Mapping the 3D position of battery cathode particles in Bragg coherent diffractive imaging.

In Bragg coherent diffractive imaging, the precise location of the measured crystals in the interior of the sample is usually missing. Obtaining this information would help the study of the spatially dependent behavior of particles in the bulk of inhomogeneous samples, such as extra-thick battery cathodes. This work presents an approach to determine the 3D position of particles by precisely aligning them at the instrument axis of rotation. In the test experiment reported here, with a 60 µm-thick LiNi0.5Mn1.5O4 battery cathode, the particles were located with a precision of 20 µm in the out-of-plane direction, and the in-plane coordinates were determined with a precision of 1 µm.

Coherence properties of the high-energy fourth-generation X-ray synchrotron sources.

An analysis of the coherence properties of the fourth-generation high-energy storage rings with emittance values of 10 pm rad is performed. It is presently expected that a storage ring with these low emittance values will reach diffraction limit at hard X-rays. Simulations of coherence properties were performed with the XRT software and an analytical approach for different photon energies from 500 eV to 50 keV. It was demonstrated that a minimum photon emittance (diffraction limit) reached at such storage rings is λ/2π. Using mode decomposition it is shown that, for the parameters of the storage ring considered in this work, the diffraction limit will be reached for soft X-ray energies of 500 eV. About ten modes will contribute to the radiation field at 12 keV photon energy and even more modes give a contribution at higher photon energies. Energy spread effects of the electron beam in a low-emittance storage ring were analysed in detail. Simulations were performed at different relative energy spread values from zero to 2 × 10-3. A decrease of the degree of coherence with an increase of the relative energy spread value was observed. This analysis shows that, to reach the diffraction limit for high photon energies, electron beam emittance should go down to 1 pm rad and below.

Diffraction based Hanbury Brown and Twiss interferometry at a hard x-ray free-electron laser.

X-ray free-electron lasers (XFELs) provide extremely bright and highly spatially coherent x-ray radiation with femtosecond pulse duration. Currently, they are widely used in biology and material science. Knowledge of the XFEL statistical properties during an experiment may be vitally important for the accurate interpretation of the results. Here, for the first time, we demonstrate Hanbury Brown and Twiss (HBT) interferometry performed in diffraction mode at an XFEL source. It allowed us to determine the XFEL statistical properties directly from the Bragg peaks originating from colloidal crystals. This approach is different from the traditional one when HBT interferometry is performed in the direct beam without a sample. Our analysis has demonstrated nearly full (80%) global spatial coherence of the XFEL pulses and an average pulse duration on the order of ten femtoseconds for the monochromatized beam, which is significantly shorter than expected from the electron bunch measurements.

Structural studies of the bond-orientational order and hexatic-smectic transition in liquid crystals of various compositions.

We report on the 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 the 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 ß ≈ 0.1 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 an exponent equal to the harmonic number. This indicates a nonlinear coupling of the BO order parameters of different order. We demonstrate that compounds of various compositions, possessing different phase sequences at low temperatures, display the same thermodynamic behavior in the hexatic phase and in the vicinity of the smectic-hexatic phase transition.

Erratum: Hanbury Brown-Twiss Interferometry at a Free-Electron Laser [Phys. Rev. Lett. 111, 034802 (2013)].

This corrects the article DOI: 10.1103/PhysRevLett.111.034802.

Direct reconstruction of the two-dimensional pair distribution function in partially ordered systems with angular correlations.

An x-ray scattering approach to determine the two-dimensional (2D) pair distribution function (PDF) in partially ordered 2D systems is proposed. We derive relations between the structure factor and PDF that enable quantitative studies of positional and bond-orientational (BO) order in real space. We apply this approach in the x-ray study of a liquid crystal (LC) film undergoing the smectic-A-hexatic-B phase transition, to analyze the interplay between the positional and BO order during the temperature evolution of the LC film. We analyze the positional correlation length in different directions in real space.

Revealing Three-Dimensional Structure of an Individual Colloidal Crystal Grain by Coherent X-Ray Diffractive Imaging.

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.

Sorting algorithms for single-particle imaging experiments at X-ray free-electron lasers.

Modern X-ray free-electron lasers (XFELs) operating at high repetition rates produce a tremendous amount of data. It is a great challenge to classify this information and reduce the initial data set to a manageable size for further analysis. Here an approach for classification of diffraction patterns measured in prototypical diffract-and-destroy single-particle imaging experiments at XFELs is presented. It is proposed that the data are classified on the basis of a set of parameters that take into account the underlying diffraction physics and specific relations between the real-space structure of a particle and its reciprocal-space intensity distribution. The approach is demonstrated by applying principal component analysis and support vector machine algorithms to the simulated and measured X-ray data sets.

Theoretical study of electronic damage in single-particle imaging experiments at x-ray free-electron lasers for pulse durations from 0.1 to 10 fs.

X-ray free-electron lasers (XFELs) may allow us to employ the single-particle imaging (SPI) method to determine the structure of macromolecules that do not form stable crystals. Ultrashort pulses of 10 fs and less allow us to outrun complete disintegration by Coulomb explosion and minimize radiation damage due to nuclear motion, but electronic damage is still present. The major contribution to the electronic damage comes from the plasma generated in the sample that is strongly dependent on the amount of Auger ionization. Since the Auger process has a characteristic time scale on the order of femtoseconds, one may expect that its contribution will be significantly reduced for attosecond pulses. Here we study the effect of electronic damage on the SPI at pulse durations from 0.1 to 10 fs and in a large range of XFEL fluences to determine optimal conditions for imaging of biological samples. We analyzed the contribution of different electronic excitation processes and found that at fluences higher than 10(13)-10(15) photons/µm(2) (depending on the photon energy and pulse duration) the diffracted signal saturates and does not increase further. A significant gain in the signal is obtained by reducing the pulse duration from 10 to 1 fs. Pulses below a duration of 1 fs do not give a significant gain in the scattering signal in comparison with 1-fs pulses. We also study the limits imposed on SPI by Compton scattering.

Spatially resolved x-ray studies of liquid crystals with strongly developed bond-orientational order.

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.

The linac coherent light source single particle imaging road map.

Intense femtosecond x-ray pulses from free-electron laser sources allow the imaging of individual particles in a single shot. Early experiments at the Linac Coherent Light Source (LCLS) have led to rapid progress in the field and, so far, coherent diffractive images have been recorded from biological specimens, aerosols, and quantum systems with a few-tens-of-nanometers resolution. In March 2014, LCLS held a workshop to discuss the scientific and technical challenges for reaching the ultimate goal of atomic resolution with single-shot coherent diffractive imaging. This paper summarizes the workshop findings and presents the roadmap toward reaching atomic resolution, 3D imaging at free-electron laser sources.

Intensity interferometry of single x-ray pulses from a synchrotron storage ring.

We report on measurements of second-order intensity correlations at the high-brilliance storage ring PETRA III using a prototype of the newly developed adaptive gain integrating pixel detector. The detector records individual synchrotron radiation pulses with an x-ray photon energy of 14.4 keV and repetition rate of about 5 MHz. The second-order intensity correlation function is measured simultaneously at different spatial separations, which allows us to determine the transverse coherence length at these x-ray energies. The measured values are in a good agreement with theoretical simulations based on the Gaussian Schell model.

Characterization of spatial coherence of synchrotron radiation with non-redundant arrays of apertures.

A method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern is presented. The technique is based on scattering from non-redundant arrays (NRAs) of slits and records the degree of spatial coherence at several relative separations from 1 to 15 µm, simultaneously. Using NRAs the spatial coherence of the X-ray beam at the XUV X-ray beamline P04 of the PETRA III synchrotron storage ring was measured as a function of different beam parameters. To verify the results obtained with the NRAs, additional Young's double-pinhole experiments were conducted and showed good agreement.

X-ray cross-correlation analysis of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition.

We present an x-ray study of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition by means of angular x-ray cross-correlation analysis. 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.

In situ X-ray crystallographic study of the structural evolution of colloidal crystals upon heating.

The structural evolution of colloidal crystals made of polystyrene hard spheres has been studied in situ upon incremental heating of a crystal in a temperature range below and above the glass transition temperature of polystyrene. Thin films of colloidal crystals having different particle sizes were studied in transmission geometry using a high-resolution small-angle X-ray scattering setup at the P10 Coherence Beamline of the PETRA III synchrotron facility. The transformation of colloidal crystals to a melted state has been observed in a narrow temperature interval of less than 10 K.

Hanbury Brown-Twiss interferometry at a free-electron laser.

We present measurements of second- and higher-order intensity correlation functions (so-called Hanbury Brown-Twiss experiment) performed at the free-electron laser (FEL) FLASH in the non-linear regime of its operation. We demonstrate the high transverse coherence properties of the FEL beam with a degree of transverse coherence of about 80% and degeneracy parameter of the order 10(9) that makes it similar to laser sources. Intensity correlation measurements in spatial and frequency domain gave an estimate of the FEL average pulse duration of 50 fs. Our measurements of the higher-order correlation functions indicate that FEL radiation obeys Gaussian statistics, which is characteristic to chaotic sources.

Single pulse coherence measurements in the water window at the free-electron laser FLASH.

The spatial coherence of free-electron laser radiation in the water window spectral range was studied, using the third harmonic (λ<(3rd) = 2.66 nm) of DESY's Free-electron LASer in Hamburg (FLASH). Coherent single pulse diffraction patterns of 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) multilamellar lipid stacks have been recorded. The intensity histogram of the speckle pattern around the first lamellar Bragg peak, corresponding to the d = 5 nm periodicity of the stack, reveals an average number of transverse modes of M¯ = 3.0 of the 3rd harmonic. Using the lipid stack as a 'monochromator', pulse-to-pulse fluctuations in the third harmonic λ(3rd) have been determined to be 0.033 nm.

Spectrometer for hard X-ray free-electron laser based on diffraction focusing.

X-ray free-electron lasers (XFELs) generate sequences of ultra-short spatially coherent pulses of X-ray radiation. A diffraction focusing spectrometer (DFS), which is able to measure the whole energy spectrum of the radiation of a single XFEL pulse with an energy resolution of ΔE/E 2 × 10(-6), is proposed. This is much better than for most modern X-ray spectrometers. Such resolution allows one to resolve the fine spectral structure of the XFEL pulse. The effect of diffraction focusing occurs in a single-crystal plate due to dynamical scattering, and is similar to focusing in a Pendry lens made from a metamaterial with a negative refraction index. Such a spectrometer is easier to operate than those based on bent crystals. It is shown that the DFS can be used in a wide energy range from 5 keV to 20 keV.

Impact of ultrafast electronic damage in single-particle x-ray imaging experiments.

In single-particle coherent x-ray diffraction imaging experiments, performed at x-ray free-electron lasers (XFELs), samples are exposed to intense x-ray pulses to obtain single-shot diffraction patterns. The high intensity induces electronic dynamics on the femtosecond time scale in the system, which can reduce the contrast of the obtained diffraction patterns and adds an isotropic background. We quantify the degradation of the diffraction pattern from ultrafast electronic damage by performing simulations on a biological sample exposed to x-ray pulses with different parameters. We find that the contrast is substantially reduced and the background is considerably strong only if almost all electrons are removed from their parent atoms. This happens at fluences of at least one order of magnitude larger than provided at currently available XFEL sources.

Spatial and temporal coherence properties of single free-electron laser pulses.

The experimental characterization of the spatial and temporal coherence properties of the free-electron laser in Hamburg (FLASH) at a wavelength of 8.0 nm is presented. Double pinhole diffraction patterns of single femtosecond pulses focused to a size of about 10×10 µm(2) were measured. A transverse coherence length of 6.2 ± 0.9 µm in the horizontal and 8.7 ± 1.0 µm in the vertical direction was determined from the most coherent pulses. Using a split and delay unit the coherence time of the pulses produced in the same operation conditions of FLASH was measured to be 1.75 ± 0.01 fs. From our experiment we estimated the degeneracy parameter of the FLASH beam to be on the order of 10(10) to 10(11), which exceeds the values of this parameter at any other source in the same energy range by many orders of magnitude.