The reflection shift δ2Θ caused by a radial shift δr of the sample away from its tangential position at the focusing circle is examined for grazing incidence diffraction and grazing excidence diffraction. Experimental results for residual strain/stress evaluation on thin films using a Bragg–Brentano diffractometer with a grazing incidence equipment are presented. Grazing excidence diffraction is less sensitive to δr than grazing incidence diffraction.

The first object was to develop an X-ray diffractometric method for the detection and quantification of crystalline sucrose when it occurs as a mixture with amorphous sucrose. Standards consisting of amorphous sucrose physically mixed with 1 to 5 weight percent crystalline sucrose were prepared. The sum of the background subtracted integrated intensities of the 12.7°2θ (6.94 Å) and 13.1°2θ (6.73 Å) sucrose diffraction peaks were linearly related to the weight percent crystalline sucrose. The limits of detection and quantitation of crystalline sucrose were 0.9% and 1.8% w/w, respectively. The second object was to study the kinetics of crystallization of sucrose as a function of temperature (at 102, 105 and 110 °C under a water vapor pressure of 0 Torr) and water vapor pressure (17.4, 19.8 and 21.4 Torr at 27 °C). In all cases, the crystallization kinetics was best described by the Avrami-Erofe’ev model (three-dimensional nucleation).

More isostructural compounds would have the same Pearson Symbol Code (PSC) if the hydrogen atom is not counted in computing the numeric portion of the PSC.

A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The existence of such singularities, therefore, has a practical impact on the indexing of powder patterns. For example, when experimental data from ζ-LiBO2 were indexed, two solutions (a rhombohedral and a monoclinic lattice) with approximately the same figure of merit were found. These two lattices yield the same set of unique d-spacings even though they are characterized by different reduced cells with cell volumes in the ratio 2 to 1. From the indexing point of view, both answers are correct. A singularity of this type is common and not a mathematical rarity. In fact, any rhombohedral cell of this kind has a derivative monoclinic subcell, each of which gives the same set of unique calculated d-spacings. In actual cases like this, one can run into a trap. Due to experimental error and input parameters, an indexing program may determine only one of the cells with a high figure of merit. When this happens, it is critical to recognize that another solution exists, especially if one has determined the lower symmetry lattice.

Rietveld quantitative X-ray diffraction analysis of the fly ash Standard Reference Materials (SRMs) issued by the National Institute of Standards and Technologies was performed. A rutile (TiO2) internal standard was used to enable quantitation of the glass content, which ranged from 65% to 78% by weight. The GSAS Rietveld code was employed. Precision was obtained by performing six replicates of an analysis, and accuracy was estimated using mixtures of fly ash crystalline phases and an amorphous phase. The three low-calcium (ASTM Class F) fly ashes (SRM 1633b, 2689 and 2690) contained four crystalline phases: quartz, mullite, hematite, and magnetite. SRM 1633b also contained a detectable level of gypsum, which is not common for this type of fly ash. The high-calcium (ASTM Class C) fly ash, SRM 2691, had eleven crystalline phases and presented a challenge for the version of GSAS employed, which permits refinement of only nine crystalline phases. A method of analyzing different groups of nine phases and averaging the results was developed, and tested satisfactorily with an eleven-phase simulated fly ash. The results were compared to reference intensity ratio method semiquantitative analyses reported for most of these SRMs a decade ago.

A computer program is presented that allows for the analysis of powder X-ray diffraction (XRD) patterns. Some peculiar features of the program are: the aptitude for dealing with diffractograms obtained from semicrystalline polymer samples and the ability to evaluate XRD patterns collected with CPS 120 detectors. The program is available as freeware via anonymous ftp at: ftp.cc.uniud.it under the directory/pulwin/.

The capability of whole-powder-pattern decomposition in the quantitative phase analysis (QPA) of natural products was investigated using three- to six-component mixtures and pottery bodies. Here, the term pottery body means plastic clay suitable for making pottery and it is compounded of ceramic raw materials. Average errors of the weight fractions for each phase were within 1 weight percent in each mixture of natural products. The amounts of reduced oxides in pottery bodies derived from the X-ray diffraction technique were in good agreement with results obtained by X-ray fluorescence analysis. The present procedure does not require knowledge of crystal structures; it appears adequate for the QPA of natural products.

Crystalline phases present in the three NIST SRM Standard Portland cement clinkers 8486, 8487, and 8488 have been quantified from XRD powder patterns, (CoKα radiation), using the full-profile Rietveld method. Included in the Rietveld refinement are rhombohedral (R), monoclinic (M), and triclinic (T) crystal polymorphic forms of C3S, as well as crystal polymorphs of C2S and C3A. It is necessary to specify the phase crystallography including polymorphs, because of the extreme superposition of alite and belite XRD lines in the clinker patterns. Unsatisfactory results occur when only one or two of the C3S polymorphs are used in the Rietveld quantification; best results occur when all three polymorphs for C3S are included. The latter are called RMT-type refinements. The Rietveld full-profile XRD method is as precise as the microscope point-counting (MPC) method, but much less labor-intensive. The Rietveld method can quantify the C3S phase polymorphs, as well as total C3S. Rietveld and MPC methods give the same phase weight percentages for the three NIST standard clinkers. Calculated oxide weight percentages obtained from Rietveld phase weight percentages agree well with oxide percentages determined by XRF analysis. Bogue mineral weight percentages do not agree with Rietveld or MPC data, while transformation of the Bogue mineral percentages to oxides does not compare well with XRF analysis.

An external standard method using mica for angular calibration of powder diffractometers is described. This is useful especially when standard referee materials certified by the US National Institute of Standards and Technology are not accessible.

The powder pattern of calcium galactarate tetrahydrate (CaC6H8O8·4H2O) is presented. The compound was found in white wine stored for 4 years. A Rietveld refinement using the atomic coordinates from a single crystal study as starting values was refined with 55 parameters and without preferred orientation to RB=5.97%, RF=4.44%, Rp=10.39%, and Rwp=13.43% for 84 reflections. Crystal data: Mr=320.14, orthorhombic, Pcan, a=7.3359(1) Å, b=11.6296(3) Å, c=15.0978(6) Å, V=1288.05(6) Å3, Z=4, Dx=1.651 g/cm3, λ(CuKα1)=1.54060 Å, μ=46.76 cm−1.

The crystal structure of the new ternary phase CuSnTi is determined by full profile Rietveld analysis of the powder diffractogram. 104 reflections were refined to a final RBragg value of 5.60%. CuSnTi crystallizes with the spacegroup P63/mmc and is isostructural to InNi2. The lattice parameters are a=0.439 555(5) nm and c=0.601 505(9) nm.

Extensive analyses of low-temperature powder x-ray diffraction data for spinel LiMn2O4 (Fd3¯m at room temperature) make it clear that two structural phase transitions occur: first around 285 K from cubic to orthorhombic, second around 65 K from orthorhombic to tetragonal. At temperatures under 285 K, superlattice peaks appear in the diffraction pattern that were successfully indexed by tripling the a and b axes of the spinel unit cell. At 250 K, the unit cell is face-centered orthorhombic, Fddd, F2dd, or Fd2d, with a=24.855(1), b=24.755(2), c=8.2014(3) Å, V=5046.1(4) Å3, Dx=4.284 g/cm3, Z=72. The unit cell at 30 K was confirmed to be body-centered tetragonal I41/amd or I41/a, with a=17.5176(3), c=8.1961(2) Å, V=2515.1(1) Å3, Dx=4.298 g/cm3, Z=36.

The crystal structure of the two isostructural rare earth tungstates Ln6WO12 (Ln=Y, Ho) has been refined by the Rietveld method from X-ray powder diffraction data. They crystallize with a three-dimensional rhombohedral structure (S.G. R3¯ and Z=3 for the R-centered setting) closely related to that of the binary oxides Ln7O12 and deriving from the ideal fluorite structure. Final refinements, with isotropic thermal motion for each atom, resulted in profile and structure factors Rwp=0.166, RF=0.037 with Ln=Y and Rwp=0.121, RF=0.040 with Ln=Ho. The rare earth element is sevenfold coordinated with Ln–O bond lengths ranging from 2.19 to 2.70 Å for Y6WO12 and from 2.18 to 2.68 Å for Ho6WO12; the coordination polyhedron may be described as a monocapped trigonal prism. The tungsten atom is located at the center of a WO6 octahedron with a unique W–O distance of 1.98 and 1.92 Å for Y6WO12 and Ho6WO12, respectively.

The crystal structure of the low-temperature oxidized form of Sr49.5Ca16.5Bi34O151 has been determined using a combination of neutron, synchrotron, and laboratory X-ray powder diffraction data. The structure is pseudo-orthorhombic; systematic absences and successful refinement indicated the true structure to be monoclinic, with space group P2l/n. Structural refinement using only neutron powder data yielded the lattice parameters a=8.38 898(29) Å, b=5.99 334(21) Å, c=5.89 586(20) Å, β=89.997(8)°, and V=296.43(3) Å3. This compound is a distorted perovskite phase [described in the perovskite ABO3 formula as Sr(Bi0.7Ca0.3)O3] with ordering of the M-site cations, resulting in the formula A2MM′O6. In this ordered structure, the A sites are solely occupied by Sr, the M sites mainly by Bi, while on the M′ sites Bi and Ca are distributed in an approximate ratio of 2:3. The MO6 and M′O6 octahedra share corners, and are tilted with respect to the neighboring layers with an angle of ∼15° around all three axes. The tilt system symbol is a+a−a− according to Glazer notation. All Bi ions are in the 5+ oxidation state.

New powder X-ray diffraction data for magnesio-, ferro-, and manganaxinite, obtained from samples closely corresponding to the three end-members of the axinite mineral group, were obtained using a conventional Bragg–Brentano diffractometer. Space group is P 1¯. Powder patterns were indexed using Peacock's normal orientation, which gave: a=7.1381(3), b=9.1626(4), c=8.9421(4) Å, α=91.903(4), β=98.105(3), γ=77.468(4)° for magnesioaxinite; a=7.1479(4), b=9.1962(5), c=8.9576(4) Å, α=91.857(4), β=98.177(4), γ=77.359(4)° for ferroaxinite, and a=7.1849(4), b=9.2152(5), c=8.9765(4) Å, α=91.761(4), β=98.153(4), γ=77.150(4)° for manganaxinite. Peacock's orientation has been adopted in all recent structural and crystal chemical studies of axinite, but it differs from that reported on the JCPDS cards (29-344, 27-076 and 27-084, respectively). New data include an increased number of indexed peaks.

The new phase LaCr(NO3)6·12H2O was synthesized from a nitric acid solution. The symmetry is trigonal with the parameters a=10.9564(4) Å and c=16.835(1) Å [V=1750.2(2) Å3, space group R-3]. The thermal decomposition, studied by temperature-dependent X-ray powder diffraction and thermogravimetry, gave successively the cubic phase LaCr(NO3)6·6H2O [a=12.301(1) Å, space group P213] and the chromate(V) LaCrO4. The reduction of LaCrO4 to LaCrO3 occurred at a temperature depending on the oxygen pressure in the reaction atmosphere.

The principal aim of this study was to assess a new approach to the characterization of uroliths using synchrotron radiation. To achieve this, a detailed investigation of the crystalline nature of a human bladder urolith has been undertaken. Changes in the phase composition and crystalline mineral nature have been measured from the urolith core center to its outer surface. Data were collected using a microbeam, synchrotron probe, and image plate. Rietveld analysis has enabled us to determine that the unit cell dimensions of the majority phases (anhydrous uric acid and calcium oxalate monohydrate) are significantly greater in the core region but become progressively smaller from the outer to inner regions. The crystallites of both phases are also shown to possess significant radial orientation which varies through the urolith and reaches a maximum at a point of principal fracture. The analysis has also allowed us to study the change in average crystallite morphology; the crystallites of both phases are shown to decrease in size toward the outer parts of the urolith although this is in a nonuniform fashion. Evidence of calcium oxalate dihydrate was also found, but only within the outermost region of the urolith.