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.

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).

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 1878b, the third generation of this powder diffraction SRM. SRM 1878b is intended for use in the preparation of calibration standards for the quantitative analyses of α-quartz by X-ray powder diffraction in accordance to National Institute for Occupational Safety and Health Analytical Method 7500, or equivalent. A unit of SRM 1878b consists of approximately 5 g of α-quartz 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.

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 1976b, the third generation of this powder diffraction SRM. SRM 1976b consists of a sintered alumina disc, approximately 25.6 mm in diameter by 2.2 mm in thickness, intended for use in the calibration of X-ray powder diffraction equipment with respect to line position and intensity as a function of 2θ-angle. The sintered form of the SRM eliminates the effect of sample loading procedures on intensity measurements. Certified data include the lattice parameters and relative peak intensity values from 13 lines in the 2θ region between 20° and 145° using CuKα radiation. A NIST-built diffractometer, incorporating many advanced and unique design features was used to make the certification measurements.

This report describes SRM 660b, the third generation of this powder diffraction SRM used primarily for determination of the instrument profile function (IPF). It is certified with respect to unit-cell parameter. It consists of approximately 6 g LaB6 powder prepared using a 11B isotopically enriched precursor material so as to render the SRM applicable to the neutron diffraction community. The microstructure of the LaB6 powder was engineered to produce 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 unit-cell parameter of the LaB6 powder. Both type A, statistical, and type B, systematic, errors have been assigned to yield a certified value for the unit-cell parameter of a=0.415691(8) nm at 22.5°C.

The National Institute of Standards and Technology (NIST) certifies a variety of standard reference materials (SRM) to address specific aspects of instrument performance for divergent beam diffractometers. This paper describes SRM 640d, the fifth generation of this powder diffraction SRM, which is certified with respect to the lattice parameter. It consists of approximately 7.5 g silicon powder specially prepared to produce strain-free particles in a size range between 1 and 10 μm to eliminate size-broadening effects. It is typically used for calibrating powder diffractometers for the line position and line shape. A NIST built diffractometer, incorporating many advanced design features, was used to certify the lattice parameter of the silicon powder measured at 22.5 °C. Both type A, statistical, and type B, systematic, errors have been assigned to yield a certified value for the lattice parameter of a=0.543 159±0.000 020 nm.

The peak angle 2θp is one of the most commonly measured parameters in powder diffractometry, but there is little understanding of the extent to which the instrument affects this measurement. The majority of theoretical and experimental studies of the effects of instrumental aberrations have been based on the peak centroid 29c. In this investigation we have examined the extent to which peak angles in a conventional powder diffractometer shift for different combinations of divergence slit, Soller slits and receiving slit. The line profile standard SRM 660 (LaB6) was used to generate instrument profiles and X-ray data were collected from a diffractometer fitted with a fine focus Cu X-ray tube and a graphite post-monochromator set for CuKa. The effect of the instrument is greatest at low angles, but shifts arising from axial divergence can also be detected above 2θ=120°. Below 2θ = 40° changing the divergence slits from 0.3° to 1.0°, or removing one of the Soller slits, can move 2θp by up to 0.025°.

The accuracy of Quantitative Rietveid Analysis (QRA) was examined in terms of the plausibility of the set of refined parameters as well as the realization of the expected quantitative result. This route was pursued due to the two mutually exclusive characteristics that a powder exhibiting the calculated (ideal) diffraction intensity would possess; it would have infinitesimal domains to alleviate the effects of extinction but at the same time infinitesimal surface area to eliminate the volume of the disordered surface or amorphous phase. The specimens were mixtures of NIST Standard Reference Material (SRM) 640b, a silicon powder with a mean particle size of 7 pin (certified with respect to lattice parameters), and SRM 676, an alumina powder with a submicrometer crystallite size (certified for quantitative analysis). Good agreement between the particle size of SRM 640b, determined by laser scattering measurements, and its domain size, determined by using the Sabine model for extinction, were obtained with the use of improved background functions in refinements of neutron time-of-flight (TOF) powder diffraction data. These data, in conjunction with the plausibility of other refined parameters such as temperature factors, led to a credible measurement of the amorphous content of SRM 676 and a verification that TOF data can yield unbiased quantitative results. A new SRM for quantitative analysis of silicon nitride was certified with respect to the a, p and amorphous (impurity) phase content with the use of TOF diffraction and SRM 676 as the reference phase. Results from XRD data were found to be less sensitive to background function, though improvements in the Rietveid analysis of XRD data were achieved.

This paper reviews several procedures for the removal of instrumental contributions from measured x-ray diffraction profiles, including: direct convolution, unconstrained and constrained deconvolution, an iterative technique, and a maximum entropy method (MEM) which we have adapted to x-ray diffraction profile analysis. Decorevolutions using the maximum entropy approach were found to be the most robust with simulated profiles which included Poisson-distributed noise and uncertainties in the instrument profile function (IPF). The MEM procedure is illustrated by application to the analysis for domain size and microstrain carried out on the four calcined α-alumina candidate materials for Standard Reference Material (SRM) 676 (a quantitative analysis standard for I/Ic determinations), along with the certified material. Williamson-Hall plots of these data were problematic with respect to interpretation of the microstrain, indicating that the line profile standard, SRM 660 (LaB6), exhibits a small amount of strain broadening, particularly at high 2θ angle. The domain sizes for all but one of the test materials were much smaller than the crystallite (particle) size; indicating the presence of low angle grain boundaries.

The Rietveld method entails the calculation of a powder diffraction pattern from crystallographic, microstructural and equipment characteristics. These characteristics are related to the form of the pattern through a series of model functions. The difference between an observed and calculated pattern is then minimized by sequentially refining the physical parameters contained within the mode) functions to obtain an accurate and precise description of the specimen. A powder diffraction pattern from a specimen exhibiting cry stallo graphic texture, or preferred orientation, will display intensity values which differ systematically from those calculated for a specimen of random orientation. This systematic discrepancy can be addressed by incorporating into the Rietveld refinement a model function for sample texture. A successful model for texture will accurately assess the phase abundance and degree of texture from both oriented and randomized specimens. In this study we use the March-Dollase model function to characterize texture development in sintered alumina with respect to processing variables and sintering time.

A project was undertaken to compare the Williamson-Hall and Fourier teclrniques for analyzing particle-size and micro-strain induced x-ray line profile broadening. The four alumina powders analyzed in the study were the candidates from which SRM 676, a quantitative analysis Standard Reference Material, was chosen. SRM 660 (LaB6) was used to determine the instrument profile function, IPF. However, difficulty was encountered in fitting an appropriate mathematical model to the IPF data; this prevented the application of Fourier analysis methods and restricted the number of profiles that could be analyzed with the Williamson-Hall method. The size/stain data compared favorably with other microstructural data collected on these specimens.

Improvements in sample preparation methods have resulted in increased accuracy in x-ray powder diffraction intensity measurements. This improvement has focused scrutiny on the instrument as a potential source of error. NIST Standard Reference Material, SRM, 1976 consists of a sintered α alumina, corundum, plate certified with respect to 12 relative intensity values from 25 to 145 degrees 2θ. Its function is to allow for standardization of powder diffraction intensity as a function of 2θ angle (instrument sensitivity). An increase in the accuracy of interlaboratory comparisons of diffraction intensity and related determinations will result. Utilization of the SRM requires the user to collect intensity data from the test instrument in a manner which conforms to that used in the certification. Graphical interpretation of the ratio of these data to those on the certificate will allow for appropriate judgment as to the condition of the test instrument. Discontinuities in the data indicate a malfunctioning or misaligned instrument. Systematic bias, introduced by design characteristics of the test instrument, manifests itself in terms of a pattern in the data other than a horizontal straight line with value of one. This bias may be removed with the calculation and application of a correction curve.

Preferred orientation has long been considered the primary source of systematic error involved in quantitative analysis by X-ray powder diffraction. Techniques of spherical agglomeration have been shown to eliminate preferred orientation provided that the agglomerate size is made sufficiently larger than the particle size. These techniques invariably employ the surface energy minimization of a liquid phase dispersed within a second fluid to create the spherical form desired. Spray drying has been the only method to date which has been successfully used to prepare spherical agglomerates suitable for X-ray diffraction. This study was undertaken to investigate possible deleterious effects of spray drying as a diffraction sample preparation technique.