rather than epitaxial or thermal strain during thin-film deposition and growth via the Volmer-Weber (island) growth mode.

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GAPD, a graphics-processing-unit (GPU)-accelerated atom-based polychromatic diffraction simulation code for direct, kinematics-based, simulations of X-ray/electron diffraction of large-scale atomic systems with mono-/polychromatic beams and arbitrary plane detector geometries, is presented. This code implements GPU parallel computation via both real- and reciprocal-space decompositions. With GAPD, direct simulations are performed of the reciprocal lattice node of ultralarge systems (∼5 billion atoms) and diffraction patterns of single-crystal and polycrystalline configurations with mono- and polychromatic X-ray beams (including synchrotron undulator sources), and validation, benchmark and application cases are presented.

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The symmetry of graphene is usually determined by a low-energy electron diffraction (LEED) method when the graphene is on the conductive substrates, but LEED cannot handle graphene transferred to SiO2/Si substrates due to the charging effect. While transmission electron microscopy can generate electron diffraction on post-transferred graphene, this method is too localized. Herein, we employed an azimuthal reflection high-energy electron diffraction (RHEED) method to construct the reciprocal space mapping and determine the symmetry of wafer-size graphene both pre- and post-transfer. In this work, single-crystalline Cu(111) films were prepared on sapphire(0001) and spinel(111) substrates with sputtering. Then the graphene was epitaxially grown on single-crystalline Cu(111) films with a low pressure chemical vapor deposition. The reciprocal space mapping using azimuthal RHEED confirmed that the graphene grown on Cu(111) films was single-crystalline, no matter the form of the monolayer or multilayer structure. While the Cu(111) film grown on sapphire(0001) may occasionally consist of 60° in-plane rotational twinning, the reciprocal space mapping revealed that the in-plane orientation of graphene grown atop was not affected. The proposed method for checking the crystalline integrity of the post-transferred graphene sheets is an important step in the realization of the graphene as a platform to fabricate electronic and optoelectronic devices.

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New methods are needed in microsystems technology for evaluating microelectromechanical systems (MEMS) because of their reduced size. The assessment and characterization of mechanical and structural relations of MEMS are essential to assure the long-term functioning of devices, and have a significant impact on design and fabrication. Within this study a concept for the investigation of mechanically loaded MEMS materials on an atomic level is introduced, combining high-resolution X-ray diffraction (HRXRD) measurements with finite element analysis (FEA) and mechanical testing. In situ HRXRD measurements were performed on tensile loaded single crystal silicon (SCSi) specimens by means of profile scans and reciprocal space mapping (RSM) on symmetrical (004) and (440) reflections. A comprehensive evaluation of the rather complex XRD patterns and features was enabled by the correlation of measured with simulated, 'theoretical' patterns. Latter were calculated by a specifically developed, simple and fast approach on the basis of continuum mechanical relations. Qualitative and quantitative analysis confirmed the admissibility and accuracy of the presented method. In this context [001] Poisson's ratio was determined providing an error of less than 1.5% with respect to analytical prediction. Consequently, the introduced procedure contributes to further going investigations of weak scattering being related to strain and defects in crystalline structures and therefore supports investigations on materials and devices failure mechanisms.

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Oxygen vacancies have a profound effect on the magnetic, electronic, and transport properties of transition metal oxide materials. Here, we studied the influence of oxygen vacancies on the magnetoresistance (MR) properties of SrRu1 - x Fe x O3 - δ epitaxial thin films (x = 0.10, 0.20, and 0.30). For this purpose, we synthesized highly strained epitaxial SrRu1 - x Fe x O3 - δ thin films with atomically flat surfaces containing different amounts of oxygen vacancies using pulsed laser deposition. Without an applied magnetic field, the films with x = 0.10 and 0.20 showed a metal-insulator transition, while the x = 0.30 thin film showed insulating behavior over the entire temperature range of 2-300 K. Both Fe doping and the concentration of oxygen vacancies had large effects on the negative MR contributions. For the low Fe doping case of x = 0.10, in which both films exhibited metallic behavior, MR was more prominent in the film with fewer oxygen vacancies or equivalently a more metallic film. For semiconducting films, higher MR was observed for more semiconducting films having more oxygen vacancies. A relatively large negative MR (~36.4%) was observed for the x = 0.30 thin film with a high concentration of oxygen vacancies (δ = 0.12). The obtained results were compared with MR studies for a polycrystal of (Sr1 - x La x )(Ru1 - x Fe x )O3. These results highlight the crucial role of oxygen stoichiometry in determining the magneto-transport properties in SrRu1 - x Fe x O3 - δ thin films.

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The polarization fields in c-plane InGaN/(In)GaN multiple quantum well (MQW) structures grown on sapphire substrate by metal-organic chemical vapor deposition are investigated in this paper. The indium composition in the quantum wells varies from 14.8 to 26.5% for different samples. The photoluminescence wavelengths are calculated theoretically by fully considering the related effects and compared with the measured wavelengths. It is found that when the indium content is lower than 17.3%, the measured wavelengths agree well with the theoretical values. However, when the indium content is higher than 17.3%, the measured ones are much shorter than the calculation results. This discrepancy is attributed to the reduced polarization field in the MQWs. For the MQWs with lower indium content, 100% theoretical polarization can be maintained, while, when the indium content is higher, the polarization field decreases significantly. The polarization field can be weakened down to 23% of the theoretical value when the indium content is 26.5%. Strain relaxation is excluded as the origin of the polarization reduction because there is no sign of lattice relaxation in the structures, judging by the X-ray diffraction reciprocal space mapping. The possible causes of the polarization reduction are discussed.

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BINoculars is a tool for data reduction and analysis of large sets of surface diffraction data that have been acquired with a two-dimensional X-ray detector. The intensity of each pixel of a two-dimensional detector is projected onto a three-dimensional grid in reciprocal-lattice coordinates using a binning algorithm. This allows for fast acquisition and processing of high-resolution data sets and results in a significant reduction of the size of the data set. The subsequent analysis then proceeds in reciprocal space. It has evolved from the specific needs of the ID03 beamline at the ESRF, but it has a modular design and can be easily adjusted and extended to work with data from other beamlines or from other measurement techniques. This paper covers the design and the underlying methods employed in this software package and explains how BINoculars can be used to improve the workflow of surface X-ray diffraction measurements and analysis.