We report precision X-ray powder-diffraction (XRD) data of single phase pure Ti2ZrAl. Ti2ZrAl samples were prepared by an arc melting method and annealed at 1000 °C for 30 days. XRD analysis was carried out on these samples and it was found that Ti2ZrAl has a DO19 structure (space group P63/mmc, No. 194). The lattice parameters are found to be a=5.961±0.001 Å and c=4.793±0.001 Å.

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.

Recipes are given to assist in setting up rigid bodies for common molecules and coordination polyhedra, to define satellite groups, to perform rotations around arbitrary axes through the origin of the rigid body, and to refine intramolecular degrees of freedom under consideration of the special needs of powder diffraction. To the greatest possible extent, the notation follows that of the well known Rietveld refinement program GSAS (Larson and Von Dreele, 1994).

The variables of reflection overlap, crystallinity and crystallite size, primary extinction, microabsorption, chemical substitutions, preferred orientation, and analytical procedures affect quantitative analysis by powder X-ray diffraction. The intensity of the strongest reflection (I) of 39 minerals from a typical sedimentary environment divided by the intensity of the strongest reflection (Ic) of corundum, I/Ic, may be used to determine mineral percentages. Because of the numerous variables mentioned above, the I/Ic ratios used should be taken from multi-mineral specimens that occur either in the same geological formation for quantitative analysis (±7%) or in a similar geological formation for quantitative analysis (±30%).

An X-ray powder diffraction quantitative analysis has been developed to determine the relative amounts of the principal crystalline phases (α-Li2SiO3, α-Li2Si2O5 and the α-cristobalite form of SiO2) contained in selected Li2O–SiO2 glass-ceramics. The analysis was extended to estimate the amorphous-to-crystalline content ratio of individual samples. The method utilized is an external-standard intensity ratio technique that employs cristobalite, a component common to each sample, for a standard.

In the framework of the study of the relationship between crystal packing of solid dyes and their visible reflectance spectra, the crystal structure of 3-methoxy-7H-benz[de]anthracen-7-one (Disperse Yellow 13, C18H12O2) has been determined using a combined set of Bragg–Brentano diffractometer and Guinier–Johannson photographic data with the grid search procedure. Parameters of the orthorhombic cell (P212121, No.19, Z=4) at 295 K are a=15.265(9) Å, b=20.524(9) Å, c=3.990(2) Å. Rietveld refinement gave Rp=0.085, Rb=0.135. The molecules form stacks along [001] with an interplanar spacing of 3.46 Å.

The procedure of whole-powder-pattern fitting without reference to a structural model has been applied to the determination of direction-dependent crystallite size and strain. The fitting function used is defined as the sum of (1) background intensity and (2) contributions from individual reflections given as the convolution of the observed instrumental function with the true data function in analytical form. Crystallite size and strain parameters are adjustable, together with unit-cell parameters and the integrated intensities of all reflections, during the whole-powder-pattern fitting. The procedure requires neither structural parameters nor intensity correction for preferred orientation in calculating profile intensity. The two models are incorporated for line broadening, one for isotropic size and strain effects and the other for the anisotropic size effect of cylindrical shape. The procedure has been tested for these two models using the observed data of 4 mole % Y2O3-doped tetragonal ZrO2 and hydroxyapatite, Ca5(PO4)3OH, respectively, and been shown to be effective for determining crystallite size and strain from the powder pattern with a relatively high peak density.

High resolution X-ray powder diffraction data have been collected with Bragg-Brentano geometry on samples of MgO using Ni-filtered and graphite-monochromated CuKαradiation. Selection of the characteristic radiation by Ni-filtering produces severe peak asymmetry, truncates the low-angle foot of the peak, lowers the general level of background on the low angle side, and leaves a remnant Kβpeak for all foils of reasonable thickness. When step-scan data produced by this method are used for Rietveld analysis, all of these features cause difficulties in fitting a smooth function to the background and in successfully modelling the detailed profiles of the peaks. On the other hand, Kαradiation from a diffracted-beam monochromator provides inherently more symmetric peaks and a smoothly varying background on both sides of the peak centre, both of which effects can be adequately modelled during Rietveld analysis. The primary disadvantage with monochromation is that, even with very careful setting of the pulse height discrimination, the monochromator may pass a small proportion of the λ/2 component of the incident radiation. In samples containing small quantities (i.e., 2 wt%, or less) of impurity phases, the undesirable features of the diffractometer profile (i.e., asymmetric and truncated background, and Kβand λ/2 peaks) can be of similar intensity to the main peaks arising from the impurities (as well as substructure peaks from the primary phases), thereby leading to difficulties in their identification and quantification. Nevertheless, with due care and long data collection times, the abundances of minor phases can be measured with Rietveld analysis down to levels of the order of 0.1 wt%.

FARHAN is a PC interactive, graphically oriented search–match–identification–quantification computer program for X-ray powder diffraction, which uses a variable intensity-error window (IEW). Both the intensity scale factor and the IEW for each standard phase are estimated by a simple iterative procedure. A new tunable combined figure-of-merit (agreement function) is suggested for estimating the goodness-of-fit of matches. The concentrations of the identified phases may be determined by normalized or generalized RIR quantification methods, if the RIRs of the identified phases are known.

New X-ray powder data for CaWO4 (synthetic scheelite) are presented and compared with the current PDF patterns and with a calculated pattern.

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°).

A well-crystallized sample of powdered KCl has been distributed among several laboratories in order to test the reproducibility of the lattice parameter measurement on different X-ray powder diffraction instruments. The precision of the determined unit-cell dimension is in the 10−5 Å range, while the discrepancies among the results from different laboratories using the same numerical analysis are at least one order of magnitude higher. It is shown that if different numerical analyses, including full pattern refinement, are used, values differing in the third decimal digit are obtained for the same data set.