Calculations of crystal size distributions in oriented clays (montmorillonite and kaolinite) are carried out utilizing X-ray diffraction data together with a method based on information theory. Two different procedures for dealing with the available data are compared. One of them involves some points of the corresponding spectrum, the other correlates the data by means of their moments.

The General Structure and Analysis Software II (GSAS-II) package is an all-new crystallographic analysis package written to replace and extend the capabilities of the universal and widely used GSAS and EXPGUI packages. GSAS-II was described in a 2013 article, but considerable work has been completed since then. This paper describes the advances, which include: rigid body fitting and structure solution modules; improved treatment for parametric refinements and equation of state fitting; and small-angle scattering data reduction and analysis. GSAS-II offers versatile and extensible modules for import and export of data and results. Capabilities are provided for users to select any version of the code. Code documentation has reached 150 pages and 17 web-tutorials are offered.

A study examining the feasibility, and possible necessity, of using transmission data from capillary mounted samples for quantitative analysis of hydrated cement systems was conducted. In order to obtain true quantitative results, the amorphous contents were determined by the addition of an internal standard. The amorphous content of the starting tricalcium silicate was found to be approximately 21–22 wt %, in close agreement with previously published results. The study revealed that the spherical harmonics preferential orientation correction may not be reliable with unmicronized hydrated cement materials in reflection geometry, as chemically unreasonable progressions in Portlandite content with time were observed. The data obtained from capillary measurements, however, exhibited little or no preferential orientation, and appeared to produce the progression of phase contents expected from the reaction. The use of capillaries would appear to be justified in some circumstances to obtain reliable quantitative results from hydrated cementitious materials. In this particular system, a significant fraction of calcium carbonate was present as aragonite, as well as the more usual calcite.

A general expression is proposed for the peak profile produced by a system of simple-shape crystalline domains (sphere, cube, tetrahedron, octahedron) whose size is dispersed according to a gamma distribution. The analytical expression obtained is particularly suited to “on the fly” pattern simulation or profile fitting for nanocrystalline materials. An advantage of using the proposed profile expression is that it always corresponds to a physically meaningful, though a priori fixed, size distribution, whereas the traditionally employed Voigtian profiles can produce unphysical negative size distributions for certain combinations of profile parameters. The peak profile depends on the distribution mean and variance instead of the more common empirical parameters of peak width and shape.

GSAS instrument parameters are tabulated for a variety of laboratory and synchrotron diffractometers to give users an idea of the typical ranges of profile parameters when they generate their own instrument parameter files. For modern high-resolution laboratory diffractometers, the parameters fall in the ranges 0<U<3, V=0, 0<W<4, 1<X<3, 0<Y<3, 1<asym<3, and 0<S/L<0.03. For synchrotron diffractometers, the parameters fall in the ranges 0<U<1.2, −1<V<0, 0<W<1, 0<X<1, 0<Y<1, 0<asym<0.5, 0<S/L<0.001, and 0<H/L<0.007. FULLPROF equivalents are also reported. The factors which are convoluted together to generate the instrument profile are described.

The structure of a birefringent andradite–grossular sample was refined using single-crystal X-ray diffraction (SCD) and synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. Electron-microprobe results indicate a homogeneous composition of {Ca2.88Mn2+0.06Mg0.04Fe2+0.03}Σ3[Fe3+1.29Al0.49Ti4+0.17Fe2+0.06] Σ2(Si2.89Al0.11) Σ3O12. The Rietveld refinement reduced χ2 = 1.384 and overall R (F2) = 0.0315. The HRPXRD data show that the sample contains three phases. For phase-1, the weight %, unit-cell parameter (Å), distances (Å), and site occupancy factor (sof) are 62.85(7)%, a = 12.000 06(2), average <Ca–O> = 2.4196, Fe–O = 1.9882(5), Si–O = 1.6542(6) Å, Ca(sof) = 0.970(2), Fe(sof) = 0.763(1), and Si(sof) = 0.954(2). The corresponding data for phase-2 are 19.14(9)%, a = 12.049 51(2), average <Ca–O> = 2.427, Fe–O = 1.999(1), Si–O = 1.665(1) Å, Ca(sof) = 0.928(4), Fe(sof) = 0.825(3), and Si(sof) = 0.964(4). The corresponding data for phase-3 are 18.01(9)%, a = 12.019 68(3), average <Ca–O> = 2.424, Fe–O = 1.992(2), Si–O = 1.658(2) Å, Ca(sof) = 0.896(5), Fe(sof) = 0.754(4), and Si(sof) = 0.936(5). The fine-scale coexistence of the three phases causes strain that arises from the unit-cell and bond distances differences, and gives rise to strain-induced birefringence. The results from the SCD are similar to the dominant phase-1 obtained by the HRPXRD, but the SCD misses the minor phases.

X-ray diffraction analysis on small samples or micro-area of large samples is always a challenge due to weak diffraction and poor statistics, especially when dealing with samples containing large grain size, inhomogeneous phase distribution, and preferred orientation. Two-dimensional X-ray diffraction has many advantages in microdiffraction analysis. A two-dimensional detector can collect a large amount of data both in terms of speed and angular coverage. This paper covers some aspects about instrumentation of two-dimensional X-ray diffraction and its applications in phase identification and stress analysis on small samples and micro-area of large samples.

A unified matrix-flushing theory and its practical applications for quantitative multicomponent analysis by X-ray diffraction are presented.

In this method, a fundamental “matrix-flushing” concept is introduced; the calibration curve procedure is shunted; the matrix (absorption) effect is totally eliminated; all components, crystalline or amorphous, can be determined.

X-ray powder diffraction data for κ-Al2O3 are reported. It was concluded that κ-Al2O3 belongs to the orthorhombic crystal system with space group Pna21. The lattice parameters were found to be a=4.8351(3) Å, b=8.3109(5) Å, c=8.9363(3) Å. There are 16 Al3+ and 24 O2− in the unit cell, and thus the number of chemical formulas in the unit cell, Z, is 8. The volume V of the unit cell is equal to 359.09(6) Å3 and the theoretical density Dx is 3.772 g/cm3. The Smith–Snyder (F20) and the de Wolff (M20) values for these data are 136.1 (0.0059, 25) and 98.4, respectively.

An interlaboratory study (ILS, round robin) was conducted to assess the accuracy and precision of the phase quantification of calcium phosphate (CaP) bioceramics by X-ray diffraction (XRD) and Rietveld refinement. For that purpose, a mixture of hydroxyapatite and β-tricalcium phosphate, two CaP phases commonly used in synthetic bone graft substitutes, was prepared and sent to 12 laboratories for XRD analysis. Results from 26 different instruments were received and evaluated statistically according to ASTM E691 – 13. The statistical analysis revealed that the reproducibility standard deviation of phase quantities was approximately two times greater than the repeatability standard deviation, which is obtained by repeating the analysis on a single instrument configuration multiple times. The 95% reproducibility limit for phase quantities was R = ±1.67 wt%. The study also demonstrated that several participants overinterpreted their data in an attempt to refine crystallite sizes of the minor phase.

In spite of the wide availability of automated diffractometers and advanced data reduction software, numerous traditional problems still exist that make highly precise and accurate quantitative analyses of complex mixtures difficult. The problems include particle statistics, primary extinction, microabsorption, preferred orientation, overlapping and broad reflections, variation in standard data with composition, availability of pure standards, and detection of amorphous and trace phases. Our analyses of rocks use the matrix flushing method on < 5μm particle-size material mixed with a 1.0-μm corundum internal standard to minimize the first four effects. Integrated intensities are used, and we employ several peaks from each phase whenever possible. We overcame overlap problems through iterative calculations using integral, multiple peaks or with profile refinement. Use of observed and calculated diffraction patterns for every phase enables us to predict the effects of composition and preferred orientation on RIRs. This allows us to correct for these effects if reference intensity ratios (RIRs) are known as a function of composition and orientation. Detection of amorphous phases is a significant problem, and standard mixtures reveal that amounts of amorphous components below 30% are difficult to detect. The poor detection limit and the nature of the diffraction band from amorphous phases make internal standard or spiking methods the best approach for analyzing samples containing amorphous materials. The Rietveld method of quantitative analysis has the potential to minimize all of the above problems. This method requires a knowledge of the crystal structures of all component crystalline phases, but no calibration data are necessary, structural and cell parameters can be varied during the refinement process, so that compositional effects can be accommodated and precise cell parameters can be obtained for every phase. Since this method fits the entire diffraction pattern and explicitly uses all reflections from every phase, complex, overlapped patterns can be easily analysed. In addition, this method presents the opportunity to correct for preferred orientation and microabsorption during data analysis.

Since Boeke's finding of a reversible phase transition of calcite (calcium carbonate, CaCO3) at elevated temperatures [Boeke, H. E. (1912). Neues Jahrb. Mineral. 1, 91–121], and following W. L. Bragg's determination of the structure of the room-temperature Phase I [Bragg, W. L. (1914). Proc. R. Soc. Lond. A 89, 468–489.], the high-temperature Phase V of calcite has been an enduring mystery. Here, we summarize a paper on the structure of Phase V [Ishizawa, N., Setoguchi, H. and Yanagisawa, K. (2013). Sci. Rep. 3, 2832], as well as the intermediate Phase IV which exists between Phases I and V, and add new aspects. An in situ single-crystal X-ray diffraction study revealed that the I–IV and IV–V transitions occurred reversibly at approximately 985 and 1240 K, respectively, in a carbon dioxide atmosphere. Phase V was stable only over a narrow temperature range between 1240 and 1275 K. The crystal decomposed immediately at temperatures above 1275 K, leaving a nanoporous calcium oxide reaction product which retained the shape of the parent calcite crystal. The I–IV transition can be described as an orientational order/disorder transition of the carbonate group, occurring within the same space group $R\bar 3c$. In Phase V, the oxygen sublattice is melted. The joint-probability density function obtained from the anharmonic atomic displacement parameters of the oxygen atoms revealed that the oxygen triangles of the carbonate group in Phase V do not sit still at specified Wyckoff positions in the space group $R\bar 3m$, but are instead distributed with equal probability along the undulated circular orbital about the central carbon. The carbonate group in Phase V is no longer flat on the basal plane when the oxygen triangle comes to troughs or peaks in the undulated orbital, but is instead deformed like an umbrella. Assuming that the oxygen triangle migrates about carbon, the carbonate group should repeat the umbrella inversion in Phase V as a function of time. Finally, possible thermal decomposition mechanisms of calcite are briefly discussed.

Ba(3−x)Srx(PO4)2 orthophosphates (0≤x≤3) have been prepared by solid state reaction. The final temperature was 1000°C. The X-ray diffraction analyses show the existence of a continuous solid solution. Ba(3−x)Srx(PO4)2 orthophosphates (0≤x≤3) crystallize in the hexagonal system with the space group R3m. Their structure is based on a three-dimensional framework constructed of infinite layers of Ba1/Sr1O12 linked and parallel to infinite layers of Ba2/Sr2O10 polyhedra and PO4 tetrahedra.

Amino acids often cocrystallize with water molecules, which make them pseudopolymorphs of their anhydrous forms. In this work, we discuss in detail the hydrogen bond patterns in anhydrous L-proline and DL-proline and its pseudopolymorphic forms: L-proline monohydrate and DL-proline monohydrate. For this propose, the crystal structure of L-proline anhydrous was determined from synchrotron X-ray powder diffraction data and refined using the Rietveld method. Special emphasis is given to the role played by the water molecule in the hydrogen bond network observed in the crystalline structures.

Without experimental or predicted literature crystal structures for succinonitrile at low temperature, structure solution was attempted from powder diffraction data taken at 173 and 90 K from a solid sample. Its room-temperature plastic-crystal state makes production of a sample with good particle statistics and random orientation almost impossible. Combining constrained models, simulated annealing, and careful application of second-order spherical harmonic corrections nevertheless produced viable-looking structures at 90 and 173 K, yielding two distinct structure models with the same projection down c. VASP optimization of atom coordinates in the experimental cell agreed well with the 90 K model but poorly with the model derived from the 173 K data. The refined 90 K structure changed little on optimization and fitted all datasets from 85 to 225 K. Plots of cell data, torsion angles, and isotropic displacement parameters against temperature suggest possible phase transitions around 100, 120, and 180 K. Cell data at 90 K: monoclinic P21/a, a=9.0851(5) Å, b=8.5617(5) Å, c=5.8343(3) Å, β=79.295(2)°, and Z=4. Succinonitrile has gauche conformation, in agreement with literature spectroscopy data.

The importance of software continues to grow for all areas of scientific research, no less for powder diffraction. Knowing how to program a computer is a basic and useful skill for scientists. This paper explains the three approaches for programming languages and why scripting languages are preferred for non-expert programmers. The Python-scripting language is extremely efficient for science and its use by scientists is growing. Python is also one of the easiest languages to learn. The language is introduced, as well as a few of the many add-on packages available that extend its capabilities, for example, for numerical computations, scientific graphics, and graphical user interface programming. Resources for learning Python are also provided.

ZnGa2Te4 was found to crystallize in a defect tetrahedral structure with possible space group I4(82) with Z=2. Complete X-ray powder diffraction data were obtained and the unit cell parameters a and c and X-ray density were calculated. These were a=0.5930(1) nm, c=1.1859(3) nm, and Dx=5.7×103 kg/m3.

The residual stress left on the fracture surface is one of the important parameters in X-ray fractography and has been used to analyse fracture mechanisms in fracture toughness, stress corrosion cracking and fatigue tests especially of high strength steels.

In this study, the distribution of residual stress near fatigue fracture surfaces made in air and in 3.5% NaCl solution was measured by the X-ray diffraction method. The effect of aqueous environment on the plastic deformation near fatigue fracture surfaces was discussed on the basis of the residual stress distribution.

A computer program is presented that allows for the merging of diffraction patterns collected at multiple positions on the Powder Diffraction beamline of the Australian Synchrotron. It is also generally applicable to detector systems based on other modular detectors. The program allows for the interpolation of data to a constant 2θ step size and to normalise intensities to beam current and/or monitor count rate.

The purpose of this paper is to give a rapid overview of the recent developments in the field of X-ray diffraction on polycrystalline materials from the viewpoint of the instruments. After a brief historical report, the main types of laboratory diffractometers are presented. At the end of the twentieth century the apparition of position sensitive detectors and artificial crystal monochromators have induced the conception of new diffractometer often based on old geometrical arrangements. Those modern diffractometers are described with respect to the more conventional ones. Among the experimental parameters which can characterize a given diffractometer, the instrumental resolution function and the acquisition time of the pattern are of primary importance. The different apparatus are compared with respect to those two parameters.