A new satellite of manganese revealed by extended-range high-energy-resolution fluorescence detection.

The discovery of a new physical process in manganese metal is reported. This process will also be present for all manganese-containing materials in condensed matter. The process was discovered by applying our new technique of XR-HERFD (extended-range high-energy-resolution fluorescence detection), which was developed from the popular high-resolution RIXS (resonant inelastic X-ray scattering) and HERFD approaches. The acquired data are accurate to many hundreds of standard deviations beyond what is regarded as the criterion for `discovery'. Identification and characterization of many-body processes can shed light on the X-ray absorption fine-structure spectra and inform the scientist on how to interpret them, hence leading to the ability to measure the dynamical nanostructures which are observable using the XR-HERFD method. Although the many-body reduction factor has been used universally in X-ray absorption spectroscopy in analysis over the past 30 years (thousands of papers per year), this experimental result proves that many-body effects are not representable by any constant reduction factor parameter. This paradigm change will provide the foundation for many future studies and X-ray spectroscopy.

High-accuracy transmission and fluorescence XAFS of zinc at 10†K, 50†K, 100†K and 150†K using the hybrid technique.

The most accurate measurements of the mass attenuation coefficient for metals at low temperature for the zinc K-edge from 9.5 keV to 11.5 keV at temperatures of 10 K, 50 K, 100 K and 150 K using the hybrid technique are reported. This is the first time transition metal X-ray absorption fine structure (XAFS) has been studied using the hybrid technique and at low temperatures. This is also the first hybrid-like experiment at the Australian Synchrotron. The measured transmission and fluorescence XAFS spectra are compared and benchmarked against each other with detailed systematic analyses. A recent method for modelling self-absorption in fluorescence has been adapted and applied to a solid sample. The XAFS spectra are analysed using eFEFFIT to provide a robust measurement of the evolution of nanostructure, including such properties as net thermal expansion and mean-square relative displacement. This work investigates crystal dynamics, nanostructural evolution and the results of using the Debye and Einstein models to determine atomic positions. Accuracies achieved, when compared with the literature, exceed those achieved by both relative and differential XAFS, and represent a state-of-the-art for future structural investigations. Bond length uncertainties are of the order of 20-40 fm.

High-accuracy mass attenuation coefficients and X-ray absorption spectroscopy of zinc - the first X-ray Extended Range Technique-like experiment in Australia.

The first X-ray Extended Range Technique (XERT)-like experiment at the Australian Synchrotron, Australia, is presented. In this experiment X-ray mass attenuation coefficients are measured across an energy range including the zinc K-absorption edge and X-ray absorption fine structure (XAFS). These high-accuracy measurements are recorded at 496 energies from 8.51 keV to 11.59 keV. The XERT protocol dictates that systematic errors due to dark current nonlinearities, correction for blank measurements, full-foil mapping to characterize the absolute value of attenuation, scattering, harmonics and roughness are measured over an extended range of experimental parameter space. This results in data for better analysis, culminating in measurement of mass attenuation coefficients across the zinc K-edge to 0.023-0.036% accuracy. Dark current corrections are energy- and structure-dependent and the magnitude of correction reached 57% for thicker samples but was still large and significant for thin samples. Blank measurements scaled thin foil attenuation coefficients by 60-500%; and up to 90% even for thicker foils. Full-foil mapping and characterization corrected discrepancies between foils of up to 20%, rendering the possibility of absolute measurements of attenuation. Fluorescence scattering was also a major correction. Harmonics, roughness and bandwidth were explored. The energy was calibrated using standard reference foils. These results represent the most extensive and accurate measurements of zinc which enable investigations of discrepancies between current theory and experiments. This work was almost fully automated from this first experiment at the Australian Synchrotron, greatly increasing the possibility for large-scale studies using XERT.

High-accuracy measurement of mass attenuation coefficients and the imaginary component of the atomic form factor of zinc from 8.51†keV to 11.59†keV, and X-ray absorption fine structure with investigation of zinc theory and nanostructure.

High-accuracy X-ray mass attenuation coefficients were measured from the first X-ray Extended Range Technique (XERT)-like experiment at the Australian Synchrotron. Experimentally measured mass attenuation coefficients deviate by ∼50% from the theoretical values near the zinc absorption edge, suggesting that improvements in theoretical tabulations of mass attenuation coefficients are required to bring them into better agreement with experiment. Using these values the imaginary component of the atomic form factor of zinc was determined for all the measured photon energies. The zinc K-edge jump ratio and jump factor are determined and results raise significant questions regarding the definitions of quantities used and best practice for background subtraction prior to X-ray absorption fine-structure (XAFS) analysis. The XAFS analysis shows excellent agreement between the measured and tabulated values and yields bond lengths and nanostructure of zinc with uncertainties of from 0.1% to 0.3% or 0.003 Što 0.008 Å. Significant variation from the reported crystal structure was observed, suggesting local dynamic motion of the standard crystal lattice. XAFS is sensitive to dynamic correlated motion and in principle is capable of observing local dynamic motion beyond the reach of conventional crystallography. These results for the zinc absorption coefficient, XAFS and structure are the most accurate structural refinements of zinc at room temperature.

High accuracy determination of photoelectric cross sections, X-ray absorption fine structure and nanostructure analysis of zinc selenide using the X-ray extended range technique.

Measurements of mass attenuation coefficients and X-ray absorption fine structure (XAFS) of zinc selenide (ZnSe) are reported to accuracies typically better than 0.13%. The high accuracy of the results presented here is due to our successful implementation of the X-ray extended range technique, a relatively new methodology, which can be set up on most synchrotron X-ray beamlines. 561 attenuation coefficients were recorded in the energy range 6.8-15 keV with measurements concentrated at the zinc and selenium pre-edge, near-edge and fine-structure absorption edge regions. This accuracy yielded detailed nanostructural analysis of room-temperature ZnSe with full uncertainty propagation. Bond lengths, accurate to 0.003 Što 0.009 Å, or 0.1% to 0.3%, are plausible and physical. Small variation from a crystalline structure suggests local dynamic motion beyond that of a standard crystal lattice, noting that XAFS is sensitive to dynamic correlated motion. The results obtained in this work are the most accurate to date with comparisons with theoretically determined values of the attenuation showing discrepancies from literature theory of up to 4%, motivating further investigation into the origin of such discrepancies.

Structural investigation of mM Ni(II) complex isomers using transmission XAFS: the significance of model development.

High-accuracy transmission XAFS determined using the hybrid technique has been used to refine the geometries of bis(N-n-propyl-salicylaldiminato) nickel(II) (n-pr Ni) and bis(N-i-propyl-salicylaldiminato) nickel(II) (i-pr Ni) complexes which have approximately square planar and tetrahedral metal coordination. Multiple-scattering formalisms embedded in FEFF were used for XAFS modelling of the complexes. Here it is shown that an IFEFFIT-like package using weighting from experimental uncertainty converges to a well defined XAFS model. Structural refinement of (i-pr Ni) was found to yield a distorted tetrahedral geometry providing an excellent fit, χr(2) = 2.94. The structure of (n-pr Ni) is best modelled with a distorted square planar geometry, χr(2) = 3.27. This study demonstrates the insight that can be obtained from the propagation of uncertainty in XAFS analysis and the consequent confidence which can be obtained in hypothesis testing and in analysis of alternate structures ab initio. It also demonstrates the limitations of this (or any other) data set by defining the point at which signal becomes embedded in noise or amplified uncertainty, and hence can justify the use of a particular k-range for one data set or a different range for another. It is demonstrated that, with careful attention to data collection, including the correction of systematic errors with statistical analysis of uncertainty (the hybrid method), it is possible to obtain reliable structural information from dilute solutions using transmission XAFS data.

High-accuracy X-ray absorption spectra from mM solutions of nickel (II) complexes with multiple solutions using transmission XAS.

A new approach is introduced for determining X-ray absorption spectroscopy (XAS) spectra on absolute and relative scales using multiple solutions with different concentrations by the characterization and correction of experimental systematics. This hybrid technique is a development of standard X-ray absorption fine structure (XAFS) along the lines of the high-accuracy X-ray extended range technique (XERT) but with applicability to solutions, dilute systems and cold cell environments. This methodology has been applied to determining absolute XAS of bis(N-n-propyl-salicylaldiminato) nickel(II) and bis(N-i-propyl-salicylaldiminato) nickel(II) complexes with square planar and tetrahedral structures in 15 mM and 1.5 mM dilute solutions. It is demonstrated that transmission XAS from dilute systems can provide excellent X-ray absorption near-edge structure (XANES) and XAFS spectra, and that transmission measurements can provide accurate measurement of subtle differences including coordination geometries. For the first time, (transmission) XAS of the isomers have been determined from low-concentration solutions on an absolute scale with a 1-5% accuracy, and with relative precision of 0.1% to 0.2% in the active XANES and XAFS regions after inclusion of systematic corrections.

Measurement of the X-ray mass attenuation coefficients of silver in the 5-20†keV range.

The X-ray mass attenuation coefficients of silver were measured in the energy range 5-20 keV with an accuracy of 0.01-0.2% on a relative scale down to 5.3 keV, and of 0.09-1.22% on an absolute scale to 5.0 keV. This analysis confirms that with careful choice of foil thickness and careful correction for systematics, especially including harmonic contents at lower energies, the X-ray attenuation of high-Z elements can be measured with high accuracy even at low X-ray energies (<6 keV). This is the first high-accuracy measurement of X-ray mass attenuation coefficients of silver in the low energy range, indicating the possibility of obtaining high-accuracy X-ray absorption fine structure down to the L1 edge (3.8 keV) of silver. Comparison of results reported here with an earlier data set optimized for higher energies confirms accuracy to within one standard error of each data set collected and analysed using the principles of the X-ray extended-range technique (XERT). Comparison with theory shows a slow divergence towards lower energies in this region away from absorption edges. The methodology developed can be used for the XAFS analysis of compounds and solutions to investigate structural features, bonding and coordination chemistry.

A step toward standardization: development of accurate measurements of X-ray absorption and fluorescence.

This paper explains how to take the counting precision available for XAFS (X-ray absorption fine structure) and attenuation measurements, of perhaps one part in 10(6) in special cases, to produce a local variance below 0.01% and an accuracy of attenuation of the order 0.01%, with an XAFS accuracy at a similar level leading to the determination of dynamical bond lengths to an accuracy similar to that obtained by standard and experienced crystallographic measurements. This includes the necessary corrections for the detector response to be linear, including a correction for dark current and air-path energy dependencies; a proper interpretation of the range of sample thicknesses for absorption experiments; developments of methods to measure and correct for harmonic contamination, especially at lower energies without mirrors; the significance of correcting for the actual bandwidth of the beam on target after monochromation, especially for the portability of results and edge structure from one beamline to another; definitions of precision, accuracy and XAFS accuracy suitable for theoretical model analysis; the role of additional and alternative high-accuracy procedures; and discusses some principles regarding data formats for XAFS and for the deposition of data sets with manuscripts or to a database. Increasingly, the insight of X-ray absorption and the standard of accuracy needed requires data with high intrinsic precision and therefore with allowance for a range of small but significant systematic effects. This is always crucial for absolute measurements of absorption, and is of equal importance but traditionally difficult for (usually relative) measurements of fluorescence XAFS or even absorption XAFS. Robust error analysis is crucial so that the significance of conclusions can be tested within the uncertainties of the measurements. Errors should not just include precision uncertainty but should attempt to include estimation of the most significant systematic error contributions to the results. This is essential if the results are to be subject to deposition in a central accessible reference database; it is also crucial for specifying a standard data format for portability and ease of use by depositors and users. In particular this will allow development of theoretical formulations to better serve the world-wide XAFS community, and a higher and more easily comparable standard of manuscripts.

Quantitative phase imaging with polychromatic x-ray sources.

We introduce theoretically and demonstrate experimentally a contrast transfer function based phase retrieval algorithm that reconstructs the projected thickness of an homogeneous sample using a polychromatic x-ray source. We show excellent quantitative recovery of test samples in 2D using a synchrotron source with significant harmonic contamination, and in 3D using a laboratory source.

Multi-wavelength elemental contrast absorption imaging.

We report experimental demonstrations of a quantitative technique for elemental mapping. The technique operates in full-field imaging mode and uses three intensity measurements at energies across an absorption edge of an element of interest to obtain its elemental distribution. The experimental results show that the technique can overcome some limitations in the conventional Absorption Edge Contrast Imaging. The technique allows for an accurate determination of the elemental distribution in a compound sample even at a low level of percentage composition. It is also robust to the choice of energy intervals.

Extracting coherent modes from partially coherent wavefields.

A method for numerically recovering the coherent modes and their occupancies from a known mutual optical intensity function is described. As an example, the technique is applied to previously published experimental data from an x-ray undulator source. The data are found to be described by three coherent modes, and the functional forms and relative occupancies of these modes are recovered.

Phase-space reconstruction of focused x-ray fields.

We apply the method of phase-space tomography to reconstruct x-ray beams focused using a compound refractive lens. We show that it is possible to decouple the effect of aberrations in the optical system from the field and hence measure both them and the original field. We recover the complex coherence function and find that it is consistent with expectations.

X-ray imaging: a generalized approach using phase-space tomography.

We discuss the role of coherence in x-ray imaging and consider how phase-space tomography can be used to extract information about partial coherence. We describe the application of phase-space tomography to x-ray imaging and recover the spatial coherence properties of a one-dimensional soft (1.5 keV) x-ray beam from a synchrotron undulator source. We present phase-space information from a Young's experiment and observe negative regions in the quasi-probability distribution. We show that, given knowledge of the coherence of the beam, we can use partially coherent diffraction data to recover fully coherent information, and we present some simple experimental demonstrations of this capability.

Observation of an x-ray vortex.

Phase singularities are a ubiquitous feature of waves of all forms and represent a fundamental aspect of wave topology. An optical vortex phase singularity occurs when there is a spiral phase ramp about a point phase singularity. We report an experimental observation of an optical vortex in a field consisting of 9-keV x-ray photons. The vortex is created with an x-ray optical structure that imparts a spiral phase distribution to the incident wave field and is observed by use of diffraction about a wire to create a division-of-wave-front interferometer.