Polarized x-radiation produced by scatter at 90° from boron carbide is shown to be a superior excitation source for the measurement of trace elements by energy dispersive x-ray fluorescence. In a close-coupled system which uses a high power x-ray tube as the primary source, the losses due to the geometric requirements and scattering efficiency of the polarizer can be more than compensated. With the system described here which uses a Mo anode x-ray tube, detection limits for the element between K and Sr in NBS orchard leaves are approximately 2 to 4.5 times lower using polarized excitation in comparison to direct excitation, and about <1 to 3 times lower in comparison to secondary excitation.

Lead stearate and lead lignocerate multilayer soap-film structures are used to disperse the K emission lines of boron and beryllium respectively. Data are presented showing the dependence of the peak height and half-width on the number of layers in the lignocerate structure. Spectra are presented and compared for the pure element and several compounds of each element. Both electron and X-ray excitation are used. Detection is by a thin-window flow-proportional counter.

From pole figure data, the orientation of a crystallographic direction R in any reference direction Q in a sample can be quantitatively expressed by the average <cos2σ>, where σ is the angle between Q and R in a crystal. In general, <cos2σ> can be evaluated in terms of the experimental averages <cos2ϕhkl> whereϕhkl is the angle between Q and the normal to the (hkl) planes. The number of independent <cos2ϕhkl> measurements needed varies from one to five depending on the crystal system, hkl indices, and other factors discussed. Experimental techniques found useful for measuring <cos2φ> are described.

A previous paper portrayed sample preparation by fusion methodology and the XRF analysis conditions for the calibration of cement materials [Bouchard et al., 2009. “Global cement and raw materials fusion/XRF analytical solution,” Adv. X-Ray Anal. 53, 263–279]. The results of two well known cement chemical analysis Standard Methods were also presented. These results proved that this robust analytical method is able to qualify by the ASTM C114 [ASTM C114-08 (2008). “Standard test methods for chemical analysis of hydraulic cement,” Annual Book of ASTM Standards Vol. 04.01 (ASTM International, West Conshohocken, PA), pp. 150–157)] and ISO/DIS 29581-2 [Draft Standard, 2007-07 (2007). “Methods of testing cement—Chemical analysis of cement—Part 2: Analysis by X-ray fluorescence” ISO/DIS 29581-2, 2007, pp. 1–30]. This robust analytical method was developed using an automated fusion instrument for the sample preparation and a WDXRF spectrometer for the determination of all elements of interest relating to the cement industry. This method was used to prepare finished products, process materials, as well as a very large range of raw materials. The first part of this second paper examines all the XRF analysis conditions for the calibration of the raw materials using the robust fusion sample preparation methodology as well as the numerous reference materials (RMs) used for this analytical application. All interesting results will be presented. The second part of this paper reveals the rapid analytical method results using sample preparation by fusion on nonignited samples. It will also be proven that this faster method, combined with the WDXRF spectrometer, complies with both cement analysis Standard Methods: ASTM C114 and ISO/DIS 29581-2.

In this work, the reduction mechanism of potassium chromate (K2CrO4) was investigated via in situ high-temperature X-ray diffraction coupled with Fourier transform infrared spectroscopy. During the hydrogen reduction of K2CrO4, the formation of K3CrO4, KCrO2, and KxCrO2 were detected for the first time. The study discovered that K2CrO4 was firstly reduced to K3CrO4 and an amorphous Cr(III) intermediate product at low temperature (400–500 °C). Moreover, the K3CrO4 was the only crystalline material at this stage. As the temperature increased, a stabilized amorphous CrOOH was formed. At a high temperature (550–700 °C), KCrO2 was generated. Interestingly, a portion of KCrO2 was spontaneously decomposed during the hydrogen reduction, accompanying by the formation of K0.7CrO2. Finally, the results clearly illustrated the reduction mechanism of K2CrO4: K2CrO4 → K3CrO4 → amorphous intermediate → KCrO2.

The microstructure evolution in pure copper deformed by rolling at liquid nitrogen temperature was determined by using X-ray diffraction peak profile analysis. The crystallite size distribution and defects evolution were determined as a function of different reduction levels (e.g., 67%, 74%, 87%, and 97%). By using the Multiple Whole-Profile fitting procedure the Fourier transforms of the experimental X-ray peak profiles were fitted all at once by theoretical calculated functions. Here it is assumed that the crystallites are spherical shape and have a log-normal size distribution. It is also supposed that the strain broadening of the profiles is caused by 〈110〉 {111}-type dislocations. The results show that the median and the variance of the crystallite size distribution decreases as the deformation reduction increases. The dislocation density has a minimum value at 74% reduction. The increase of the dislocation density at higher deformation levels is due to the nucleation of new generation of dislocations from the crystallite grain boundaries. It was found that the edge dislocation type dominate, the dislocation network formed during the deformation process.

The powder diffraction pattern of the perovskite AgNbO3 has been measured using CuKα1 radiation with an incident beam focusing monochromator to eliminate the Kα2 component. Indexing the pattern shows that the multipartite cell is 2×2×4 times that of the pseudocubic subcell. Comparison is made with the diffraction pattern of NaNbO3, which has a similar multipartite unit cell. There are strong similarities, but close inspection shows that the structures are not isomorphous. The paper concludes with a discussion of the figure of merit FN for pseudosymmetric structures. It is suggested that two figures of merit be reported. The first should be the standard one using either all measured reflections or just the first 30. The proposed second figure of merit does not include any superlattice reflections. These superlattice reflections tend to be very weak, resulting in a low completeness factor and relatively large error in the measurement of their position. This effect produces an unrealistically low value of the standard figure of merit. By including only “main” reflections, i.e., those reflections that are common to both the low-symmetry and high-symmetry parent phase (if it exists), a much better estimate of the quality of the fitting of the measured diffraction pattern is obtained.

The determination of thin film thickness by four X-ray reflectivity methods (namely, the peak separation, the Fourier transform, the modified Bragg equation, and the curve-fitting methods) has been studied. An analysis of SrS and BaF2 thin films showed thickness values determined by the methods agreed to within 4%. The curve-fitting method had the highest accuracy but was time-consuming. The peak separation, the Fourier transform, and the modified Bragg equation methods are considerably faster and, on average, gave 2.8%, 0.9%, and 0.2% larger thicknesses than those of the curve-fitting method.

A new semi-empirical approximation for the asymmetry function to be used in the X-ray Rietveld analysis has resulted in lower values of the so-called goodness-of-fit index, defined as S = Rwp/Rexp, where Rwp is the R-weighted pattern and Rexp is the R-expected [R. A. Young, The Rietveld Method (Oxford U.P., Oxford, 1993)], with respect to the corresponding values obtained with the classical approximation used by Rietveld in his fundamental paper. A comparing test of the two asymmetry functions was carried out for the cubic Y2O3 and for αAl2O3 using either pseudo-Voigt or Pearson VII symmetrical functions and two diffractometers. As in the case of the Rietveld approximation, the present one, which employs an exponential function, is optimized using only one fitting parameter. Experimentally, the asymmetry can be considerably diminished by using Soller slits with a small opening angle (≤2°).

Ternary Al–Cu–Ir phases, isostructural to the Al–Cu–Rh ω and C2 phases, were found to be around the Al70Cu20Ir10 and Al60Cu15Ir25 compositions, respectively. Using powder X-ray diffraction, the former was found to have a tetragonal structure (space group P4/mnc) with a=6.4142(9) Å and c=14.842(4) Å, and the latter has a cubic structure (space group Fm3) with a=15.3928(6) Å.

The ICDD sponsored a round robin on the quantitative Rietveld phase analysis of pharmaceuticals. 11 participating laboratories from the pharmaceutical community submitted both raw data and processed quantitative results. The purpose of the round robin was to evaluate current practices in laboratories, so procedures and methods were not specified, but they were recorded. Cluster analysis tools were applied to all the data sets and their use helped identify the root causes of several types of errors in specimen preparation, data treatment, and Rietveld analysis. The authors considered this round robin to be difficult. Sample homogeneity was an issue and molecular orientation was observed in many data sets. Each material studied has structural polymorphs so the selection of starting parameters and their refinement was nontrivial. Similar to prior round robins on inorganic materials and minerals, this round robin identified operator errors as the major contributor to poor results. Four laboratories achieved excellent results on all phases in all three samples, with accuracy within relative errors of 5% to 10%.

Multivariate statistical analysis (MSA) is applied to the extraction of chemically relevant signals acquired with a micro-X-ray fluorescence (μ-XRF) mapping (full-spectral imaging) system. The separation of components into individual histograms enables separation of overlapping peaks, which is useful in qualitatively determining the presence of chemical species that have overlapping emission lines, and holds potential for quantitative analysis of constituent phases via these same histograms. The usefulness of MSA for μ-XRF analysis is demonstrated by application to a geological rock core obtained from a subsurface compressed air energy storage (CAES) site. Coupling of the μ-XRF results to those of quantitative powder X-ray diffraction analysis enables improved detection of trace phases present in the geological specimen. The MSA indicates that the spatial distribution of pyrite, a potentially reactive phase by oxidation, has low concentration and thus minimal impact on CAES operations.

In the last few decades, X-ray diffraction (XRD) systems have been paramount and irreplaceable in controlling bauxite exploration, as well as Bayer and reduction processes. XRD quantitative phase analysis in the aluminum industry witnessed a steady deployment of the Rietveld method, which at present progressively replaces existing methodologies in research and plant laboratories. Rietveld analysis not only helped to surpass traditional XRD calibration methods, it also opened the door for new applications previously not possible. The use of the Rietveld method to characterize selected materials unique to the aluminum industry, such as bauxite, red mud, and alumina is demonstrated and discussed. This paper also presents how synchrotron-based diffractograms obtained for bauxite and red mud samples allowed a much better understanding of mineralogical representation, and made it possible to leverage their Rietveld quantification. Despite clear advantages, the Rietveld method also has limitations that are revealed. For alumina phase quantification, a dedicated Rietveld analytical program was built with structure data for eight alumina mineralogical phases: alpha, beta (β-Al2O3 = Na2O•11Al2O3), delta, gamma (2), kappa, sigma, and theta. The paper gives unique examples of phase quantification in aluminas of various origins and phase composition.

For more than 80 years, the scientific community has extensively used International Centre for Diffraction Data's (ICDD®) Powder Diffraction File (PDF®) for material characterization, including powder X-ray diffraction analysis. Historically, PDF was made available for two major material types: one for inorganic analysis and the other for organic analysis. In the early years of the PDF, this two-material approach was implemented due to limited computer capabilities. With Release 2024, ICDD provides a comprehensive database consisting of the entire PDF in one database called PDF-5+, comprised of more than one million entries (1,061,898). The PDF-5+ with a relational database (RDB) construct houses extensive chemical, physical, bibliographic, and crystallographic data, including atomic coordinates and raw data, enabling qualitative and quantitative phase analysis. This wealth of information in one database is advantageous for phase identification, materials characterization, and several data mining applications in materials science. A database of this size needs rigorous data curation and structural and chemical classifications to optimize pattern search/match and characterization methods. Each entry in the PDF has an editorially assigned quality mark. An editorial comment will describe the reason if an entry does not meet the top-quality mark. The editorial processes of ICDD's quality management system are unique in that they are ISO 9001:2015 certified. Among several classifications implemented in PDF-5+, subfiles (such as Bioactive, Pharmaceuticals, Minerals, etc.) directly impact the search/match in minimizing false positives. Scientists with specific field expertise continuously review these subfiles to maintain their quality. This paper describes the features of PDF with an emphasis on the newly released PDF-5+.

Residual stress measurements on strongly textured materials using the standard sin2ψ evaluation show significant non-linearities. According to EN 15305 there is currently no existing solution for this problem. A method is presented that solves this problem. It is based on two tools. (i) The use of a one-dimensional detector having a large capture angle that yields the full diffraction profiles at each point of the pole figures. Therefore, some hundreds of d-values can be used for the stress calculation. (ii) Data evaluation with the recently developed generalized sin2ψ method. This has the advantage of being based on a flawless theory (Hooke's law in the special form of Dölle–Hauk's equation) and being able to handle any distribution of measurement directions and any number of measured data. The method was successfully tried out at a sheet of brass with significant texture.

Several hitherto unknown hydrates of magnesium selenate have been formed by quenching aqueous solutions of MgSeO4 in liquid nitrogen. MgSeO4·11H2O is apparently isostructural with the mineral meridianiite (MgSO4·11H2O), being triclinic, $P{\rm \bar 1}$, Z = 2, with unit-cell parameters a = 6.779 00(8) Å, b = 6.965 16(9) Å, c = 17.4934(2) Å, α = 87.713(1)°, β = 89.222(1)°, γ = 63.121(1)°, and V = 736.15(1) Å3 at −25 °C. MgSeO4·9H2O represents a new hydration state in the MgSeO4–H2O system; it is monoclinic, space-group P21/c, Z = 4, with unit-cell parameters a = 7.270 24(6) Å, b = 10.510 94(9) Å, c = 17.4030(2) Å, β = 109.447(1)°, and V = 1254.02(1) Å3 at −22 °C. The heavy-atom structure of MgSeO4·9H2O has been determined by direct-space methods from X-ray powder diffraction data and consists of isolated Mg(H2O)62+ octahedra and SeO42− tetrahedra linked by hydrogen bonds. The remaining three water molecules occupy the space between the polyhedral ions, contributing to the H-bonded network, which comprises 4-, 5-, and 6-membered rings. A third phase has been observed to crystallise prior to the 11-hydrate upon warming of liquid-nitrogen-quenched glass, but this transforms rapidly to the meridianiite-structured 11-hydrate and the identity of this phase is unclear.

The structure of the metal–organic framework (MOF) compound [{Ca(H2O)6}{CaGd(oxydiacetate)3}2]·4H2O was determined by single-crystal X-ray diffraction and refined using conventional single-crystal X-ray diffraction data. In addition, the structure was refined using powder diffraction data collected from two sources, a conventional X-ray diffractometer in Bragg–Brentano geometry and a 12-detector high resolution synchrotron-based diffractometer in transmission geometry. Data from the latter were processed in three different ways to account for crystalline decay or radiation damage. One dataset was obtained by averaging the multiple detector patterns, another dataset was obtained by cutting the non-overlapping portions of each detector to consider only the first few minutes of data collection and a dose-corrected dataset was obtained by fitting the independent peaks in every dataset and extrapolating the intensity and peak position to the initial time of data collection or to zero-absorbed dose. The compared structural models obtained show that special processing of powder diffraction data produced a much accurate model, close to the single-crystal-based model for this particular compound with heavy atoms in high symmetry positions that do not contribute to a significant number of diffraction intensities.

A position-sensitive proportional counter suitable for the X-ray stress measurement has been developed and residual stresses were measured with an apparatus that uses this PSD system. The counter was designed to have a good angular resolution over the counter length for the diffracted X-ray beam and high counting rates. The mean angular resolution measured was about 0.2° in 2θ (FWHM) at 200 mm, and the maximum allowable counting rate reached about 40,000 cps.

The time required for the data accumulation was shown to be 1/10 to 1/30 of the time required with a standard diffractometer.

Smectites are clay minerals that expand and contract dramatically in response to changes in water vapor pressure. The expansion/contraction behavior of smectite has considerable importance in engineering applications (such as the stability of building foundations and the integrity of clay barriers) and affects hydrologic properties. To understand this behavior we have analyzed several purified, homoionic smectite standards over a wide range of relative humidities using X-ray powder diffraction (XRD) and a new computer-automated humidity-control system.

Humidity was controlled by mixing dry N2 with H2O-saturated (“wet”) N2 produced with a gas-washing bubbler held in a constant-temperature bath set at 35°C. Mixing of wet and dry N2 was controlled with automated MKS mass-flow controllers.