Water Window Ptychographic Imaging with Characterized Coherent X-rays

We report on a ptychographical coherent diffractive imaging experiment in the water window with focused soft X-rays at $500~\mathrm{eV}$. An X-ray beam with high degree of coherence was selected for ptychography at the P04 beamline of the PETRA III synchrotron radiation source. We measured the beam coherence with the newly developed non-redundant array method. A pinhole $2.6~\mathrm{\mu m}$ in size selected the coherent part of the beam and was used for ptychographic measurements of a lithographically manufactured test sample and fossil diatom. The achieved resolution was $53~\mathrm{nm}$ for the test sample and only limited by the size of the detector. The diatom was imaged at a resolution better than $90~\mathrm{nm}$.Comment: 22 pages. 7 figure

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

We present results of an x-ray study of structural properties of semicrystalline polymer films using nanofocused x-ray beam. We applied the x-ray cross-correlation analysis (XCCA) to scattering data from blends of poly(3-hexylthiophene) (P3HT) embedded 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.Comment: 10 pages, 6 figures, 53 reference

Quantum Imaging with Incoherently Scattered Light from a Free-Electron Laser

The advent of accelerator-driven free-electron lasers (FEL) has opened new avenues for high-resolution structure determination via diffraction methods that go far beyond conventional x-ray crystallography methods. These techniques rely on coherent scattering processes that require the maintenance of first-order coherence of the radiation field throughout the imaging procedure. Here we show that higher-order degrees of coherence, displayed in the intensity correlations of incoherently scattered x-rays from an FEL, can be used to image two-dimensional objects with a spatial resolution close to or even below the Abbe limit. This constitutes a new approach towards structure determination based on incoherent processes, including Compton scattering, fluorescence emission or wavefront distortions, generally considered detrimental for imaging applications. Our method is an extension of the landmark intensity correlation measurements of Hanbury Brown and Twiss to higher than second-order paving the way towards determination of structure and dynamics of matter in regimes where coherent imaging methods have intrinsic limitations

Disorder Dynamics in Battery Nanoparticles During Phase Transitions Revealed by Operando Single-Particle Diffraction

Structural and ion-ordering phase transitions limit the viability of sodium-ion intercalation materials in grid scale battery storage by reducing their lifetime. However, the combination of phenomena in nanoparticulate electrodes creates complex behavior that is difficult to investigate, especially on the single nanoparticle scale under operating conditions. In this work, operando single-particle x-ray diffraction (oSP-XRD) is used to observe single-particle rotation, interlayer spacing, and layer misorientation in a functional sodium-ion battery. oSP-XRD is applied to Na$_{2/3}$[Ni$_{1/3}$Mn$_{2/3}$]O$_{2}$, an archetypal P2-type sodium-ion positive electrode material with the notorious P2-O2 phase transition induced by sodium (de)intercalation. It is found that during sodium extraction, the misorientation of crystalline layers inside individual particles increases before the layers suddenly align just prior to the P2-O2 transition. The increase in the long-range order coincides with an additional voltage plateau signifying a phase transition prior to the P2-O2 transition. To explain the layer alignment, a model for the phase evolution is proposed that includes a transition from localized to correlated Jahn-Teller distortions. The model is anticipated to guide further characterization and engineering of sodium-ion intercalation materials with P2-O2 type transitions. oSP-XRD therefore opens a powerful avenue for revealing complex phase behavior in heterogeneous nanoparticulate systems.Comment: 23 pages, 4 main figures, 9 supplemental figure

Real-space imaging of polar and elastic nano-textures in thin films via inversion of diffraction data

Exploiting the emerging nanoscale periodicities in epitaxial, single-crystal thin films is an exciting direction in quantum materials science: confinement and periodic distortions induce novel properties. The structural motifs of interest are ferroelastic, ferroelectric, multiferroic, and, more recently, topologically protected magnetization and polarization textures. A critical step towards heterostructure engineering is understanding their nanoscale structure, best achieved through real-space imaging. X-ray Bragg coherent diffractive imaging visualizes sub-picometer crystalline displacements with tens of nanometers spatial resolution. Yet, it is limited to objects spatially confined in all three dimensions and requires highly coherent, laser-like x-rays. Here we lift the confinement restriction by developing real-space imaging of periodic lattice distortions: we combine an iterative phase retrieval algorithm with unsupervised machine learning to invert the diffuse scattering in conventional x-ray reciprocal-space mapping into real-space images of polar and elastic textures in thin epitaxial films. We first demonstrate our imaging in PbTiO3/SrTiO3 superlattices to be consistent with published phase-field model calculations. We then visualize strain-induced ferroelastic domains emerging during the metal-insulator transition in Ca2RuO4 thin films. Instead of homogeneously transforming into a low-temperature structure (like in bulk), the strained Mott insulator splits into nanodomains with alternating lattice constants, as confirmed by cryogenic scanning transmission electron microscopy. Our study reveals the type, size, orientation, and crystal displacement field of the nano-textures. The non-destructive imaging of textures promises to improve models for their dynamics and enable advances in quantum materials and microelectronics

Coherent Methods in X-Ray Scattering

X-ray radiation has been used to study structural properties of materials for morethan a hundred years. Construction of extremely coherent and bright X-ray radiationsources such as free electron lasers (FELs) and latest generation storage rings led torapid development of experimental methods relying on high radiation coherence.These methods allow to perform revolutionary studies in a wide range of fields fromsolid state physics to biology. In this thesis I focus on several important problemsconnected with the coherent methods.The first part considers applications of dynamical diffraction theory on crystals tostudies with coherent X-ray radiation. It presents the design of a high-resolution spectrometerfor free electron lasers that should allow to resolve spectral structure of individualFEL pulses. The spectrometer is based on the principle of dynamical diffractionfocusing. The knowledge of individual FEL pulse spectra is necessary for understandingFEL longitudinal coherence. In the same part I present quasi-kinematicalapproximation to dynamical theory which allows to treat analytically phase effectsobserved in X-ray coherent imaging on nanocrystals. These effects may play a bigrole when methods such as ptychography are used to study crystalline samples.The second part deals with measurements of FEL coherence properties using intensity- intensity interferometry. Results of several experiments performed at FELsFLASH and LCLS are revealed in this section. I have developed models and theoriesto explain the behavior observed in experiments on FLASH. These models allowedto extract information about external positional jitter of FEL pulses and secondarybeams present in FEL radiation. In the LCLS experiment the Hanbury Brown andTwiss type interferometry was performed on Bragg peaks from colloidal crystal. Thisdid not require additional measurements without the sample and information wasextracted directly from diffraction patterns. Therefore intensity-intensity interferometrycan in principle be used directly on sample diffraction patterns to understandstatistical behavior of the FEL during the measurements.Another problem that is considered in this thesis is the problem of electronic damagefrom bright FEL pulses. I have considered the effect of many ionization processeson single-particle imaging experiments on biological objects. Simulations were performedto understand the effect of shortening pulse durations and increasing intensitieson the diffraction pattern, its fluctuations from pulse to pulse and Comptonbackground. As a result of these simulations, bounds on the feasible intensities andpulse durations are suggested