This work provides a short summary of techniques for formally-correct handling of statistical uncertainties in Poisson-statistics dominated data, with emphasis on X-ray powder diffraction patterns. Correct assignment of uncertainties for low counts is documented. Further, we describe a technique for adaptively rebinning such data sets to provide more uniform statistics across a pattern with a wide range of count rates, from a few (or no) counts in a background bin to on-peak regions with many counts. This permits better plotting of data and analysis of a smaller number of points in a fitting package, without significant degradation of the information content of the data set. Examples of the effect of this on a diffraction data set are given.

A method to remove small CuKβ peaks and step structures caused by NiK-edge absorption as well as CuKα2 sub-peaks from powder diffraction intensity data measured with Cu-target X-ray source and Ni-foil filter is proposed. The method is based on deconvolution–convolution treatment applying scale transform of abscissa, Fourier transform, and a realistic spectroscopic model for the source X-ray. The validity of the method has been tested by analysis of the powder diffraction data of a standard LaB6 powder (NIST SRM660a) sample, collected with the combination of CuKα X-ray source, Ni-foil Kβ filter, flat powder specimen and one-dimensional Si strip detector. The diffraction intensity data treated with the method have certainly shown background intensity profile without CuKβ peaks and NiK-edge step structures.

We report the structure and physical properties of two quasi-two-dimensional triangular antiferromagnetic materials, Co0.66Al2Se3.53 and Ni0.61Al2Se3.55, which show highly magnetically frustrated characters. Powder X-ray diffractions demonstrate that Co0.66Al2Se3.53 and Ni0.61Al2Se3.55 possess identical space group of P-3m1 with lattice parameters a = 3.8089(1) Å, c = 12.676(1) Å and a = 3.7880(1) Å, c = 12.650(1) Å, respectively. Analyzing the susceptibility data of Co0.66Al2Se3.53 reveal a Curie Weiss temperature of −216 K, and a spin-freezing transition temperature of 4.5 K, giving a frustration index f = −θcw/Tf ≈ 48. Ni0.61Al2Se3.55 possesses an effective moment of 2.38 µB, a Curie–Weiss temperature of −62 K with no sign of spin-freezing transition down to 2 K. The AC susceptibility data of Co0.66Al2Se3.53 suggest a spin glass-like transition, but no intersite mixing between Co2+ and Al3+ was observed from the X-ray photoelectron spectroscopy measurements.

A function has been proposed to evaluate the electron density model constructed by inverse Fourier transform using the observed structure amplitudes and trial phase set. The strategy of this function is applying an imaginary electron density modification to the model, and then measuring how well the calculated structure amplitudes of the modified model matches the expected structure amplitudes for the modified correct model. Since the correct model is not available in advance, a method has been developed to estimate the structure amplitudes of the modified correct model. With the estimated structure amplitudes of the modified correct model, the evaluation function can be calculated approximately. Limited tests on simulated diffraction data indicate that this evaluation function may be valid at the data resolution better than 2.5 Å.

The pharmacy (spezieria) Santa Maria della Scala was founded in Rome by the Discalced Carmelites Order in the 17th century, and during the 18th and 19th centuries it became the official supplier of medicines for Vatican Popes. The laboratory and the cases of this spezieria still preserve glass jars with organic and inorganic materials, which were presumably used for medicine and artistic material preparation, whose composition is unknown to date. A research project was initiated with the aim to study the stored materials and the role that the pharmacy played in regional, national and international contexts. In this manuscript, the compounds were analysed through X-ray powder diffraction with the scope to derive the quantitative mineralogical composition of the inorganic fraction, their possible use in pharmacopoeias and as mineral pigments. Most of the analysed samples are salts (sulphates, chlorides, carbonates, phosphates, borates, sulphides), sulphates being the predominant class; oxides were also detected.

Ga2−xFexO3 (GFO) bulks with x from 0.7 to 1.3 have been fabricated using the classic solid-state route. The structural, optical, and magnetic properties have been investigated systematically. X-ray diffraction spectra and FULLPROF profile fitting indicate that GFO bulks belong to the orthorhombic structure with the space group Pc21n. Phase separation appears at the Fe content of x = 1.3. The optical bandgap decreases almost linearly with the increase of iron content, which means that the bandgap of GFO bulks can be controlled by adjusting the Fe content in the samples. The magnetic property measurements suggest that GFO is ferromagnetic, and the magnetic properties are enhanced compared with other reported works, exhibiting the application in ferromagnetic semiconductors devices.

Roman bronze coins from the 3rd and 4th century AD exhibit a wide variety of chemistries on their surfaces. This variation has been attributed to the variable methods used to produce the coins, a large number of mints producing bronze currency, and the periods of currency devaluation within the Roman Empire. Besides the base bronze metallurgy (Cu,Sn), Ag, Pb, and Zn were frequently used as coinage metals. Silver coatings were often applied to increase the apparent value of the coins. Over the centuries these surfaces corroded producing a range of patinas. Non-destructive X-ray diffraction and X-ray fluorescence methods were used to evaluate ancient bronze coins. These methods are limited by their half depth of penetration into the coins, so the focus was on the chemistry of the patina's and how they related to the current appearance. Several 3rd-century bronze coins exhibited a very dark patina that was often composed of CuCl, Cu2O (cuprite) and several forms of copper hydroxyl chloride, resulting from surface deterioration caused by corrosion and is often referred to as bronze disease. Coins of the latter 3rd century and 4th century often exhibit patinas that are corrosion products of lead, silver, and tin, as lead and tin preferentially oxidize relative to the bronze alloys.

Different experimental conditions at a versatile high-energy beamline equipped with a two-dimensional detector have been compared for powder diffraction and pair distribution function (PDF) experiments. In particular, sample size and sample to detector distances have been evaluated on a standard sample, to evaluate their effects in both Q and real space. Two illustrative cases are also discussed. The average structure and local distortions in a BaTiO3 powder with 100 nm particle size show that spurious ripples in the PDF are suppressed by increased counting statistics. Effects of small amounts of a crystalline impurity phase on a SiO2.Al2O3.Na2O.CaO glass have been quantified.

A series of double-perovskite oxides, Sr2RNbO6 (R = Sm, Gd, Dy, Ho, Y, Tm, and Lu) were prepared and their crystal structure and powder diffraction reference patterns were determined using the Rietveld analysis technique. The crystal structure of each of the Sr2RNbO6 phase is reported in this paper. The R = Gd, Ho, and Lu samples were studied using synchrotron radiation, while R = Sm, Dy, Y, and Tm samples were studied using laboratory X-ray diffraction. Members of Sr2RNbO6 are monoclinic with a space group of P21/n and are isostructural with each other. Following the trend of “lanthanide contraction”, from R = Sm to Lu, the lattice parameters “a” of these compounds decreases from 5.84672(10) to 5.78100(3) Å, b from 5.93192(13) to 5.80977(3) Å, c from 8.3142(2) to 8.18957(5) Å, and V decreases from 288.355(11) to 275.057(2) Å3. In this double-perovskite series, the R3+ and Nb5+ ions are structurally ordered. The average Nb–O bond length is nearly constant, while the average R–O bond length decreases with the decreasing ionic radius of R3+. Powder diffraction patterns for these compounds have been submitted to the Powder Diffraction File (PDF).

The crystal structures of calcium citrate hexahydrate, calcium citrate tetrahydrate, and anhydrous calcium citrate have been solved using laboratory and synchrotron X-ray powder diffraction data, and optimized using density functional techniques. Both the hexahydrate and tetrahydrate structures are characterized by layers of edge-sharing Ca coordination polyhedra, including triply chelated Ca. An additional isolated Ca is coordinated by water molecules, and two uncoordinated water molecules occur in the hexahydrate structure. The previously reported polymorph of the tetrahydrate contains the same layers, but only two H2O coordinated to the isolated Ca and two uncoordinated water molecules. Anhydrous calcium citrate has a three-dimensional network structure of Ca coordination polyhedra. The new polymorph of calcium citrate tetrahydrate is the major crystalline phase in several commercial calcium supplements.

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.

Several methods can be used to obtain, from powder diffraction patterns, crystallite size and lattice strain of polycrystalline samples. Some examples are the Scherrer equation, Williamson–Hall plots, Warren/Averbach Fourier decomposition, Whole Powder Pattern Modeling, and Debye function analysis. To apply some of these methods, it is necessary to remove the contribution of the instrument to the widths of the diffraction peaks. Nowadays, one of the main samples used for this purpose is the LaB6 SRM660b commercialized by the National Institute of Standard Technology; the width of the diffraction peak of this sample is caused only by the instrumental apparatus. However, this sample can be expensive for researchers in developing countries. In this work, the authors present a simple route to obtain micron-sized polycrystalline CeO2 that have a full width at half maximum comparable with the SRM660b and therefore it can be used to remove instrumental broadening.

Four series of small parasite peaks observed in powder diffraction data recorded with a Cu-target X-ray tube and a Ni filter on the diffracted beam side in Bragg–Brentano geometry are investigated. One series of the parasite peaks is assigned to the tungsten Lα-emission. Other three types of the parasite peak series are likely to be caused by the K-emissions of Ni, but the peak locations are deviated from those predicted by the Bragg's law. An empirical formula to locate the parasite peaks and a method to remove them from observed powder diffraction data are proposed. The method is based on the whole-pattern deconvolution–convolution treatment on the transformed scale of abscissa. The parameters optimized for the diffraction data measured for Si powder has been applied on treatment of the data of LaB6 powder recorded under the same experimental conditions. It has been confirmed that the parasite peaks in the observed data can effectively be removed by the deconvolution treatment with parameters determined by a reference measurement.

Synchrotron X-ray diffraction was used to monitor the hydrothermal precipitation of akaganeite (β-FeOOH) and its transformation to hematite (Fe2O3) in situ. Akaganeite was the first phase to form and hematite was the final phase in our experiments with temperatures between 150 and 200 °C. Akaganeite was the only phase that formed at 100 °C. Rietveld analyses revealed that the akaganeite unit-cell volume contracted until the onset of dissolution, and subsequently expanded. This reversal at the onset of dissolution was associated with a substantial and rapid increase in occupancy of the Cl site, perhaps by OH− or Fe3+. Rietveld analyses supported the incipient formation of an OH-rich, Fe-deficient hematite phase in experiments between 150 and 200 °C. The inferred H concentrations of the first crystals were consistent with “hydrohematite.” With continued crystal growth, the Fe occupancies increased. Contraction in both a- and c-axes signaled the loss of hydroxyl groups and formation of a nearly stoichiometric hematite.

Single-phase polycrystalline samples of RBa2Cu2.9Zn0.1Oy (R = Y, Nd, Gd, Er, and Tm) (ZnR123) were synthesized using the standard solid-state reaction method. They were characterized by X-ray powder diffraction (XRD) and scanning electron microscope. XRD shows that all samples consist essentially of a single phase and retain the orthorhombic structure. The structure of the samples was refined by the Rietveld method with the help of the bond valence sum method. The variation of the lattice parameters and some meaningful bond angles and lengths with the ionic radius are discussed. In these compounds, the variations of the buckling angles Cu2–O(2,3)–Cu2 and Cu2–Cu2–O(2,3) are unique: the bond angles Cu2–O3–Cu2 and Cu2–Cu2–O2 increase, whereas the bond angles Cu2–O2–Cu2 and Cu2–Cu2–O3 decrease. The variation of these bond angles brings about a strong curvature of the Cu2O plane. Furthermore, we have found tree fixed triangles formed by the Cu2, O2, and O3 atoms in addition to another fixed triangle O1–Ba–O1 observed for the first time. BVS of Cu2 atom shows a specific and unique variation compared with other compounds.