Real-space imaging of periodic nanotextures in thin films via phasing of diffraction data.

New properties and exotic quantum phenomena can form due to periodic nanotextures, including Moire patterns, ferroic domains, and topologically protected magnetization and polarization textures. Despite the availability of powerful tools to characterize the atomic crystal structure, the visualization of nanoscale strain-modulated structural motifs remains challenging. Here, we develop nondestructive real-space imaging of periodic lattice distortions in thin epitaxial films and report an emergent periodic nanotexture in a Mott insulator. Specifically, we combine iterative phase retrieval with unsupervised machine learning to invert the diffuse scattering pattern from conventional X-ray reciprocal-space maps into real-space images of crystalline displacements. Our imaging in PbTiO3/SrTiO3 superlattices exhibiting checkerboard strain modulation substantiates published phase-field model calculations. Furthermore, the imaging of biaxially strained Mott insulator Ca2RuO4 reveals a strain-induced nanotexture comprised of nanometer-thin metallic-structure wires separated by nanometer-thin Mott-insulating-structure walls, as confirmed by cryogenic scanning transmission electron microscopy (cryo-STEM). The nanotexture in Ca2RuO4 film is induced by the metal-to-insulator transition and has not been reported in bulk crystals. We expect the phasing of diffuse X-ray scattering from thin crystalline films in combination with cryo-STEM to open a powerful avenue for discovering, visualizing, and quantifying the periodic strain-modulated structures in quantum materials.

Shear displacement gradient in X-ray Bragg coherent diffractive imaging.

Bragg coherent X-ray diffractive imaging is a cutting-edge method for recovering three-dimensional crystal structure with nanoscale resolution. Phase retrieval provides an atomic displacement parallel to the Bragg peak reciprocal lattice vector. The derivative of the displacement along the same vector provides the normal strain field, which typically serves as a proxy for any structural changes. In this communication it is found that the other component of the displacement gradient, perpendicular to the reciprocal lattice vector, provides additional information from the experimental data collected from nanocrystals with mobile dislocations. Demonstration on published experimental data show how the perpendicular component of the displacement gradient adds to existing analysis, enabling an estimate for the external stresses, pinpointing the location of surface dislocations, and predicting the dislocation motion in in situ experiments.

Wigner distribution of self-amplified spontaneous emission free-electron laser pulses and extracting its autocorrelation.

The emerging concept of `beam by design' in free-electron laser (FEL) accelerator physics aims for accurate manipulation of the electron beam to tailor spectral and temporal properties of the radiation for specific experimental purposes, such as X-ray pump/X-ray probe and multiple wavelength experiments. `Beam by design' requires fast, efficient, and detailed feedback on the spectral and temporal properties of the generated X-ray radiation. Here a simple and cost-efficient method to extract information on the longitudinal Wigner distribution function of emitted FEL pulses is proposed. The method requires only an ensemble of measured FEL spectra and is rather robust with respect to accelerator fluctuations. The method is applied to both the simulated SASE spectra with known radiation properties as well as to the SASE spectra measured at the European XFEL revealing underlying non-linear chirp of the generated radiation. In the Appendices an intuitive understanding of time-frequency representations of chirped SASE radiation is provided.

Structural Changes in a Single GaN Nanowire under Applied Voltage Bias.

GaN nanowires (NWs) are promising building blocks for future optoelectronic devices and nanoelectronics. They exhibit stronger piezoelectric properties than bulk GaN. This phenomena may be crucial for applications of NWs and makes their study highly important. We report on an investigation of the structure evolution of a single GaN NW under an applied voltage bias along polar [0001] crystallographic direction until its mechanical break. The structural changes were investigated using coherent X-ray Bragg diffraction. The three-dimensional (3D) intensity distributions of the NWs without metal contacts, with contacts, and under applied voltage bias in opposite polar directions were analyzed. Coherent X-ray Bragg diffraction revealed the presence of significant bending of the NWs already after metal contacts deposition, which was increased at applied voltage bias. Employing analytical simulations based on elasticity theory and a finite element method (FEM) approach, we developed a 3D model of the NW bending under applied voltage. From this model and our experimental data, we determined the piezoelectric constant of the GaN NW to be about 7.7 pm/V in [0001] crystallographic direction. The ultimate tensile strength of the GaN NW was obtained to be about 1.22 GPa. Our work demonstrates the power of in operando X-ray structural studies of single NWs for their effective design and implementation with desired functional properties.

Ptychographic X-Ray Imaging of Colloidal Crystals.

Ptychographic coherent X-ray imaging is applied to obtain a projection of the electron density of colloidal crystals, which are promising nanoscale materials for optoelectronic applications and important model systems. Using the incident X-ray wavefield reconstructed by mixed states approach, a high resolution and high contrast image of the colloidal crystal structure is obtained by ptychography. The reconstructed colloidal crystal reveals domain structure with an average domain size of about 2 µm. Comparison of the domains formed by the basic close-packed structures, allows us to conclude on the absence of pure hexagonal close-packed domains and confirms the presence of random hexagonal close-packed layers with predominantly face-centered cubic structure within the analyzed part of the colloidal crystal film. The ptychography reconstruction shows that the final structure is complicated and may contain partial dislocations leading to a variation of the stacking sequence in the lateral direction. As such in this work, X-ray ptychography is extended to high resolution imaging of crystalline samples.

Quantifying Angular Correlations between the Atomic Lattice and the Superlattice of Nanocrystals Assembled with Directional Linking.

We show that the combination of X-ray scattering with a nanofocused beam and X-ray cross correlation analysis is an efficient way for the full structural characterization of mesocrystalline nanoparticle assemblies with a single experiment. We analyze several hundred diffraction patterns at individual sample locations, that is, individual grains, to obtain a meaningful statistical distribution of the superlattice and atomic lattice ordering. Simultaneous small- and wide-angle X-ray scattering of the same sample location allows us to determine the structure and orientation of the superlattice as well as the angular correlation of the first two Bragg peaks of the atomic lattices, their orientation with respect to the superlattice, and the average orientational misfit due to local structural disorder. This experiment is particularly advantageous for synthetic mesocrystals made by the simultaneous self-assembly of nanocrystals and surface-functionalization with conductive ligands. While the structural characterization of such materials has been challenging so far, the present method now allows correlating the mesocrystalline structure with optoelectronic properties.

Water window ptychographic imaging with characterized coherent X-rays.

A ptychographical coherent diffractive imaging experiment in the water window with focused soft X-rays at 500 eV is reported. An X-ray beam with high degree of coherence was selected for ptychography at the P04 beamline of PETRA III synchrotron radiation source. The beam coherence was measured with the newly developed non-redundant array method, and a coherence length of 4.1 µm and global degree of coherence of 35% at 100 µm exit slit opening in the vertical direction were determined. A pinhole, 2.6 µm in size, selected the coherent part of the beam that was used to obtain ptychographic reconstruction results of a lithographically manufactured test sample and a fossil diatom. The achieved resolution was 53 nm for the test sample and was only limited by the size of the detector. The diatom was imaged at a resolution better than 90 nm.

Structural evolution of colloidal crystal films in the process of melting revealed by Bragg peak analysis.

In situ X-ray diffraction studies of structural evolution of colloidal crystal films formed by polystyrene spherical particles upon incremental heating are reported. The Bragg peak parameters, such as peak position, integrated intensity, and radial and azimuthal widths were analyzed as a function of temperature. A quantitative study of colloidal crystal lattice distortions and mosaic spread as a function of temperature was carried out using Williamson-Hall plots based on mosaic block model. The temperature dependence of the diameter of polystyrene particles was obtained from the analysis of Bragg peaks, and the form factor contribution extracted from the diffraction patterns. Four stages of structural evolution in a colloidal crystal upon heating were identified. Based on this analysis, a model of the heating and melting process in the colloidal crystal film is suggested.

Local structure of semicrystalline P3HT films probed by nanofocused coherent X-rays.

The hidden structural properties of semicrystalline polymer films are revealed by nanofocused X-ray scattering studies. X-ray cross-correlation analysis (XCCA) is employed to diffraction patterns from blends of poly(3-hexylthiophene) (P3HT) with gold nanoparticles (AuNPs). Spatially resolved maps of orientational distribution of crystalline domains allow us to distinguish sample regions of predominant face-on morphology, with a continuous transition to edge-on morphology. The average size of crystalline domains was determined to be of the order of 10 nm. As compared to pristine P3HT film, the P3HT/AuNPs blend is characterized by substantial ordering of crystalline domains, which can be induced by Au nanoparticles. The inhomogeneous structure of the polymer film is clearly visualized on the spatially resolved nanoscale 2D maps obtained using XCCA. Our results suggest that the observed changes of the polymer matrix within crystalline regions can be attributed to nanoconfinement in the presence of gold nanoparticles.

Spontaneous Supercrystal Formation During a Strain-Engineered Metal-Insulator Transition.

Mott metal-insulator transitions possess electronic, magnetic, and structural degrees of freedom promising next-generation energy-efficient electronics. A previously unknown, hierarchically ordered, and anisotropic supercrystal state is reported and its intrinsic formation characterized in-situ during a Mott transition in a Ca2RuO4 thin film. Machine learning-assisted X-ray nanodiffraction together with cryogenic electron microscopy reveal multi-scale periodic domain formation at and below the film transition temperature (TFilm ≈ 200-250 K) and a separate anisotropic spatial structure at and above TFilm. Local resistivity measurements imply an intrinsic coupling of the supercrystal orientation to the material's anisotropic conductivity. These findings add a new degree of complexity to the physical understanding of Mott transitions, opening opportunities for designing materials with tunable electronic properties.

In Situ Nanoscale Dynamics Imaging in a Proton-Conducting Solid Oxide for Protonic Ceramic Fuel Cells.

Hydrogen fuel cells and electrolyzers operating below 600 °C, ideally below 400 °C, are essential components in the clean energy transition. Yttrium-doped barium zirconate BaZr0.8 Y0.2 O3-d (BZY) has attracted a lot of attention as a proton-conducting solid oxide for electrochemical devices due to its high chemical stability and proton conductivity in the desired temperature range. Grain interfaces and topological defects modulate bulk proton conductivity and hydration, especially at low temperatures. Therefore, understanding the nanoscale crystal structure dynamics in situ is crucial to achieving high proton transport, material stability, and extending the operating range of proton-conducting solid oxides. Here, Bragg coherent X-ray diffractive imaging is applied to investigate in situ and in 3D nanoscale dynamics in BZY during hydration over 40 h at 200 °C, in the low-temperature range. An unexpected activity of topological defects and subsequent cracking is found on a nanoscale covered by the macroscale stability. The rearrangements in structure correlate with emergent regions of different lattice constants, suggesting heterogeneous hydration. The results highlight the extent and impact of nanoscale processes in proton-conducting solid oxides, informing future development of low-temperature protonic ceramic electrochemical cells.

High spatial coherence and short pulse duration revealed by the Hanbury Brown and Twiss interferometry at the European XFEL.

Second-order intensity interferometry was employed to study the spatial and temporal properties of the European X-ray Free-Electron Laser (EuXFEL). Measurements were performed at the soft x-ray Self-Amplified Spontaneous Emission (SASE3) undulator beamline at a photon energy of 1.2 keV in the Self-Amplified Spontaneous Emission (SASE) mode. Two high-power regimes of the SASE3 undulator settings, i.e., linear and quadratic undulator tapering at saturation, were studied in detail and compared with the linear gain regime. The statistical analysis showed an exceptionally high degree of spatial coherence up to 90% for the linear undulator tapering. Analysis of the measured data in spectral and spatial domains provided an average pulse duration of about 10 fs in our measurements. The obtained results will be valuable for the experiments requiring and exploiting short pulse duration and utilizing high coherence properties of the EuXFEL.

Femtosecond laser produced periodic plasma in a colloidal crystal probed by XFEL radiation.

With the rapid development of short-pulse intense laser sources, studies of matter under extreme irradiation conditions enter further unexplored regimes. In addition, an application of X-ray Free-Electron Lasers (XFELs) delivering intense femtosecond X-ray pulses, allows to investigate sample evolution in IR pump - X-ray probe experiments with an unprecedented time resolution. Here we present a detailed study of the periodic plasma created from the colloidal crystal. Both experimental data and theory modeling show that the periodicity in the sample survives to a large extent the extreme excitation and shock wave propagation inside the colloidal crystal. This feature enables probing the excited crystal, using the powerful Bragg peak analysis, in contrast to the conventional studies of dense plasma created from bulk samples for which probing with Bragg diffraction technique is not possible. X-ray diffraction measurements of excited colloidal crystals may then lead towards a better understanding of matter phase transitions under extreme irradiation conditions.

Setting Carriers Free: Healing Faulty Interfaces Promotes Delocalization and Transport in Nanocrystal Solids.

Superlattices of epitaxially connected nanocrystals (NCs) are model systems to study electronic and optical properties of NC arrays. Using elemental analysis and structural analysis by in situ X-ray fluorescence and grazing-incidence small-angle scattering, respectively, we show that epitaxial superlattices of PbSe NCs keep their structural integrity up to temperatures of 300 °C; an ideal starting point to assess the effect of gentle thermal annealing on the superlattice properties. We find that annealing such superlattices between 75 and 150 °C induces a marked red shift of the NC band-edge transition. In fact, the post-annealing band-edge reflects theoretical predictions on the impact of charge carrier delocalization in these epitaxial superlattices. In addition, we observe a pronounced enhancement of the charge carrier mobility and a reduction of the hopping activation energy after mild annealing. While the superstructure remains intact at these temperatures, structural defect studies through X-ray diffraction indicate that annealing markedly decreases the density of point defects and edge dislocations. This indicates that the connections between NCs in as-synthesized superlattices still form a major source of grain boundaries and defects, which prevent carrier delocalization over multiple NCs and hamper NC-to-NC transport. Overcoming the limitations imposed by interfacial defects is therefore an essential next step in the development of high-quality optoelectronic devices based on NC solids.

Publisher Correction: Seeded X-ray free-electron laser generating radiation with laser statistical properties.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Seeded X-ray free-electron laser generating radiation with laser statistical properties.

The invention of optical lasers led to a revolution in the field of optics and to the creation of such fields of research as quantum optics. The reason was their unique statistical and coherence properties. The emerging, short-wavelength free-electron lasers (FELs) are sources of very bright coherent extreme-ultraviolet and X-ray radiation with pulse durations on the order of femtoseconds, and are presently considered to be laser sources at these energies. FELs are highly spatially coherent to the first-order but in spite of their name, behave statistically as chaotic sources. Here, we demonstrate experimentally, by combining Hanbury Brown and Twiss interferometry with spectral measurements that the seeded XUV FERMI FEL-2 source does indeed behave statistically as a laser. The results may be useful for quantum optics experiments and for the design and operation of next generation FEL sources.