In-situ X-ray monitoring of solidification and related processes of metal alloys

X-ray radioscopy enables the in-situ monitoring of metal alloy processes and then gives access to crucial information on the dynamics of the underlying phenomena. In the last decade, the utilisation of this powerful imaging technique has been adapted to microgravity platforms such as sounding rockets and parabolic flights. The combination of microgravity experimentation with X-ray radioscopy has resulted in a leap in the understanding of fundamental science and has opened new paths in the fields of materials science. The present review focuses on the short history of this research, which includes facility developments, microgravity experiments and results obtained by partners of the XRMON (In-situ X-Ray MONitoring of advanced metallurgical processes under microgravity and terrestrial conditions) research project in the framework of the MAP (Microgravity Application Promotion) programme of the European Space Agency. Three illustrative research topics that were advanced significantly through the use of X-ray radioscopy will be detailed: solidification of metal alloys, metallic foam formation and diffusion in melts.

Imaging microstructural dynamics and strain fields in electro-active materials in situ with dark field x-ray microscopy

The electric-field-induced and temperature induced dynamics of domains, defects, and phases play an important role in determining the macroscopic functional response of ferroelectric and piezoelectric materials. However, distinguishing and quantifying these phenomena remains a persistent challenge that inhibits our understanding of the fundamental structure-property relationships. In situ dark field x-ray microscopy is a new experimental technique for the real space mapping of lattice strain and orientation in bulk materials. In this paper, we describe an apparatus and methodology for conducting in situ studies of thermally and electrically induced structural dynamics and demonstrate their use on ferroelectric BaTiO₃ single crystals. The stable temperature and electric field apparatus enables simultaneous control of electric fields up to ≈2 kV/mm at temperatures up to 200 °C with a stability of ΔT = ±0.01 K and a ramp rate of up to 0.5 K/min. This capability facilitates studies of critical phenomena, such as phase transitions, which we observe via the microstructural change occurring during the electric-field-induced cubic to tetragonal phase transition in BaTiO₃ at its Curie temperature. With such systematic control, we show how the growth of the polar phase front and its associated ferroelastic domains fall along unexpected directions and, after several cycles of electric field application, result in a non-reversible lattice strain at the electrode-crystal interface. These capabilities pave the way for new insights into the temperature and electric field dependent electromechanical transitions and the critical influence of subtle defects and interfaces.

Analytical transmission cross-coefficients for pink beam X-ray microscopy based on compound refractive lenses

Analytical expressions for the transmission cross-coefficients for x-ray microscopes based on compound refractive lenses are derived based on Gaussian approximations of the source shape and energy spectrum. The effects of partial coherence, defocus, beam convergence, as well as lateral and longitudinal chromatic aberrations are accounted for and discussed. Taking the incoherent limit of the transmission cross-coefficients, a compact analytical expression for the modulation transfer function of the system is obtained, and the resulting point, line and edge spread functions are presented. Finally, analytical expressions for optimal numerical aperture, coherence ratio, and bandwidth are given.

Zernike phase contrast in high-energy x-ray transmission microscopy based on refractive optics

The current work represents the first implementation of Zernike phase contrast for compound refractive lens based x-ray microscopy, and also the first successful Zernike phase contrast experiment at photon energies above 12 keV. Phase contrast was achieved by fitting a compound refractive lens with a circular phase plate. The resolution is demonstrated to be sub-micron, and can be improved using already existing technology. The possibility of combining the technique with polychromatic radiation is considered, and a preliminary test experiment was performed with positive results.

Nebula: reconstruction and visualization of scattering data in reciprocal space

Two-dimensional solid-state X-ray detectors can now operate at considerable data throughput rates that allow full three-dimensional sampling of scattering data from extended volumes of reciprocal space within second to minute time-scales. For such experiments, simultaneous analysis and visualization allows for remeasurements and a more dynamic measurement strategy. A new software, Nebula, is presented. It efficiently reconstructs X-ray scattering data, generates three-dimensional reciprocal space data sets that can be visualized interactively, and aims to enable real-time processing in high-throughput measurements by employing parallel computing on commodity hardware.

Rochelle salt - a structural reinvestigation with improved tools. I. The high-temperature para-electric phase at 308 K

The crystal structure of the high-temperature paraelectric phase of Rochelle salt (K(+)·Na(+)·C4H4O6 (2-)·4H2O) at 308 K has been reinvestigated using synchrotron X-ray diffraction with refinement parameters R(int) = 0.0123, final (shift/e.s.d.)max = 0.019, R 1(all) = 0.0371 and wR 2(all) = 0.0608. The application of a new gas-flow sample cell designed to control both temperature and relative humidity permitted collection of data of excellent quality and enabled unrestrained refinement of all parameters, including those of the isotropic hydrogen atoms. A precise description of the structure has ensued. One K atom is disordered between two symmetry-equivalent sites; three O atoms in three of the four water molecules exhibit very strong anisotropy. Refining one O atom as a split atom was successful, yielding small improvements in the bonding parameters of several H atoms. The H atoms of all water molecules behave as single pairs. Their final U values are of moderate magnitude indicating that these atoms do not participate in the anisotropy of the parent O atoms. It is suggested that the three water O atoms are in part statically disordered, while the bonded H atoms are not. Except for the split K atom and the three water O atoms there is no evidence of general disorder in the structure.

Compact x-ray microradiograph for in situ imaging of solidification processes: bringing in situ x-ray micro-imaging from the synchrotron to the laboratory

A laboratory based high resolution x-ray radiograph was developed for the investigation of solidification dynamics in alloys. It is based on a low-power microfocus x-ray tube and is potentially appropriate for x-ray diagnostics in space. The x-ray microscope offers a high spatial resolution down to approximately 5 μm. Dynamic processes can be resolved with a frequency of up to 6 Hz. In reference experiments, the setup was optimized to yield a high contrast for AlCu-alloys. With samples of about 150 μm thickness, high quality image sequences of the solidification process were obtained with high resolution in time and space.

Three-beam resonant X-ray diffraction in germanium - Laue transmission cases

Perturbation of the two-beam diffracted power owing to the influence of a third lattice node has been examined for various three-beam cases in a small finite germanium crystal in the vicinity of the K-absorption edge. Although the crystal was slightly imperfect, the main parts of the experimental results are very well described within the framework of the fundamental theory of X-ray diffraction in conjunction with Cromer-Liberman calculations for the resonant scattering terms. Beam divergence and dynamical block size are treated as adjustable parameters in the analysis. Observed changes in the three-beam profile asymmetry are mainly attributed to size and not to resonance effects associated with the triplet phase sum of the involved reflections. Close to the absorption edge there is however some evidence indicating that f' values should be reduced in magnitude compared to the tabulated ones.

The charge density of urea from synchrotron diffraction data

The charge density of urea is studied using very high precision single-crystal synchrotron-radiation diffraction data collected at the Swiss-Norwegian Beam Lines at ESRF. An unprecedented resolution of 1.44 A(-1) in sin theta;/lambda is obtained at 123 K. The optimization of the experiment for charge-density studies is discussed. The high precision of the data allowed the refinement of a multipole model extending to hexadecapoles and quadrupoles on the heavy and H atoms, respectively, as well as a liberal treatment of radial functions. The topological properties of the resulting electron density are analysed and compared with earlier experimental results as well as with periodic Hartree-Fock calculations. The properties of the strongly polarized C-O bond agree with trends derived from previous experimental results while the ab initio calculations differ significantly. The results indicate that the description of the C-O bond requires more flexible basis sets in the theoretical calculations. The calculated integrated atomic charges are much larger than the observed ones. It is suggested that the present experimental results provide new target values for validation of future ab initio calculations. The molecular dipole moment derived from the integrated atomic properties is the same as the one obtained from the multipole model even though the individual atomic contributions differ. Comparison with literature data for urea in solution and the gas phase yields a dipole enhancement in the solid of about 1.5 D. The thermal expansion of urea is determined using synchrotron powder diffraction data. With decreasing temperature, an increasing anisotropic strain is observed.

Physical estimation of triplet phases from two new proteins

Three-beam interference experiments have been performed with crystals of two glycosidases: guinea-fowl hexagonal lysozyme, MW 14.3 kDa, and C. thermocellum endoglucanase CelA, MW 40 kDa. In both cases triplet phases could be estimated. Experimental parameters and details of the procedure are presented along with some examples of the results. The average differences between the estimated phases and those calculated from the crystallographic refinements were 17.9 and 15.9 degrees, respectively. A brief discussion of alternative methods for physical phase acquisition is given, including possible strategies for the measurement and application of experimental phases in macromolecular crystallography.

Angle calculations for a six-circle κ diffractometer

By parametrizing the conic surfaces spanned by the reciprocal-lattice vector under the action of the rotation axes, a new procedure for angle calculations for a κ diffractometer is presented. It is applied to obtain angle settings in various modes for a newly developed six-circle diffractometer.

Physical estimation of triplet phases--effects of different radiation sources and modes for profile scans

A comparative study has been made of the intensity profiles from three-beam experiments to estimate triplet phases using radiation from a conventional sealed-tube X-ray source and two different synchrotron sources. Synchrotron radiation, with its much smaller angular divergence, narrower spectral bandwidth and higher flux, distinctly improves the experimental conditions for physical phase estimation. Pure psi scans about the primary diffraction vector, such as can be made with a six-circle diffractometer, further improve the conditions compared with combined omega/psi scans with a four-circle instrument, where the rotation in psi is accomplished by combining rotations about the three axes omega, chi and varphi. Interference profiles collected by pure psi scans and unfocused synchrotron radiation have FWHM values reduced by factors in the range 20-35 relative to those obtained with combined omega-2theta/psi scans and radiation from a conventional source. As a consequence of these changes, which also involve greatly increased peak amplitudes, the 0/pi-type asymmetry of the profiles is exposed much more pronounced closer to the three-beam point, enabling unambiguous phase assignment for all triplets that were studied. The superiority of the pure psi scan will be even more important in studies of general phases for which the phase information lies also in the relative heights of the (sharp) interference maxima for a triplet and the Friedel-related triplet.

Application of known triplet phases in the crystallographic study of bovine pancreatic trypsin inhibitor. II: study at 2.0 A resolution

Direct methods strengthened by the application of about 130 triplet phases, assumed known with a mean error of about +/- 20 degrees, were used to re-determine the structure of BPTI with data at 2.0 A resolution. The triplet phases served to shift the mean direction and enhance the concentration parameter in the corresponding Cochran distributions. These phases were used in combination with the partial structure extracted from successive density maps to control the gradual expansion and refinement of Fourier coefficients. Single phases were developed iteratively from tangent-formula estimation following the path of the convergence map. The a priori triplet phase information was sufficient to initiate solution of the structure at 2.0 A.

Application of Known Triplet Phases in the Crystallographic Study of Bovine Pancreatic Trypsin Inhibitor. I: Studies at 1.55 and 1.75 Å Resolution

The structure of bovine pancreatic trypsin inhibitor could be re-determined both with data at 1.55 and 1.75 A resolution using direct methods strengthened by the application of about 90 and 130 triplet phases, respectively, assumed known with a mean error of +/-20 degrees. From the known triplets a similar number of single phases were derived and used as starting values, thereby reducing or eliminating the need for permuting reflections in the starting set. The known triplets provide better estimates for the mean direction parameters in the corresponding Cochran distributions. This improvement is crucial for obtaining a structure solution. Single phases derived from these triplets could be combined to yield a larger set of triplets which forms the basis for a new figure of merit (FOM). The new FOM appears superior to the conventional ones for initial selection of the best phase model, and can also be used for assessing the correctness of structure expansion if the number of triplet phase relationships is sufficient.

Application of Known X-ray Phases in the Crystallographic Study of a Small Protein

Phase information, assumed known from three-beam diffraction experiments, has been used successfully as input to direct methods to re-determine the crystal structure of rubredoxin. With data at 1.54 A resolution, starting sets containing 26 single phases, or alternatively 45 triplet phases, in both cases known with a mean error of +/-22.5 degrees, were sufficient to initiate solution of the structure. Conventional figures of merit were employed in the early stages to reject the majority of the incorrect phase models. The presence of a FeS(4) cluster in the structure was used in the interpretation of the initial maps. Phase sets including 2500 E's with a mean single phase error <Deltaphi> approximately 70 degrees or a mean triplet phase error <DeltaPhi(3)> approximately 80 degrees, both relative to the model from the crystallographic refinement, could be refined and expanded by Fourier recycling using the SAYTAN formalism. Several parameters have been varied to study their influence on phase expansion and refinement.