Estimation of reference intensity ratios (ki or RIR) can be made on the basis of an atomic scattering function. Tests of regression equations for 50 compounds that predict an approximate reference intensity ratio from the easily computed scattering function have shown usefulness in multicomponent semiquantitative X-ray diffraction analysis. The method is best applied whenever only one or two minor components of a multicomponent sample have no readily measurable or calculable ki values and must be estimated. Where the difference between observed and predicted constants is large, these tests show that the ratios of true- to test-weight fractions are proportional to the corresponding ki ratios. The largest absolute errors occur whenever the ki must be predicted for components with medium weight fraction values. Estimation of ki for components of less than 10 weight percent results in only small errors in both predicted component and the other components of the sample. Where more than two components require predicted ki in a given sample, unacceptable errors for all components may result.

The crystal structure of the layered cadmium hydroxide sulfate Cd4SO4(OH)6.1.5H2O has been solved from X-ray powder diffraction data. The compound crystallizes with hexagonal symmetry, a=9.145(1) Å, c=15.099(3) Å, V=1093.5 Å3, Z=4, space group P63. Due to the unusual environment of one cadmium atom and to the fact that a suitable thin tabular crystal could be found later, a single-crystal X-ray diffraction experiment was also carried out. In both cases the structure was solved applying direct-methods. The refinements converged to the residual factors Rwp=0.152 and RF=0.059 from the powder data and R1=0.058 and wR=0.165 for the single crystal data case. The structure is built from brucite-type layers based on CdO6 octahedra, in which one-seventh of the octahedral sites are empty. Directly above and below these empty sites, two additional octahedrically coordinated Cd atoms are located. The crystal chemistry of the cadmium hydroxide sulfate family is discussed.

The crystal structure of monoclinic CuF2 has been refined by the Rietveld method from X-ray powder diffraction data. The structure is monoclinic, space group P21/n, a = 3.2973(2), b = 4.5624(3), c = 4.6157(3) Å, β = 83.293(3)°, V = 68.96(2) Å3, with Cu+2 at (0,0,0) and F−1 at (−0.04176(68), 0.29410(35), 0.29410(35)). Final RB = 0.97%, RP = 1.99%, Rwp = 2.32%, RWP(expected) = 1.46%. The structure has a rutile-type arrangement, but with a monoclinic distortion that produces a highly distorted octahedral coordination around the Cu2+ ion with equatorial and apical Cu-F distances of 1.92 and 2.32 Å respectively.

X-ray powder diffraction data are reported for α-brass with the composition Cu: 63.44±0.04 wt %, Zn: 36.45±0.06 wt %. No valid reference card for this material is present in the JCPDS-ICDD database. The investigated brass composition is cubic (Fm3m) with a0: 3.69612±0.00014 Å, unit cell volume: 50.4938±0.0058 Å3, density calculated: 8.44±0.05 g/cm3, density measured: 8.43±0.03 g/cm3. The X-ray diffraction pattern presented resembles that of deleted reference card 6-657 in great detail.

Advances in X-ray texture solutions require new methods and descriptions for the texture analysis process, e.g., when using general area detector diffraction systems. A new method is presented that defines a general pole figure resolution and provides the possibility to optimize strategies for efficient pole figure data collection. Application of the new method improves resolution and (!) speed. New software enables simultaneous monitoring of pole and detector space. This allows a fundamentally better understanding of the collected information, e.g., in situations where peaks overlap or high backgrounds compromise data quality.

Experimental X-ray powder diffraction patterns and refined unit cell parameters for two barium hollandite-type compounds, BaxFe2xTi8−2xO16, with x=1.143 and 1.333, are reported here. Compared to the tetragonal parent structure, both compounds exhibit monoclinic distortions that increase with Ba content [Ba1.333Fe2.666Ti5.334O16: a=10.2328(8), b=2.9777(4), c=9.899(1) Å, β=91.04(1)°, V=301.58(5) Å3, Z=1, ρcalc=4.64 g/cc; Ba1.143Fe2.286Ti5.714O16: a=10.1066(6), b=2.9690(3), c=10.064(2) Å, β=90.077(6)°, V=301.98(4) Å3, Z=1, ρcalc=4.48 g/cc]. The X-ray powder patterns for both phases contain a number of broad, weak superlattice peaks attributed to ordering of the Ba2+ ions within the tunnels of the hollandite framework structure. According to the criteria developed by Cheary and Squadrito [Acta Crystallogr. B 45, 205 (1989)], the observed positions of the (0k1)/(1k0) superlattice peaks are consistent with the nominal x-values of both compounds, and the k values calculated from the corresponding d-spacings suggest that the Ba ordering within the tunnels is commensurate for x=1.333 and incommensurate for x=1.143. High-temperature X-ray diffraction data indicate that the x=1.333 compound undergoes a monoclinic→tetragonal phase transition between 310 and 360 °C.

The mathematical relationships are developed which are pertinent to the quantitative analysis of powder mixtures for the case of diffraction from the surface of a flat powder specimen. These formulas relate the diffracted intensity to the absorptive properties of the sample. Three important cases are treated: (1) Mixture of n components; absorbing powder of the unknown equal to that of the matrix; concentration proportional to intensity. Direct analysis is permitted. (2) Binary mixture; absorbing powder of the unknown not equal to that of the diluent; concentration not proportional to intensity. Direct analysis is possible by means of calibration curves prepared from synthetic mixtures. (3) Mixture of n components; absorbing power of the unknown not equal to that of the matrix; general case. Analysis is accomplished by the addition of an internal standard. Concentration is proportional to the ratio of the intensity of a selected reflection from the unknown to the intensity of a reflection from the internal standard.

The structure of pyrochlore type Y2Sn2O7 has been refined by Rietveld analysis from 1.4925 Å neutron powder diffraction data collected at 295 K and containing 46 independent reflections. The refinement figures of merit were Rp = 0.041, Rwp = 0.055, Rexp = 0.039, and RB = 0.006. The structure is a pyrochlore type, space group (S.G.) with a = 10.3723(1) Å, Dx = 6.21 g cm−3, and with the oxygen position parameter of 0.33694(5). The Sn atoms are in a nearly regular octahedral coordination whereas the Y has a distorted 8-fold coordination geometry. The anisotropic thermal parameters were also determined. The refined model has been used to calculate a set of d-I X-ray data for search/match analysis.

The fundamental parameter method for quantitative analysis of composite elements has been a powerful technique for x-ray spectrochemical analysis in which the x-ray intensity and spectral distribution from x-ray spectrographic tubes are the moste ssential factors in the calculating process based on x- ray physics.

This work introduces a new simple approach to determine experimental X-ray elastic constants (XECs) of thin films by coupling the sin2ψ method and the substrate curvature technique. The approach is demonstrated on polycrystalline Cu thin films with the thickness 200, 800, and 2400 nm deposited on Si(100) substrates. Applying synchrotron radiation, the elastic strains in the films are determined using sin2ψ method while the macroscopic stresses are assessed by measuring the substrate curvature. The stresses are calculated using the Stoney formula from the radius of substrate curvature determined by the rocking curve measurement of substrate 400 reflection at different sample positions. Results show that the magnitude of the macroscopic stress in the films is proportional to the magnitude of the slope in the sin2ψ plots. On the basis of this observation, XECs of the films were calculated showing no dependence on the film thickness. The characterization of the samples was performed at the synchrotron source Hasylab.

A new cobalt hydroxide carbonate Co2(OH)2CO3 was successfully synthesized by a hydrothermal method. The compound is isomorphous with malachite [Cu2(OH)2CO3] and crystallizes in a monoclinic system [space group P21/a (No. 14); a=9.448(5) Å, b=12.186(9) Å, c=3.188(4) Å, β=98.593°, V=367.143(9) Å3, Z=4, and Dc=3.786(9) g/cm3]. Crystal structure of Co2(OH)2CO3 was refined by the Rietveld method with RP=4.3%, RWP=5.7%, Rexp=5.1%, RB=1.74%, and S=1.117 on the basis of the X-ray powder diffraction data. The crystal structure of Co2(OH)2CO3 obtained by the Rietveld refinement shows that all species Co2+, CO32−, and OH− ions occupy C1 site symmetry. Two crystallographically different Co2+ and OH− ions and one type CO32− ion exist in the lattice. Co(1) is coordinated to two oxygen atoms from CO32− ions and two OH− ions; Co(2) is coordinated to two oxygen atoms from CO32− ions and four OH− ions, thus forming a distorted octahedron with (4+2) coordination.

The crystal structure of the novel metal organic framework (MOF) Zn(C3H5NO2S)2 is described. This MOF can serve as a model for active sites in metalloproteins, on diverse activities such as structural or catalytic functions. Each half of the amino acid act as a bidentate ligand to one Zn and as a monodentate ligand to another Zn, while the disulphide bond presents an important structural function, stabilizing the crystal packing. The structure has been obtained ab initio from synchrotron X-ray powder diffraction data. The compound crystallizes in the orthorhombic system (space group P212121), with a = 20.0906(7), b = 9.5842(3), c = 5.018 89(13), and V = 966.40(5) Å3, with Z = 4. The structure was determined using a direct space approach, by means of the Monte Carlo technique, followed by Rietveld refinement.

Improvements of standard X-ray powder diffractograms of two Y-type hexagonal ferrites (Ba2Co2Fe12O22, Ba2Zn2Fe12O22) are reported.

The sin2ψ method can be formulated as a single system of simultaneous linear equations. Using this it is easy to show that the sin2ψ method is not a least-squares method. It further helps to compare the accuracies of the stress tensors obtained by the sin2ψ method and the method of least squares. Quantitative comparisons have been made for different fictitious measurements. It is shown that the unnecessary loss in accuracy by using the sin2ψ method is quite significant and by no means negligible. The same course of action has been applied to compare the so-called Dölle-Hauk method with a least-squares method; the result is similar. Some other methods for X-ray stress determination, most often similar to the sin2ψ method, and their shortcomings are also discussed briefly, together with the corresponding, more effective and more versatile least-squares method.

Crystal data are given for synthetic mixed bariumstrontium sulfates, and a powder pattern for (Ba0.50Sr0.50)SO4 is presented. Taken with previously published data for the end-member sulfates, we verify the nonlinear behavior of the unit-cell edges with composition, and present tables of interpolated data from which d-spacings for intermediate compositions can be calculated. The use of these data for analysis of complex natural samples by use of the 121 peak is described.

This paper describes new features implemented in the EXPO2014 software and aimed at assisting crystallographers in the use of quantum-chemistry calculations in combination with experimental powder diffraction data. The implemented tools are useful in particular in two important steps of the process of crystal structure determination from powder diffraction data: (1) preparing accurate structural model suitable for crystal structure determination by real-space methods; (2) validating structure determination. The combination of experimental/quantum-chemical methods in EXPO2014 is now managed easily thanks to the following capabilities: (a) converting crystallographic data in input files and reading molecular geometry from output files of a wide variety of computational chemistry packages (GAMESS-US, NWChem, Gaussian, CRYSTAL, ABINIT, QUANTUM ESPRESSO); (b) optimizing the geometry of a molecule using Open Babel's force fields; (c) a graphical interface to run semi-empirical quantum calculation by MOPAC (Molecular Orbital PACkage); (d) producing input file for dispersion-corrected density functional theory.

The International Centre for Diffraction Data has an ongoing program to ensure the quality of data in the Powder Diffraction File (PDF) reflects current requirements of the powder diffraction community. Annual updates are made available, comprising of around 1800 new patterns and 200 replacement patterns, but current statistics indicate that only about 20% of users of the PDF take advantage of these updates. This paper reviews changes which have been inplemented in the editorial review process to continuously monitor and review pattern quality and gives examples of better data which have resulted from these changes.

The crystal structure of a morimotoite garnet, ideally Ca3(Ti4+Fe2+)Si3O12, from the Ice River alkaline complex, British Columbia, Canada was refined by the Rietveld method, space group $Ia\overline 3 d$ , and monochromatic synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. Electron-microprobe analysis indicates a homogeneous sample with a formula {Ca2.91Mg0.05Mn2+ 0.03}Σ3[Ti1.09Fe3+ 0.46Fe2+ 0.37Mg0.08]Σ2(Si2.36Fe3+ 0.51Al0.14)Σ3O12. The HRPXRD data show a two-phase intergrowth. The reduced χ 2 and overall R(F 2) Rietveld refinement values are 1.572 and 0.0544, respectively. The weight percentage, unit-cell parameter (Å), distances (Å), and site occupancy factors (sofs) for phase-1 are as follows: 76.5(1)%, a = 12.156 98(1) Å, average <Ca–O> = 2.4383, Ti–O = 2.011(1), Si–O = 1.693(1) Å, Ca(sof) = 0.943(2), Ti(sof) = 0.966(2), and Si(sof) = 1.095(3). The corresponding values for phase-2 are 23.5(1)%, a = 12.160 67(2) Å, average <Ca–O> = 2.452, Ti–O = 1.988(3), Si–O = 1.704(3) Å, Ca(sof) = 1.063(7), Ti(sof) = 1.187(7), and Si(sof) = 1.220(8). The two phases cause strain that arises from structural mismatch and gives rise to low optical anisotropy. Because the two phases are structurally quite similar, a refinement using a single-phase model with anisotropic displacement parameters shows no unusual displacement ellipsoid for the O atom that requires a “split O-atom position”, as was done in previous studies.

The solid-state phase transformation from α- to β-copper phthalocyanine, using isothermal data obtained at T=250 °C and nonisothermal data obtained in the temperature range of 30 °C≤T≤330 °C with a constant heating rate of 1.67 °/min, was investigated by sequential and parametric full quantitative Rietveld analyses. Results obtained in this study show that the parametric Rietveld refinement technique is most suitable and applicable for kinetic studies of isothermal powder diffraction data. On the other hand, the sequential Rietveld refinement technique can give reliable results for the kinetic analysis of nonisothermal data. The main advantages of the parametric Rietveld refinement over the sequential Rietveld refinement are increased robustness against outliers, low weight fractions, and noisy data and an increase in computational speed.

A recently developed Rigaku parallel-beam X-ray diffraction system equipped with a parabolic graded-multilayer mirror in the incident beam and a parallel-slits analyzer in the diffracted beam was used for precision high-temperature diffraction studies. The lattice parameters a and c of α-Al2O3 at room temperature and up to 1473 K were determined with precision in the range of 0.6–7.3×10−5. The thermal expansion coefficients for a and c agreed with literature values to better than 3%. The system was used successfully also to determine the Debye characteristic temperature of Si and to study structural phase transition of LaCoO3 from rhombohedral at room temperature to cubic at 1700 K.