The NIST silicon lattice comparator upgrade.

The NIST silicon lattice comparator has been in service, in various forms, since the 1970s. It is capable of measuring the difference in lattice spacing between specimens of high-quality float-zone silicon to Δd/d ≈ 6 × 10-9. It has recently undergone a thorough update of its control systems and mechanics. These upgrades result in the ability to collect data with improved stability, less settling time of the instrument, and less operator intervention.

Pendellösung interferometry probes the neutron charge radius, lattice dynamics, and fifth forces.

Structure factors describe how incident radiation is scattered from materials such as silicon and germanium and characterize the physical interaction between the material and scattered particles. We used neutron Pendellösung interferometry to make precision measurements of the (220) and (400) neutron-silicon structure factors and achieved a factor-of-four improvement in the (111) structure factor uncertainty. These data provide measurements of the silicon Debye-Waller factor at room temperature and the mean square neutron charge radius rn2=−0.1101±0.0089 square femtometers. Combined with existing measurements of the Debye-Waller factor and charge radius, the measured structure factors also improve constraints on the strength of a Yukawa modification to gravity by an order of magnitude over the 20 picometer­to­10 nanometer length scale range.

The NIST Vacuum Double-Crystal Spectrometer: A Tool for SI-Traceable Measurement of X-Ray Emission Spectra.

The NIST Vacuum Double-Crystal Spectrometer (VDCS) has been modernized and is now capable of recording reference-free wavelength-dispersive spectra in the 2 keV to 12 keV x-ray energy range. The VDCS employs crystals in which the lattice spacings are traceable to the definition of the meter through x-ray optical interferometry with a relative uncertainty ﹤10-8. VDCS wavelength determination relies upon precision angle difference measurements for which the encoders of the rotation stages have been calibrated using the circle closure method for accurate, absolute angle measurement. The new vacuum-compatible area detector allows quantification of the aberration functions contributing to the observed line shape and in situ alignment of the crystal optics. This latter procedure is augmented with the use of a thin lamella as the first crystal. With these new techniques, x-ray spectra are registered with the VDCS on an absolute energy scale with a relative uncertainty of 10-6.

Certification of Standard Reference Material 660c for powder diffraction.

The National Institute of Standards and Technology (NIST) certifies a suite of Standard Reference Materials (SRMs) to evaluate specific aspects of instrument performance of both X-ray and neutron powder diffractometers. This report describes SRM 660c, the fourth generation of this powder diffraction SRM, which is used primarily for calibrating powder diffractometers with respect to line position and line shape for the determination of the instrument profile function (IPF). It is certified with respect to lattice parameter and consists of approximately 6 g of lanthanum hexaboride (LaB6) powder. So that this SRM would be applicable for the neutron diffraction community, the powder was prepared from an isotopically enriched 11B precursor material. The microstructure of the LaB6 powder was engineered specifically to yield a crystallite size above that where size broadening is typically observed and to minimize the crystallographic defects that lead to strain broadening. A NIST-built diffractometer, incorporating many advanced design features, was used to certify the lattice parameter of the LaB6 powder. Both Type A, statistical, and Type B, systematic, uncertainties have been assigned to yield a certified value for the lattice parameter at 22.5 °C of a = 0.415 682 6 ± 0.000 008 nm (95% confidence).

Certification of SRM 640f line position and line shape standard for powder diffraction.

The National Institute of Standards and Technology (NIST) certifies a suite of Standard Reference Materials (SRMs) to be used to evaluate specific aspects of the instrument performance of both X-ray and neutron powder diffractometers. This report describes SRM 640f, the seventh generation of this powder diffraction SRM, which is designed to be used primarily for calibrating powder diffractometers with respect to line position; it also can be used for the determination of the instrument profile function. It is certified with respect to the lattice parameter and consists of approximately 7.5 g of silicon powder prepared to minimize line broadening. A NIST-built diffractometer, incorporating many advanced design features, was used to certify the lattice parameter of the Si powder. Both statistical and systematic uncertainties have been assigned to yield a certified value for the lattice parameter at 22.5 °C of a = 0.5431144 ± 0.000008 nm.

High x-ray resolving power utilizing asymmetric diffraction from a quartz transmission crystal measured in the 6 keV to 22 keV energy range.

A Cauchois-type spectrometer utilizing the (203) lattice planes at an oblique angle of 11.53° to the normal to the surface of a quartz transmission crystal recorded the Kα and Kß spectral lines of six elements from Fe to Ag in the 6-22 keV energy range from a laboratory x-ray source. After deconvolving the natural lifetime widths and the image plate detector broadening from the observed spectral linewidths, the intrinsic crystal resolving power was determined to be 4000 at the lower energies and decreasing to 1000 at the higher energies. Previously, a Si wafer crystal exhibited twice this resolving power when the (331) planes had been used in asymmetric geometry. The investigation of diffraction with this quartz crystal, with a very similar lattice spacing and therefore spectral coverage, was motivated by the larger integrated reflectivity of quartz due to its well-known quasimosaicity upon elastic bending. The measured spectral linewidths were in good agreement with the widths calculated by accounting for various broadening mechanisms, including source size, crystal thickness, crystal height, crystal rocking curve width, geometrical aberrations, and possible spectrometer configuration errors. This is the first, to the best of our knowledge, demonstration of high resolving power achieved by asymmetric diffraction over a wide energy range (6-22 keV) and with detailed comparisons with theoretical broadenings. Based on these results, Cauchois spectrometers employing asymmetric planes of perfect quartz and silicon crystals can be reliably designed and optimized for high-resolution spectroscopy in the >6 keV energy range.

The Molybdenum K-shell X-ray Emission Spectrum.

We present newly measured spectra of the X-ray emission of a molybdenum metal anode subject to electron bombardment, using a very high dispersion silicon double-crystal spectrometer. The measurement includes the dipole-allowed KL, KM, and KN emission lines, based on an energy scale traceable to the Système International (SI) definition of the meter with a systematic uncertainty below ΔE/E = 10-6. The data are presented as parametrized multi-Lorentzian fits to the results, and as supplementary data with the complete spectrum of each line group, corrected for instrumental effects. The MoKL 3 (Kα 1) line energy was in complete statistical agreement with published measurements, and it showed no asymmetry. Other lines showed varying discrepancies with the literature which lie outside the bounds of probable experimental errors.

Certification of Standard Reference Material 1879b Respirable Cristobalite.

The National Institute of Standards and Technology (NIST) certifies a suite of Standard Reference Materials (SRMs) to address specific aspects of the performance of X-ray powder diffraction instruments. This report describes SRM 1879b, the third generation of this powder diffraction SRM. SRM 1879b is intended for use in the preparation of calibration standards for the quantitative analyses of cristobalite by X-ray powder diffraction in accordance with National Institute for Occupational Safety and Health (NIOSH) Analytical Method 7500, or equivalent. A unit of SRM 1879b consists of approximately 5 g of cristobalite powder bottled in an argon atmosphere. It is certified with respect to crystalline phase purity, or amorphous phase content, and lattice parameter. Neutron powder diffraction, both time-of-flight and constant-wavelength, was used to certify the phase purity using SRM 676a as an internal standard. A NIST-built diffractometer, incorporating many advanced design features was used for certification measurements for lattice parameters.

X-ray spectrometer having 12 000 resolving power at 8 keV energy.

An x-ray spectrometer employing a thin (50 µm) silicon transmission crystal was used to record high-resolution Cu Kα spectra from a laboratory x-ray source. The diffraction was from the (331) planes that were at an angle of 13.26° to the crystal surface. The components of the spectral lines resulting from single-vacancy (1s) and double-vacancy (1s and 3d) transitions were observed. After accounting for the natural lifetime widths from reference double-crystal spectra and the spatial resolution of the image plate detector, the intrinsic broadening of the transmission crystal was measured to be as small as 0.67 eV and the resolving power 12 000, the highest resolving power achieved by a compact (0.5 m long) spectrometer employing a single transmission crystal operating in the hard x-ray region. By recording spectra with variable source-to-crystal distances and comparing to the calculated widths from various geometrical broadening mechanisms, the primary contributions to the intrinsic crystal broadening were found to be the source height at small distances and the crystal apertured height at large distances. By reducing these two effects, using a smaller source size and vignetting the crystal height, the intrinsic crystal broadening is then limited by the crystal thickness and the rocking curve width and would be 0.4 eV at 8 keV energy (20 000 resolving power).

High-precision measurement of the X-ray Cu Kα spectrum.

The structure of the X-ray emission lines of the Cu Kα complex has been remeasured on a newly commissioned instrument, in a manner directly traceable to the Système Internationale definition of the meter. In this measurement, the region from 8000 eV to 8100 eV has been covered with a highly precise angular scale, and well-defined system efficiency, providing accurate wavelengths and relative intensities. This measurement updates the standard multi-Lorentzian-fit parameters from Härtwig, Hölzer, et al., and is in modest disagreement with their results for the wavelength of the Kα1 line when compared via quadratic fitting of the peak top; the intensity ratio of Kα1 to Kα2 agrees within the combined error bounds. However, the position of the fitted top of Kα1 is very sensitive to the fit parameters, so it is not believed to be a robust value to quote without further qualification. We also provide accurate intensity and wavelength information for the so-called Kα3,4 "satellite" complex. Supplementary data is provided which gives the entire shape of the spectrum in this region, allowing it to be used directly in cases where simplified, multi-Lorentzian fits to it are not sufficiently accurate.

The Lattice Spacing Variability of Intrinsic Float-Zone Silicon.

Precision lattice spacing comparison measurements at the National Institute of Standards and Technology (NIST) provide traceability of X-ray wavelength and powder diffraction standards to the international system of units (SI). Here, we both summarize and document key measurements from the last two decades on six lots of intrinsic float-zone silicon, including unpublished results and recent internal-consistency checks. The comparison measurements link the unknown lattice spacing of a test crystal to a standard crystal for which the lattice spacing has been accurately determined by X-ray/optical interferometry in units traceable to the definition of the meter. The crystal that serves as the standard in all the comparisons is WASO 04, for which the lattice spacing is known with a relative uncertainty of 5 × 10-9. Individual lattice spacing comparison results have typical uncertainties of 1 ×10-8; taking material variability into account, measurements yield relative uncertainties for the test materials of a few tens of nanometers. It is observed that in the case of nearly perfect modern intrinsic float-zone silicon, the variability of the lattice spacing is sufficiently small that for most diffraction applications, a recommended reference value may be used.

High resolution spectrometer for extended x-ray absorption fine structure measurements in the 6 keV to 15 keV energy range.

A Cauchois transmission-crystal spectrometer has been developed with high crystal resolving power in the 6 keV-15 keV energy range and sufficient sensitivity to record single-shot spectra from the Lawrence Livermore National Laboratory (LLNL) Titan laser and other comparable or more energetic lasers. The spectrometer capabilities were tested by recording the W L transitions from a laboratory source and the extended x-ray absorption fine structure (EXAFS) spectrum through a Cu foil.

Tunable hard X-ray spectrometer utilizing asymmetric planes of a quartz transmission crystal.

A Cauchois type hard x-ray spectrometer was developed that utilizes the (301) diffraction planes at an asymmetric angle of 23.51° to the normal to the surface of a cylindrically curved quartz transmission crystal. The energy coverage is tunable by rotating the crystal and the detector arm, and spectra were recorded in the 8 keV to 20 keV range with greater than 2000 resolving power. The high resolution results from low aberrations enabled by the nearly perpendicular angle of the diffracted rays with the back surface of the crystal. By using other asymmetric planes of the same crystal and rotating to selected angles, the spectrometer can operate with high resolution up to 50 keV.

Characterization of a self-calibrating, high-precision, stacked-stage, vertical dual-axis goniometer.

We present details on the alignment and calibration of a goniometer assembly consisting two stacked, optically encoded, vertical axis rotation stages. A technique for its calibration is presented that utilizes a stable, uncalibrated, third stage to position a mirror in conjunction with a nulling autocollimator. Such a system provides a self-calibrating set of angular stages with absolute accuracy of ±0.1 second of plane angle (k=2 expanded uncertainty) around the full circle, suitable for laboratory application. This calibration technique permits in situ, absolute angular calibration of an operational goniometer assembly that is requisite for fully traceable angle measurement, as the installation of the encoder is known to change its performance from the angular calibration data provided by the manufacturer.

The Optics and Alignment of the Divergent Beam Laboratory X-ray Powder Diffractometer and its Calibration Using NIST Standard Reference Materials.

The laboratory X-ray powder diffractometer is one of the primary analytical tools in materials science. It is applicable to nearly any crystalline material, and with advanced data analysis methods, it can provide a wealth of information concerning sample character. Data from these machines, however, are beset by a complex aberration function that can be addressed through calibration with the use of NIST Standard Reference Materials (SRMs). Laboratory diffractometers can be set up in a range of optical geometries; considered herein are those of Bragg-Brentano divergent beam configuration using both incident and diffracted beam monochromators. We review the origin of the various aberrations affecting instruments of this geometry and the methods developed at NIST to align these machines in a first principles context. Data analysis methods are considered as being in two distinct categories: those that use empirical methods to parameterize the nature of the data for subsequent analysis, and those that use model functions to link the observation directly to a specific aspect of the experiment. We consider a multifaceted approach to instrument calibration using both the empirical and model based data analysis methods. The particular benefits of the fundamental parameters approach are reviewed.

Ultra-thin curved transmission crystals for high resolving power (up to E/ΔE = 6300) x-ray spectroscopy in the 6-13 keV energy range.

Ultra-thin curved transmission crystals operating in the Cauchois spectrometer geometry were evaluated for the purpose of achieving high spectral resolution in the 6-13 keV x-ray energy range. The crystals were silicon (111) and sapphire R-cut wafers, each 18 µm thick, and a silicon (100) wafer of 50-µm thickness. The W Lα(1) spectral line at 8.398 keV from a laboratory source was used to evaluate the resolution. The highest crystal resolving power, E/ΔE=6300, was achieved by diffraction from the (33-1) planes of the Si(100) wafer that was cylindrically bent to a radius of curvature of 254 mm, where the (33-1) planes have an asymmetric angle of 13.26° from the normal of the crystal surface facing the x-ray source. This work demonstrates the ability to measure highly resolved line shapes of the K transitions of the elements Fe through Kr and the L transitions of the elements Gd through Th using a relatively compact spectrometer optical system and readily available thin commercial wafers. The intended application is as a diagnostic of laser-produced plasmas where the presence of multiple charged states and broadenings from high temperature and density requires high-resolution methods that are robust in a noisy source environment.

Measurement of high-energy (10-60 keV) x-ray spectral line widths with eV accuracy.

A high resolution crystal spectrometer utilizing a crystal in transmission geometry has been developed and experimentally optimized to measure the widths of emission lines in the 10-60 keV energy range with eV accuracy. The spectrometer achieves high spectral resolution by utilizing crystal planes with small lattice spacings (down to 2d = 0.099 nm), a large crystal bending radius and Rowland circle diameter (965 mm), and an image plate detector with high spatial resolution (60 µm in the case of the Fuji TR image plate). High resolution W L-shell and K-shell laboratory test spectra in the 10-60 keV range and Ho K-shell spectra near 47 keV recorded at the LLNL Titan laser facility are presented. The Ho K-shell spectra are the highest resolution hard x-ray spectra recorded from a solid target irradiated by a high-intensity laser.

Enhanced x-ray resolving power achieved behind the focal circles of Cauchois spectrometers.

Maintaining high resolving power is a primary challenge in hard x-ray spectroscopy of newly developed bright and transient x-ray sources such as laser-produced plasmas. To address this challenge, the line widths in x-ray spectra with energies in the 17 keV to 70 keV range were recorded by positioning the detectors on and behind the focal circles of Cauchois type transmission-crystal spectrometers. To analyze and understand the observed line widths, we developed a geometrical model that accounts for source broadening and various instrumental broadening mechanisms. The x-ray sources were laboratory Mo or W electron-bombarded anodes, and the spectra were recorded on photostimulable phosphor image plates. For these relatively small x-ray sources, it was found that when the detector was placed on or near the focal circle, the line widths were dominated by the effective spatial resolution of the detector. When the detector was positioned beyond the focal circle, the line widths were determined primarily by source-size broadening. Moreover, the separation between the spectral lines increased with distance behind the focal circle faster than the line widths, resulting in increased resolving power with distance. Contributions to line broadenings caused by the crystal thickness, crystal rocking curve width, geometrical aberrations, and natural widths of the x-ray transitions were in all cases smaller than detector and source broadening, but were significant for some spectrometer geometries. The various contributions to the line widths, calculated using simple analytical expressions, were in good agreement with the measured line widths for a variety of spectrometer and source conditions. These modeling and experimental results enable the design of hard x-ray spectrometers that are optimized for high resolving power and for the measurement of the x-ray source size from the line widths recorded behind the focal circle.

X-ray modulation transfer functions of photostimulable phosphor image plates and scanners.

The modulation transfer functions of two types of photostimulable phosphor image plates were determined in the 10 keV to 50 keV x-ray energy range using a resolution test pattern with up to 10 line pairs per mm (LP/mm) and a wavelength dispersive x-ray spectrometer. Techniques were developed for correcting for the partial transmittance of the high energy x rays through the lead bars of the resolution test pattern, and the modulation transfer function (MTF) was determined from the measured change in contrast with LP/mm values. The MTF was convolved with the slit function of the image plate scanner, and the resulting point spread functions (PSFs) were in good agreement with the observed shapes and widths of x-ray spectral lines and with the PSF derived from edge spread functions. The shapes and the full width at half-maximum (FWHM) values of the PSF curves of the Fuji Superior Resolution (SR) and Fuji Maximum Sensitivity (MS) image plate detectors, consisting of the image plate and the scanner, determined by the three methods gave consistent results: The SR PSF is Gaussian with 0.13 mm FWHM, and the MS PSF is Lorentzian with 0.19 mm FWHM. These techniques result in the accurate determination of the spatial resolution achievable using image plate and scanner combinations and enable the optimization of spatial resolution for x-ray spectroscopy and radiography.