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In the cuprate superconductors, the spatial coherence of the charge density wave (CDW) state grows rapidly below a characteristic temperature $T_\mathrm{CDW}$, the nature of which is debated. We have combined a set of x-ray scattering techniques to study La$_{1.88}$Sr$_{0.12}$CuO$_{4}$ ($T_\mathrm{CDW}$~$\approx$~80\,K) to shed light on this discussion. We observe the emergence of a crystal structure, which is consistent with the CDW modulation in symmetry, well above $T_\mathrm{CDW}$. This global structural change also induces strong fluctuations of local atomic disorder in the intermediate temperature region. At $T_\mathrm{CDW}$, the temperature dependence of this structure develops a kink, while the atomic disorder is minimized. We find that the atomic relaxation dynamics cross over from a cooperative to an incoherent response at $T_\mathrm{CDW}$. These results reveal a rich interplay between the CDWs and atomic fluctuations of distinct spatio-temporal scales. For example, the CDW coherence is enhanced on quasi-elastic timescales by incoherent atomic relaxation.

Employing X-ray photon correlation spectroscopy we measure the kinetics and dynamics of a pressure-induced liquid-liquid phase separation (LLPS) in a water-lysozyme solution. Scattering invariants and kinetic information provide evidence that the system reaches the phase boundary upon pressure-induced LLPS with no sign of arrest. The coarsening slows down with increasing quench depths. The $g_2$-functions display a two-step decay with a gradually increasing non-ergodicity parameter typical for gelation. We observe fast superdiffusive ($\gamma \geq 3/2$) and slow subdiffusive ($\gamma < 0.6$) motion associated with fast viscoelastic fluctuations of the network and a slow viscous coarsening process, respectively. The dynamics age linear with time $\tau \propto t_\mathrm{w}$ and we observe the onset of viscoelastic relaxation for deeper quenches. Our results suggest that the protein solution gels upon reaching the phase boundary.

We use machine learning methods for an automated classification of experimental XPCS two-time correlation functions from an arrested liquid-liquid phase separation of a protein solution. We couple simulations based on the Cahn-Hilliard equation with a glass transition scenario and classify the measured correlation maps automatically according to quench depth and critical concentration at a glass/gel transition. We introduce routines and methodologies using an autoencoder network and a differential evolution based algorithm for classification of the measured correlation functions. The here presented method is a first step towards handling large amounts of dynamic data measured at high brilliance synchrotron and X-ray free-electron laser sources facilitating fast comparison to phase field models of phase separation.

Mesocrystals are nanostructured materials consisting of individual nanocrystals having a preferred crystallographic orientation. On mesoscopic length scales, the properties of mesocrystals are strongly affected by structural heterogeneity. Here, we report the detailed structural characterization of a faceted mesocrystal grain self-assembled from 60 nm sized gold nanocubes. Using coherent X-ray diffraction imaging, we determined the structure of the mesocrystal with the resolution sufficient to resolve each gold nanoparticle. The reconstructed electron density of the gold mesocrystal reveals its intrinsic structural heterogeneity, including local deviations of lattice parameters, and the presence of internal defects. The strain distribution shows that the average superlattice obtained by angular X-ray cross-correlation analysis and the real, multidomain structure of a mesocrystal are very close to each other, with a deviation less than 10 percent. These results will provide an important impact to understanding of the fundamental principles of structuring and self-assembly including ensuing properties of mesocrystals., Comment: 28 pages, 8 figures, 50 references

Solutions of wormlike micelles can form cross-linked networks on microscopic length scales. The unique mechanical properties of these complex fluids are driven by the interplay between the network structure and dynamics which are investigated by plate-plate rheometry and X-ray photon correlation spectroscopy~(XPCS) nanorheology. Intensity auto-correlation functions of tracer nanoparticles~(NPs) dispersed in micelle solutions were recorded which captured both the slow structural network relaxation and the short-time dynamics of NPs trapped in the network. The results are indicative of a resonance-like dynamic behavior of the network on the nanoscale that develops as a consequence of the intrinsic short-range rigidity of individual micelle chains., Comment: 5 pages, 5 figures

Coexistence of phases, characterized by different electronic degrees of freedom, commonly occurs in layered superconductors. Among them, alkaline intercalated chalcogenides are model systems showing microscale coexistence of paramagnetic (PAR) and antiferromagnetic (AFM) phases, however, temporal behavior of different phases is still unknown. Here, we report the first visualization of the atomic motion in the granular phase of K$_{x}$Fe$_{2-y}$Se$_2$ using X-ray photon correlation spectroscopy. Unlike the PAR phase, the AFM texture reveals an intermittent dynamics with avalanches as in martensites. When cooled down across the superconducting transition temperature T$_c$, the AFM phase goes through an anomalous slowing behavior suggesting a direct relationship between the atomic motions in the AFM phase and the superconductivity. In addition of providing a compelling evidence of avalanche-like dynamics in a layered superconductor, the results provide a basis for new theoretical models to describe quantum states in inhomogeneous solids., Comment: 6 pages, 3 figures

The continuous development of synchrotron-based experimental techniques in the X-ray range provides new possibilities to probe the structure and the dynamics of bulk materials down to inter-atomic distances. However, the interaction of intense X-ray beams with matter can also induce changes in the structure and dynamics of materials. A reversible and non-destructive beam induced dynamics has recently been observed in X-ray photon correlation spectroscopy experiments in some oxide glasses at sufficiently low absorbed doses, and is here investigated in a (Li$_2$O)$_{0.5}$(B$_2$O$_3$)$_{0.5}$ glass. The characteristic time of this induced dynamics is inversely proportional to the intensity of the X-ray beam, with a coefficient that depends on the chemical composition and local structure of the probed glass, making it a potentially new tool to investigate fundamental properties of a large class of disordered systems. While the exact mechanisms behind this phenomenon are yet to be elucidated, we report here on the measurement of the exchanged wave-vector (and thus length-scale) dependence of the characteristic time of this induced dynamics, and show that it follows the same power-law observed in vitreous silica. This supports the idea that a unique explanation for this effect in different oxide glasses should be looked for., Comment: 9 pages, 4 figures

Defects and their interactions in crystalline solids often underpin material properties and functionality as they are decisive for stability, result in enhanced diffusion, and act as a reservoir of vacancies. Recently, lithium-rich layered oxides have emerged among the leading candidates for the next-generation energy storage cathode material, delivering 50 % excess capacity over commercially used compounds. Oxygen-redox reactions are believed to be responsible for the excess capacity, however, voltage fading has prevented commercialization of these new materials. Despite extensive research the understanding of the mechanisms underpinning oxygen-redox reactions and voltage fade remain incomplete. Here, using operando three-dimensional Bragg coherent diffractive imaging, we directly observe nucleation of a mobile dislocation network in nanoparticles of lithium-rich layered oxide material. Surprisingly, we find that dislocations form more readily in the lithium-rich layered oxide material as compared with a conventional layered oxide material, suggesting a link between the defects and the anomalously high capacity in lithium-rich layered oxides. The formation of a network of partial dislocations dramatically alters the local lithium environment and contributes to the voltage fade. Based on our findings we design and demonstrate a method to recover the original high voltage functionality. Our findings reveal that the voltage fade in lithium-rich layered oxides is reversible and call for new paradigms for improved design of oxygen-redox active materials.

We report on X-ray studies of freely suspended hexatic films of three different liquid crystal compounds. By applying angular X-ray cross-correlation analysis (XCCA) to the measured diffraction patterns the parameters of the bond-orientational (BO) order in the hexatic phase were directly determined. The temperature evolution of the BO order parameters was analyzed on the basis of the multicritical scaling theory (MCST). Our results confirmed the validity of the MCST in the whole temperature range of existence of the hexatic phase for all three compounds. The temperature dependence of the BO order parameters in the vicinity of the hexatic-smectic transition was fitted by a conventional power law with a critical exponent $\beta\approx0.1$ of extremely small value. We found that the temperature dependence of higher order harmonics of the BO order scales as the powers of the first harmonic, with exponent equal to harmonic number. This indicates a nonlinear coupling of the BO order parameters of different order. It is shown that compounds of various composition, possessing different phase sequences, display the same thermodynamic behavior in the hexatic phase and in the vicinity of the smectic-hexatic phase transition., Comment: 14 pages, 9 figures, 3 tables

We present results of a coherent x-ray diffractive imaging experiment performed on a single colloidal crystal grain. The full three-dimensional (3D) reciprocal space map measured by an azimuthal rotational scan contained several orders of Bragg reflections together with the coherent interference signal between them. Applying the iterative phase retrieval approach, the 3D structure of the crystal grain was reconstructed and positions of individual colloidal particles were resolved. As a result, an exact stacking sequence of hexagonal close-packed layers including planar and linear defects were identified., Comment: 8 pages, 5 figures

The single-layer perovskite cobaltates have attracted enormous attention due to the recent observation of hour-glass shaped magnetic excitation spectra which resemble the ones of the famous high-temperature superconducting cuprates. Here, we present an overview of our most recent studies of the spin and charge correlations in floating-zone grown cobaltate single crystals. We find that frustration and a novel kind of electronic and magnetic nano phase separation are intimately connected to the appearance of the hour-glass shaped spin excitation spectra. We also point out the difference between nano phase separation and conventional phase separation., Comment: * plenary talk SUPERSTRIPES conference 2015

It has recently been established that the high temperature (high-Tc) superconducting state coexists with short-range charge-density-wave order and quenched disorder arising from dopants and strain. This complex, multiscale phase separation invites the development of theories of high temperature superconductivity that include complexity. The nature of the spatial interplay between charge and dopant order that provides a basis for nanoscale phase separation remains a key open question, because experiments have yet to probe the unknown spatial distribution at both the nanoscale and mescoscale (between atomic and macroscopic scale). Here we report micro X-ray diffraction imaging of the spatial distribution of both the charge-density-wave puddles (domains with only a few wavelengths) and quenched disorder in HgBa2CuO4+y, the single layer cuprate with the highest Tc, 95 kelvin. We found that the charge-density-wave puddles, like the steam bubbles in boiling water, have a fat-tailed size distribution that is typical of self-organization near a critical point. However, the quenched disorder, which arises from oxygen interstitials, has a distribution that is contrary to the usual assumed random, uncorrelated distribution. The interstitials-oxygen-rich domains are spatially anti-correlated with the charge-density-wave domains, leading to a complex emergent geometry of the spatial landscape for superconductivity., Comment: 11 pages, 3 figures

The magnetic excitations in the cuprate superconductors might be essential for an understanding of high-temperature superconductivity. In these cuprate superconductors the magnetic excitation spectrum resembles an hour-glass and certain resonant magnetic excitations within are believed to be connected to the pairing mechanism which is corroborated by the observation of a universal linear scaling of superconducting gap and magnetic resonance energy. So far, charge stripes are widely believed to be involved in the physics of hour-glass spectra. Here we study an isostructural cobaltate that also exhibits an hour-glass magnetic spectrum. Instead of the expected charge stripe order we observe nano phase separation and unravel a microscopically split origin of hour-glass spectra on the nano scale pointing to a connection between the magnetic resonance peak and the spin gap originating in islands of the antiferromagnetic parent insulator. Our findings open new ways to theories of magnetic excitations and superconductivity in cuprate superconductors., Comment: Nature Communications 5, 5731 (2014)

Micro-focused X-ray beams produced by third generation synchrotron sources offer new perspective of studying strains and processes at nanoscale. Atomic force microscope setup combined with a micro-focused synchrotron beam allows precise positioning and nanomanipulation of nanostructures under illumination. In this paper, we report on integration of a portable commercial atomic force microscope setup into a hard X-ray synchrotron beamline. Details of design, sample alignment procedure and performance of the setup are presented., Comment: To be submitted to Review of Scientific Instruments

We have used scanning micro x-ray diffraction to characterize different phases in superconducting K$_{x}$Fe$_{2-y}$Se$_2$ as a function of temperature, unveiling the thermal evolution across the superconducting transition temperature (T$_c\sim$32 K), phase separation temperature (T$_{ps}\sim$520 K) and iron-vacancy order temperature (T$_{vo}\sim$580 K). In addition to the iron-vacancy ordered tetragonal magnetic phase and orthorhombic metallic minority filamentary phase, we have found a clear evidence of the interface phase with tetragonal symmetry. The metallic phase is surrounded by this interface phase below $\sim$300 K, and is embedded in the insulating texture. The spatial distribution of coexisting phases as a function of temperature provides a clear evidence of the formation of protected metallic percolative paths in the majority texture with large magnetic moment, required for the electronic coherence for the superconductivity. Furthermore, a clear reorganization of iron-vacancy order around the T$_{ps}$ and T$_c$ is found with the interface phase being mostly associated with a different iron-vacancy configuration, that may be important for protecting the percolative superconductivity in K$_{x}$Fe$_{2-y}$Se$_2$., Comment: 6 pages, 4 figures

We present an x-ray study of freely suspended hexatic films of the liquid crystal 3(10)OBC. Our results reveal spatial inhomogeneities of the bond-orientational (BO) order in the vicinity of the hexatic-smectic phase transition and the formation of large scale hexatic domains at lower temperatures. Deep in the hexatic phase up to 25 successive sixfold BO order parameters have been directly determined by means of angular x-ray cross-correlation analysis (XCCA). Such strongly developed hexatic order allowed us to determine higher order correction terms in the scaling relation predicted by the multicritical scaling theory over a full temperature range of the hexatic phase existence., Comment: 8 pages, 12 figures

We present results of x-ray study of spatial properties of $\pi-\pi$ conjugated networks in polymer thin films. We applied the x-ray cross-correlation analysis to x-ray scattering data from blends of poly(3-hexylthiophene) (P3HT) and gold nanoparticles. The Fourier spectra of the intensity cross-correlation functions for different films contain non-zero components of orders $n=2,4$ and $6$ measuring the degree of structural order in the system., Comment: 6 pages, 2 figures, Proceedings ICXOM22 Conference, 2-6 September 2013, Hamburg, Germany

We present an x-ray study of liquid crystal membranes in the vicinity of hexatic-smectic phase transition by means of angular x-ray cross-correlation analysis (XCCA). By applying two-point angular intensity cross-correlation functions to the measured series of diffraction patterns the parameters of bond-orientational (BO) order in hexatic phase were directly determined. The temperature dependence of the positional correlation lengths was analyzed as well. The obtained correlation lengths show larger values for the higher-order Fourier components of BO order. These findings indicate a strong coupling between BO and positional order that has not been studied in detail up to now., Comment: 7 pages, 3 figures, 25 references

A coherent x-ray diffraction experiment was performed on an isolated colloidal crystal grain at the coherence beamline P10 at PETRA III. Using azimuthal rotation scans the three-dimensional (3D) scattered intensity in reciprocal space from the sample was measured. It includes several Bragg peaks as well as the coherent interference around these peaks. The analysis of the scattered intensity reveals the presence of a plane defect in a single grain of the colloidal sample. We confirm these findings by model simulations. In these simulations we also analyze the experimental conditions to phase 3D diffraction pattern from a single colloidal grain. This approach has the potential to produce a high resolution image of the sample revealing its inner structure, with possible structural defects., Comment: 20 pages, 5 figures

We have implemented the newly-introduced, coherence-based technique of x-ray near-field speckle (XNFS) at 8-ID-I at the Advanced Photon Source. In the near field regime of high-brilliance synchrotron x-rays scattered from a sample of interest, it turns out, that, when the scattered radiation and the main beam both impinge upon an x-ray area detector, the measured intensity shows low-contrast speckles, resulting from interference between the incident and scattered beams. We built a micrometer-resolution XNFS detector with a high numerical aperture microscope objective and demonstrate its capability for studying static structures and dynamics at longer length scales than traditional far field x-ray scattering techniques. Specifically, we characterized the structure and dynamics of dilute silica and polystyrene colloidal samples. Our study reveals certain limitations of the XNFS technique, which we discuss., Comment: 53 pages, 16 figures

We have implemented a virtual Young's double slit experiment for hard X-ray photons with micro-fabricated bi-prisms. We observe fringe patterns with a scintillator, and quantify interferograms by detecting X-ray fluorescence from a scanned 30nm Cr metal film. The observed intensities are best modeled with a near-field, Fresnel analysis. The maximum fringe number in the overlap region is proportional to the ratio of real to imaginary parts refractive index of the prism material. The horizontal and vertical transverse coherence lengths at beamline APS 8-ID are measured., Comment: 15 pages, 4 figures, submitted for publication

We present coherent speckled x-ray diffraction patterns obtained from a monolayer of surface atoms. We measured both the specular anti-Bragg reflection and the off-specular hexagonal reconstruction peak for the Au (0 0 1) surface reconstruction. We observed fluctuations of the speckle patterns even when the integrated intensity appears static. By auto-correlating the speckle patterns, we were able to identify two qualitatively different surface dynamic behaviors of the hex reconstruction depending on the sample temperature., Comment: 15 pages, 4 figures. Accepted to Phys. Rev. Lett. 9/2009

The onset of structural arrest and glass formation in a concentrated suspension of silica nanoparticles in a water-lutidine binary mixture near its consolute point is studied by exploiting the near-critical fluid degrees of freedom to control the strength of an attraction between particles and multispeckle x-ray photon correlation spectroscopy to determine the particles' collective dynamics. This model system undergoes a glass transition both on cooling and on heating, and the intermediate liquid realizes unusual logarithmic relaxations. How vitrification occurs for the two different glass transitions is characterized in detail and comparisons are drawn to recent theoretical predictions for glass formation in systems with attractive interactions., Comment: 4 pages, 4 figures

Measurements of magnetic noise emanating from ferromagnets due to domain motion were first carried out nearly 100 years ago and have underpinned much science and technology. Antiferromagnets, which carry no net external magnetic dipole moment, yet have a periodic arrangement of the electron spins extending over macroscopic distances, should also display magnetic noise, but this must be sampled at spatial wavelengths of order several interatomic spacings, rather than the macroscopic scales characteristic of ferromagnets. Here we present the first direct measurement of the fluctuations in the nanometre-scale spin- (charge-) density wave superstructure associated with antiferromagnetism in elemental Chromium. The technique used is X-ray Photon Correlation Spectroscopy, where coherent x-ray diffraction produces a speckle pattern that serves as a "fingerprint" of a particular magnetic domain configuration. The temporal evolution of the patterns corresponds to domain walls advancing and retreating over micron distances. While the domain wall motion is thermally activated at temperatures above 100K, it is not so at lower temperatures, and indeed has a rate which saturates at a finite value - consistent with quantum fluctuations - on cooling below 40K. Our work is important because it provides an important new measurement tool for antiferromagnetic domain engineering as well as revealing a fundamental new fact about spin dynamics in the simplest antiferromagnet., Comment: 19 pages, 4 figures