Geometrical-optics formalism to model contrast in dark-field X-ray microscopy

Dark-field X-ray microscopy, DFXM, is a new full-field imaging technique that non-destructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. In DFXM an objective lens is placed along the diffracted beam to generate a magnified projection image of the local diffracted volume. In this work, a general formalism based on geometrical optics is provided for the diffraction imaging, valid for any crystallographic space group. This allows the simulation of DFXM images based on micro-mechanical models. Example simulations are presented with the formalism, demonstrating how this may be used to design new experiments or to interpret existing ones. In particular, it is shown how modifications to the experimental design may tailor the reciprocal-space resolution function to map specific components of the deformation-gradient tensor. The formalism supports multi-length-scale experiments, as it enables DFXM to be interfaced with 3D X-ray diffraction. To illustrate the use of the formalism, DFXM images are simulated from different contrast mechanisms on the basis of the strain field around a straight dislocation.

Radiation furnace for synchrotron dark-field x-ray microscopy experiments

We present a multi-purpose radiation furnace designed for x-ray experiments at synchrotrons. The furnace is optimized specifically for dark-field x-ray microscopy (DFXM) of crystalline materials at beamline ID06 of the European Synchrotron Radiation Facility. The furnace can reach temperatures above 1200 °C with a thermal stability better than 10 °C, with heating and cooling rates up to 30 K/s. The non-contact heating design enables samples to be heated either in air or in a controlled atmosphere contained within a capillary tube. The temperature was calibrated via the thermal expansion of an α-iron grain. Temperature profiles in the y and z axes were measured by scanning a thermocouple through the focal spot of the radiation furnace. In the current configuration of the beamline, this furnace can be used for DFXM, near-field x-ray topography, bright-field x-ray nanotomography, high-resolution reciprocal space mapping, and limited powder diffraction experiments. As a first application, we present a DFXM case study on isothermal heating of a commercially pure single crystal of aluminum.

Mapping of individual dislocations with dark-field X-ray microscopy

This article presents an X-ray microscopy approach for mapping deeply embedded dislocations in three dimensions using a monochromatic beam with a low divergence. Magnified images are acquired by inserting an X-ray objective lens in the diffracted beam. The strain fields close to the core of dislocations give rise to scattering at angles where weak beam conditions are obtained. Analytical expressions are derived for the image contrast. While the use of the objective implies an integration over two directions in reciprocal space, scanning an aperture in the back focal plane of the microscope allows a reciprocal-space resolution of ΔQ/Q < 5 × 10−5 in all directions, ultimately enabling high-precision mapping of lattice strain and tilt. The approach is demonstrated on three types of samples: a multi-scale study of a large diamond crystal in transmission, magnified section topography on a 140 µm-thick SrTiO3 sample and a reflection study of misfit dislocations in a 120 nm-thick BiFeO3 film epitaxially grown on a thick substrate. With optimal contrast, the half-widths at half-maximum of the dislocation lines are 200 nm.

Reciprocal space mapping and strain scanning using X-ray diffraction microscopy

Dark-field X-ray microscopy is a new full-field imaging technique for nondestructively mapping the structure of deeply embedded crystalline elements in three dimensions. Placing an objective in the diffracted beam generates a magnified projection image of a local volume. By placing a detector in the back focal plane, high-resolution reciprocal space maps are generated for the local volume. Geometrical optics is used to provide analytical expressions for the resolution and range of the reciprocal space maps and the associated field of view in the sample plane. To understand the effects of coherence a comparison is made with wavefront simulations using the fractional Fourier transform. Reciprocal space mapping is demonstrated experimentally at an X-ray energy of 15.6 keV. The resolution function exhibits suppressed streaks and an FWHM resolution in all directions of ΔQ/Q = 4 × 10−5 or better. It is demonstrated by simulations that scanning a square aperture in the back focal plane enables strain mapping with no loss in resolution to be combined with a spatial resolution of 100 nm.

X-ray diffraction microscopy based on refractive optics

A formalism is presented for dark-field X-ray microscopy using refractive optics. The new technique can produce three-dimensional maps of lattice orientation and axial strain within millimetre-sized sampling volumes and is particularly suited toin situstudies of materials at hard X-ray energies. An objective lens in the diffracted beam magnifies the image and acts as a very efficient filter in reciprocal space, enabling the imaging of individual domains of interest with a resolution of 100 nm. Analytical expressions for optical parameters such as numerical aperture, vignetting, and the resolution in both direct and reciprocal spaces are provided. It is shown that the resolution function in reciprocal space can be highly anisotropic and varies as a function of position in the field of view. Inserting a square aperture in front of the objective lens facilitates disjunct and space-filling sampling, which is key for three-dimensional reconstruction and analysis procedures based on the conservation of integrated intensity. A procedure for strain scanning is presented. Finally the formalism is validated experimentally at an X-ray energy of 17 keV.

Dark-field X-ray microscopy for multiscale structural characterization

Many physical and mechanical properties of crystalline materials depend strongly on their internal structure, which is typically organized into grains and domains on several length scales. Here we present dark-field X-ray microscopy; a non-destructive microscopy technique for the three-dimensional mapping of orientations and stresses on lengths scales from 100 nm to 1 mm within embedded sampling volumes. The technique, which allows 'zooming' in and out in both direct and angular space, is demonstrated by an annealing study of plastically deformed aluminium. Facilitating the direct study of the interactions between crystalline elements is a key step towards the formulation and validation of multiscale models that account for the entire heterogeneity of a material. Furthermore, dark-field X-ray microscopy is well suited to applied topics, where the structural evolution of internal nanoscale elements (for example, positioned at interfaces) is crucial to the performance and lifetime of macro-scale devices and components thereof.

A 31 T split-pair pulsed magnet for single crystal x-ray diffraction at low temperature

We have developed a pulsed magnet system with panoramic access for synchrotron x-ray diffraction in magnetic fields up to 31 T and at low temperature down to 1.5 K. The apparatus consists of a split-pair magnet, a liquid nitrogen bath to cool the pulsed coil, and a helium cryostat allowing sample temperatures from 1.5 up to 250 K. Using a 1.15 MJ mobile generator, magnetic field pulses of 60 ms length were generated in the magnet, with a rise time of 16.5 ms and a repetition rate of 2 pulses/h at 31 T. The setup was validated for single crystal diffraction on the ESRF beamline ID06.

Melting of chiral order in terbium manganate (TbMnO3) observed with resonant x-ray Bragg diffraction

Resonant Bragg diffraction of soft, circularly polarized x-rays has been used to observe directly the temperature dependence of chiral-order melting in a motif of Mn ions in terbium manganate. The underlying mechanism uses the b-axis component of a cycloid, which vanishes outside the polar phase. Melting is witnessed by the first and second harmonics of a cycloid, and we explain why the observed temperature dependence differs in the two harmonics. Conclusions follow from an exact treatment of diffraction by using atomic multipoles in a circular cycloid, since a standard treatment of the diffraction, based on a single material-vector identified with the magnetic dipole, does not reproduce correctly observations at the second harmonic.

High-precision x-ray polarimetry

The polarization purity of 6.457- and 12.914-keV x rays has been improved to the level of 2.4×10(-10) and 5.7×10(-10). The polarizers are channel-cut silicon crystals using six 90° reflections. Their performance and possible applications are demonstrated in the measurement of the optical activity of a sucrose solution.

Neptunium multipoles and resonant x-ray Bragg diffraction by neptunium dioxide (NpO2)

The low-temperature ordered state of neptunium dioxide (NpO(2)) remains enigmatic. After decades of experimental and theoretical efforts, long-range order of a time-odd (magnetic) high-order atomic multipole moment is now generally considered to be the fundamental order parameter, the most likely candidate being a magnetic triakontadipole (rank 5). To date, however, direct experimental observation of the primary order parameter remains outstanding. In the light of new experimental findings, we re-examine the effect of crystal symmetry on the atomic multipoles and the resulting x-ray resonant scattering signature. Our simulations use the crystallographic point group ̅3m (D(3d)), because corresponding magnetic groups ̅3m', ̅3'm', and ̅3'm are shown by us to be at odds with a wealth of experimental results. In addition to the previously observed (secondary) quadrupole order, we derive expressions for higher-order multipoles that might be observed in future experiments. In particular, magnetic octupole moments are predicted to contribute to Np M(2,3) and L(2,3) resonant scattering via E2–E2 events. The Lorentzian-squared lineshape observed at the M(4) resonance is shown to be the result of the anisotropy of the 3p(3/2) core levels. Quantitative comparison of our calculations to the measured data yields a core–hole width Γ = 2.60(7) eV and a core-state exchange energy [absolute value]ε(1/2)[absolute value] = 0.76(2) eV.

Acentric magnetic and optical properties of chalcopyrite (CuFeS2)

The absence of spatial inversion symmetry at both local (point group 4) and global (crystal class (4)2m) levels greatly influences the electronic properties of chalcopyrite (CuFeS(2)). The predicted dichroic signals (natural circular, non-reciprocal and magneto-chiral) and resonant, parity-odd Bragg diffraction patterns at space-group forbidden reflections portray the uncommon, acentric symmetry. Despite extensive experimental investigations over several decades, by mineralogists, chemists and physicists, there is no consensus view about the electrical and magnetic properties of chalcopyrite. New spectroscopic and diffraction data, gathered at various temperatures in the vicinity of the copper and iron L(2,3) edges, provide necessary confidence in the magnetic motif used in our analytic simulations of x-ray scattering. With the sample held at 10 and 65 K, our data establish beyond reasonable doubt that there is no valence transition, and ordering of the copper moments as the origin of the low-temperature phase (T(c) ≈ 53 K) is ruled out.

A 30 T pulsed magnet with conical bore for synchrotron powder diffraction

We report on the design, construction, and operation of a horizontal field, 30 T magnet system with a conical bore optimized for synchrotron x-ray powder diffraction. The magnet offers ±31° optical access downstream of the sample, which allows to measure a sufficiently large number of Debye rings for an accurate crystal structure analysis. Combined with a 290 kJ generator, magnetic field pulses of 60 ms length were generated in the magnet, with a rise time of 4.1 ms and a repetition rate of 6 pulses/h at 30 T. The coil is mounted inside a liquid nitrogen bath. A liquid helium flow cryostat reaches into the coil and allows sample temperature between 5 and 250 K. The setup was used on the European Synchrotron Radiation Facility beamlines ID20 and ID06.

Photon regeneration experiment for axion search using x-rays

In this Letter we describe our novel photon regeneration experiment for the axionlike particle search using an x-ray beam with a photon energy of 50.2 and 90.7 keV, two superconducting magnets of 3 T, and a Ge detector with a high quantum efficiency. A counting rate of regenerated photons compatible with zero has been measured. The corresponding limits on the pseudoscalar axionlike particle-two-photon coupling constant is obtained as a function of the particle mass. Our setup widens the energy window of purely terrestrial experiments devoted to the axionlike particle search by coupling to two photons. It also opens a new domain of experimental investigation of photon propagation in magnetic fields.

Direct observation of double-k lattice modulation in double-k magnetic structures. The case of CeAl(2)

Symmetry analysis is combined with x-ray scattering experiments to investigate the lattice modulation associated with the incommensurate magnetic structure in the case of a double- k structure. The expansion of the free energy shows that the components of the magnetic structure with propagation vectors k(1) and k(2) can couple via components of lattice modulations. It is shown that the classical diffraction peaks reflecting a 2k propagation vector, associated with magneto-elastic effects in single- k structures, will coexist with diffraction peaks with propagation vectors k(1)-k(2) or k(1)+k(2). The existence of these latter peaks can be considered as a signature of a double- k magnetic structure. In the case of the double- k modulated structure of CeAl(2), group theory is applied directly to the study of the charge modulation. An x-ray scattering study of the 2k satellites shows that the lattice displacements of the two Ce sites of the structure are antiparallel to each other, and perpendicular to the direction of the magnetic modulation. We also confirm experimentally the existence of k(1)+k(2) satellites.

X-ray nanointerferometer based on si refractive bilenses

We report a novel type of x-ray interferometer employing a bilens system consisting of two parallel compound refractive lenses, each of which creates a diffraction limited beam under coherent illumination. By closely overlapping such coherent beams, an interference field with a fringe spacing ranging from tens of nanometers to tens of micrometers is produced. In an experiment performed with 12 keV x rays, submicron fringes were observed by scanning and moiré imaging of the test grid. The far field interference pattern was used to characterize the x-ray coherence. Our technique opens up new opportunities for studying natural and man-made nanoscale materials.

Charge and orbital correlations at and above the Verwey phase transition in magnetite

The subtle interplay among electronic degrees of freedom (charge and orbital orderings), spin and lattice distortion that conspire at the Verwey transition in magnetite (Fe3O4) is still a matter of controversy. Here, we provide compelling evidence that these electronic orderings are manifested as a continuous phase transition at the temperature where a spin reorientation takes place at around 130 K, i.e., well above TV approximately 121 K. The Verwey transition seems to leave the orbital ordering unaffected whereas the charge ordering development appears to be quenched at this temperature and the temperature dependence below TV is controlled by the lattice distortions. Finally, we show that the orbital ordering does not reach true long range (disorder), and the correlation length along the c-direction is limited to 100 angstroms.

Direct Observation of the High Magnetic Field Effect on the Jahn-Teller State in TbVO4

We report the first direct observation of the influence of high magnetic fields on the Jahn-Teller (JT) transition in TbVO(4). Contrary to spectroscopic and magnetic methods, x-ray diffraction directly measures the JT distortion; the splitting between the (311)/(131) and (202)/(022) pairs of Bragg reflections is proportional to the order parameter. Our experimental results are compared to mean-field calculations, taking into account all possible orientations of the grains relative to the applied field, and qualitative agreement is obtained.

ID20: a beamline for magnetic and resonant X-ray scattering investigations under extreme conditions

A new experimental station at ESRF beamline ID20 is presented which allows magnetic and resonant X-ray scattering experiments in the energy range 3-25 keV to be performed under extreme conditions. High magnetic field up to 10 T, high pressure up to 30 kbar combined with low temperatures down to 1.5 K are available and experiments can be performed at the M-edges of actinide elements, L-edges of lanthanides and K-edges of transition metals.

Charge density wave dislocation as revealed by coherent x-ray diffraction

Coherent x-ray diffraction experiments have been performed on high quality crystals of the charge density wave (CDW) system K0.3MoO3. The satellite reflections associated with the CDW have been measured as a function of the 20-microm-diameter beam position. For some positions, regular fringes have been observed. We show that this observation is consistent with the presence of a single CDW dislocation. Beyond charge density wave systems, this experiment shows that coherent x-ray diffraction is a suitable tool to probe topological defects embedded in the bulk.

Triple-q(-->) octupolar ordering in NpO2

We report the results of resonant x-ray scattering experiments performed at the Np M(4,5) edges in NpO2. Below T(0)=25 K, the development of long-range order of Np electric quadrupoles is revealed by the growth of superlattice Bragg peaks. The polarization and azimuthal dependence of the intensity of the resonant peaks are well reproduced assuming anisotropic tensor susceptibility scattering from a triple-q(-->) longitudinal antiferroquadrupolar structure. Electric-quadrupole order in NpO2 could be driven by the ordering at T0 of magnetic octupoles of Gamma(5) symmetry, splitting the Np ground state quartet and leading to a singlet ground state with zero dipole-magnetic moment.

Kinetic evolution of unmixing in an AlLi alloy using x-ray intensity fluctuation spectroscopy

Irreversible decomposition of an AlLi single crystal has been studied by x-ray photon correlation spectroscopy. The precipitate coarsening follows a universal behavior, as measured by the time-resolved average scattering. Using coherent scattering, two-time correlation functions have been measured. The time evolution of the speckle pattern gives new insight into the process of unmixing; at least two regimes govern this evaporation-condensation coarsening process. One is related to the overall arrangement of precipitates, and the characteristic time is linear with annealing time. The other is related to the motion of interfaces and is related to Porod's law.

Critical adsorption and dimensional crossover in epitaxial FeCo films

The critical behavior of thin FeCo films grown on MgO has been studied using phase-sensitive synchrotron x-ray diffraction. These studies unravel several novel features of criticality in thin films, as the simultaneous appearance of the 3D-2D crossover and the truncation of the correlation length normal to the film at approximately 1/3 of the film thickness. Above the critical temperature of the film we observe a pronounced pinning of the order parameter at the MgO-FeCo interface, which indicates a novel critical adsorption behavior.

Causes and formation of cavitation in mechanical heart valves

Cavitation may develop on mechanical valvular prostheses in the mitral position; it causes blood damage and, under particularly adverse conditions, it may result in sudden failure of the prosthesis. Therefore, with regard to future development of mechanical heart valves, the pattern of cavitation and its predisposing factors in different types of prostheses were investigated in in vitro studies, which focused on the analysis of valve closure dynamics and the influence of design parameters on the cavitation-inducing pressure drop at the artificial valve. It was found that cavitation is produced primarily by the deceleration of the closing body of the valve. At 900g, the measured deceleration of the closing bodies falls in the range of the decelerations determined in oscillation experiments for investigating cavitation-induced material erosion. The pressure drop produced thereby is overlapped by the pressure drop in accelerated or turbulent flow regions produced by design characteristics at outlet struts, stop faces or sealing lips during backflow through the closing disc. These phenomena exist particularly in regions of high flow velocity, i.e. at the instant of closure at the maximum distance from the bearing axis of the closing body (12 o'clock position). The onset of cavitation is additionally promoted in this position by a tight joint between the closing body and the ring. Oscillations of the closing body generally have a negligible effect on the cavitation behavior. From these relationships one can infer that cavitation can be avoided in future in mechanical heart valves by locally limited design measures. Especially, unsteadiness in the backflow through the closing valve is to be avoided.