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.

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.

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.

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.

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.

Femtosecond control of phonon dynamics near a magnetic order critical point.

The spin-phonon interaction in spin density wave (SDW) systems often determines the free energy landscape that drives the evolution of the system. When a passing energy flux, such as photoexcitation, drives a crystalline system far from equilibrium, the resulting lattice displacement generates transient vibrational states. Manipulating intermediate vibrational states in the vicinity of the critical point, where the SDW order parameter changes dramatically, would then allow dynamical control over functional properties. Here we combine double photoexcitation with an X-ray free-electron laser (XFEL) probe to control and detect the lifetime and magnitude of the intermediate vibrational state near the critical point of the SDW in chromium. We apply Landau theory to identify the mechanism of control as a repeated partial quench and sub picosecond recovery of the SDW. Our results showcase the capabilities to influence and monitor quantum states by combining multiple optical photoexcitations with an XFEL probe. They open new avenues for manipulating and researching the behaviour of photoexcited states in charge and spin order systems near the critical point.

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.

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.

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.