Indexed X-ray powder diffraction data are reported for the homologous compound (ZnO)5(In1−xYx)2O3. The structures of (ZnO)5In2O3 and of (ZnO)5(In1−xYx)2O3 were refined by the Rietveld technique on the basis of the space group R3¯m. Refined unit cell dimensions are a=3.3285(1) Å, c=58.127(2) Å, V=557.71(3) Å3, Dx=6.11 g/cm3, Rwp=10.52, RB=8.56 for (ZnO)5In2O3, and a=3.3505(1) Å, c=57.863(1) Å, V=562.53(2) Å3, Dx=5.97 g/cm3, Rwp=9.05, RB=6.94 for (ZnO)5(In0.8Y0.2)2O3. The structure of (ZnO)5In2O3 was shown to be isostructural with (ZnO)5LuFeO3. Y3+ ions were determined to be arranged at the 3a-metal sites substituting for In3+ ions.

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.

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.

Detailed structural properties of La1−xBaxCoO3 (LBCO) have been investigated by means of X-ray powder diffraction and Rietveld analysis. A structural phase transformation from R3c to Pm3m at x=0.30–0.35 has been detected based on a comparison between the refinements of R3c and Pm3m. The Co–O bond length of the CoO6 octahedron expanded rapidly with increasing Ba content when x<0.1, and then it leveled off and kept constant at 0.1⩽x⩾0.35, where the Co–O–Co bond angle reaches 180°. The Co–O bond length expansion resumed with increasing Ba content beyond x=0.35.

XLENS is a traditional direct methods program working exclusively in reciprocal space. The distinctive feature of XLENS is the use of the modulus sum function as target function for the phase refinement. Due to its efficiency, robustness, and no need of weighting schemes, this function is specially well suited for treating powder diffraction data. The mathematical basis as well as the significance of the most important control parameters of the program will be described here. To illustrate how XLENS works, three different examples will be shown. Due to its simplicity, the modulus sum function can be easily combined with real-space filtering procedures to produce even more efficient crystal structure solving strategies.

Bright apple green millimeter-sized crystals of tavorite from the Tip Top pegmatite, near Custer, South Dakota are triclinic, space group , with refined unit-cell parameters a = 5.340(2), b = 7.283(2), c = 5.110(2)Å, α = 109.29(2)°, β = 97.86(3)°, γ = 106.32(3)°, V = 174.1(3)Å3, a:b:c = 0.7332:1:0.7016, Z = 2, D(m) (suspension in methylene iodide) = 3.32(1) and D(x) = 3.33 g/cm3 (for the theoretical formula). A fully indexed X-ray powder pattern is presented. Semiquantitative electron microprobe and secondary ion mass spectroscopic analyses indicate a formula near end-member LiFe + 3(PO4)(OH). The Tip Top tavorite is biaxial positive, α = 1.795(5), β = 1.81(1), γ = 1.86(1), 2V(meas.) = 50(2)°, 2V(calc.) = 59°, XΛa ≃ 15°, YΛb ≃ 0°, and ZΛc ≃ 38°. There is no evidence for optical absorption, pleochroism or dispersion.

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 crystal structures of some nickel hexacyanoferrates (II, III), including mixed compositions containing Na+, K+ and Cs+, were resolved and refined from XRD powder patterns. Data from infrared, Mössbauer and adsorption techniques provided complementary structural information. The crystal structures of Ni3[Fe(CN)6]2⋅16H2O and NiCs2[Fe(CN)6] were refined in space group Fm3m. NiNa2[Fe(CN)6]⋅2H2O and NiK2[Fe(CN)6]⋅2H2O were found to be orthorhombic (space group Pmn21). This structure (Pmn21) results from a distortion around the alkali ion, which appears as a monohydrated interstitial species. On ionic exchange in an aqueous solution containing Cs+, the orthorhombic distortion disappears and the cubic cell is obtained. Cs+ is a large cation and space is not available for interstitial water molecules. This orthorhombic model is also supported by the Mössbauer spectra of the ferrous analogs, FeK2[Fe(CN)6]⋅xH2O and Fe[Pt(CN)6]. © 2004 International Centre for Diffraction Data.

Residual stresses are expected to lead to a linear dependence of the interplanar spacing, d, on sin2ψ (where ψ is the sample tilt) and the stress can be obtained from the slope of this line, As a result of the linear dependence a two-tilt method is often employed to obtain the stress. However, when a specimen is subjected to extensive plastic deformation large deviations from a straight line can occur and a two-point method can lead to an erroneous stress determination. The results reported here show that: (1) this is more likely to occur in homogeneous materials than in multiphase materials (2) the oscillations follow closely the variation in peak intensity due to texture (3) the oscillations are caused by microstresses which are due to an "orientation" effect as suggested by Weidemann,

A simple, easy-to-use procedure has been developed and tested to correct the data and obtain the correct macrostress.

XRD analysis of plasma-vapor-deposited ErT2 films during aging (T decay to 3He) reveals an hkl-dependent unit-cell expansion in which (200) grains expand out-of-plane as much as 0.01 Å more than (111) out-of-plane grains. Texture analysis of an aged ErT2 film reveals a bimodal (111)/(200) out-of-plane preferred orientation. sin2 ψ analysis reveals significant in-plane macro-strain due to 3He bubble formation/growth. The mechanistic origins regarding these observations are also discussed.

The crystal structures of Mek[Fe(CN)6];l·mH2O where Me = Cu, Ni and Co, have been refined from X-ray (CuKa) powder diffraction data by means of Rietveld analyses in space group . The Fe and Me ions are octahedrally coordinated by C and N atoms respectively, forming three-dimensional bimetallic networks with the CN-groups as bridging ligands. The Me(l) sites (k = 2, l=1) and the Fe sites (k = 3, l = 2) are partially occupied. Water oxygens were placed in alternative, empty metal sites.

Diffraction peak broadening analyses were carried out on diffraction profiles of several reflections from hot-pressed α-Al2O3 containing 29, 18 and 10 volume % β-SiC whiskers. The data were analyzed and compared using four different integral breadth methods for microstrain and crystalline size. All four methods gave comparable results, within an order of magnitude, for the microstrains in each phase: (2-15 × 10−4 for the matrix and (6-19 × 10−4 for the whiskers). Microstrains in both matrix and whiskers decreased with decreasing volume % of whiskers for all four methods. Trends in the crystallite size were less consistent but for the matgrix, an incrfease from ∼665 to 1565Å was found with decreasing whisker content using DeKeijser's method.

Standard Reference Materials (SRMs) for determining instrumental line profiles should not exhibit measurable broadening from structural imperfections, but owing the effects of sample transparency and other geometrical effects, the quality of possible SRMs cannot necessarily be assessed satisfactorily with data from a conventional divergent-beam diffractometer. The problem of transparency can be avoided if parallel beam optics is used, as for instance on a synchrotron radiation powder diffraction station employing Parrish (Soller-type receiving slit assembly) geometry. Data from such a configuration are used to compare three SRMs commonly used in line-profile analysis.

The crystal structures of two manganese hexacyanometallates(II), Mn2[Fe(CN)6].8H2O and Mn2[Os(CN)6].8H2O, were refined from X-ray powder diffraction data using the Rietveld method, with the reported structure for Mn2[Ru(CN)6].8H2O used as a structural model. These compounds are isomorphous and crystallize in the monoclinic space group P21/n. Their crystallization water is not firmly bound and can be removed without disrupting the M–C≡N–Mn network. In the dehydrated complexes, the outer cation (Mn) remains linked to only three N atoms from CN ligands while the inner cation (Fe,Os) preserves its coordination sphere. The IR, Raman, and Mössbauer spectra for the hydrated and anhydrous forms are explained based on the refined structures.

Total scattering data of nanocrystalline gahnite (ZnAl2O4, 2–3 nm) have been collected with three of the most commonly used instruments: (i) ID31 high-resolution diffractometer at the European Synchrotron Radiation Facility (ESRF) (Q max = 22 Å−1); (ii) ID11 high-energy beamline at the ESRF (Q max = 26.6 Å−1); and (iii) Empyrean laboratory diffractometer by PANalytical with molybdenum anode X-ray tube (Q max = 17.1 Å−1). Pair distribution functions (PDFs) for each instrument data-set have been obtained, changing some of the parameters, by PDFgetX3 software, with the aim of testing the software in the treatment of different total scattering data. The material under analysis has been chosen for its nanometric (and possibly disordered) nature, to give rise to a challenge for all the diffractometers involved. None of the latter should have a clear advantage. The PDF and F(Q) functions have been visually compared, and then the three PDF sets have been used for refinements by means of PDFgui suite. All the refinements have been made exactly in the same way for the sake of a fair comparison. Small differences could be observed in the experimental PDFs and the derived results, but none of them seemed to be significant.

The program FAULTS has been used to simulate the X-ray powder diffraction (XRD), neutron powder diffraction (NPD), and electron diffraction (ED) patterns of several structural models for LiNi1/3Mn1/3Co1/3O2, including different types of ordering of the transition metal (TM) cations in the TM slabs, different amounts of Li+/NiII+ cation mixing and different amounts of stacking faults. The results demonstrate the relevance of the structural information provided by NPD and ED data as compared with XRD to characterize the microstructure of NMC (LiNi1−y-zMnyCozO2) compounds.

The capacity of goethite for CdII substitution has been explored in a series of synthetic samples prepared from FeIII and CdII nitrate solutions aged 21 days in alkaline media. The total metal content ([Fe]+[Cd]) was 0.071 M in all preparations. The samples have been characterized by chemical and X-ray diffraction analysis; the morphology of the solids is described. The cell parameters for all samples were obtained by the Rietveld fits to the X-ray diffraction data. Refined structures show that for samples prepared at the final molar ratio μCd≤5.50 (expressed as μCd=100×[Cd]/[Cd]+[Fe]), a (Cd, Fe)-goethite is the only crystalline product. In these samples, the unit cell parameters increased as a function of Cd concentration, indicating Cd incorporation in the structural frame. At the preparative ratio, μCd=7.03, the incorporation of Cd in the goethite structure is drastically reduced and a probable Cd-substituted hematite is formed together with the Fe,Cd-goethite.

A new and improved sample holder for use with powder X-ray diffractometry has been developed. This holder is made from a semiconductor grade silicon single crystal cut perpendicular to the [911] axis, i.e., Si (911). This crystal meets most of the basic requirements of an ideal zero background plate, with practically no interference lines. The pattern obtained, by using this crystal as background plate, is very clean, and even very low-intensity Bragg reflections of samples can be detected easily.

The objectives of this paper are: 1. to up-date the manual search system and index book described in 1936 and 1938; 2. to introduce a “work form” which serves to guide the analyst through the procedural steps involved in using the manual search index book and 3. to review briefly the literature on manual search/match systems.

Two of the basic features of the 1936 design of the search index book were first, to divide the “d” range into arbitrarily sized “groups” and “subgroups” rather than using a scale of continuously decreasing “d” values, and second, to use the “d” values of the strongest lines of the diffraction pattern in order of decreasing intensity in making the entries of the standard patterns in the search index book. These two features are still the basis of the design of the 1986 Hanawalt Search Manual published by the JCPD S International Centre for Diffraction Data.

The original use of the search index book at Dow Chemical was to lead the analyst to corresponding patterns among the thousands of Debye films which had been produced and placed on file. The “d” values and intensities of only the three or four strongest lines of the pattern were measured. Comparisons and indentifications were then made visually simply by holding the concerned films together in juxtaposition. Unfortunately, attempts to reproduce usable copies of such Debye films for general reference have not been satisfactory. Therefore, for general usage the diffraction data carried by the film negative or also the data from a diffractometer trace are recorded using the numerical values of the “d” spacings and intensities. These tables of numerical data are then used to represent the diffraction patterns. The search index book for general usage must therefore deal entirely with these numerical values.

The object of the Rietveld method is to produce refined values of crystal structural parameters from powder diffraction data. Many materials of great interest can not be made available for study in single crystal form. This may be because it is not possible to prepare a single-crystal form at all (e.g., human tooth enamel) or because the single-crystal form differs from the polycrystalline form with the properties of interest (e.g., catalysts). Thus, our basic understanding of the atomic scale mechanisms is limited on the structural side by the information that can be deduced from powder diffraction patterns. (Only diffraction and EXAFS are direct probes of the spatial arrangements of atoms.) The Rietveld method has greatly extended the amount of structural detail that we can obtain routinely from powder diffraction patterns. In this method, structural parameters such as atom coordinate, thermal motion, and site occupancy parameters are adjusted in a least-squares refinement procedure until the best fit is obtained between entire calculated and observed powder diffraction patterns, as a whole.