Commercial anodes with different state of charge are investigated by X-ray diffraction technique using Rietveld method for data collected with standard laboratory equipment. It is shown that full profile refinement gives good approximation for quantitative description of the charge/discharge process and may be used for estimation of real state of charge (SoC). Careful analysis of the diffraction profile with Rietveld method allows us to quantitatively distinguish the contribution of different LixC6 phases and estimate the real SoC.

This paper contains a review and explanation of the super conducting Ruddlesden-Popper phases in the systems Bi-Sr-Ca-Cu-O and Tl-Ba-Ca-Cu-O. Calculated powder X-ray patterns for the phases Bi-2201, 2212, 2223, and 2234 (where the numbers refer to the stoichiometric ratios of Bi:Sr:Ca:Cu) and Tl-1201, 1212, 1223, 1234, 2201, 2212, 2223, and 2234 (here the numbers refer to the molar ratios of Bi:Ba:Ca:Cu) generated from the reviewed crystal structures are presented. Observed powder patterns for Tl-2201, Tl-2212, Bi-2201 and Bi-2212 are included and compared to the calculated patterns of these phases.

A perfect general purpose standard specimen for high accuracy line-profile analysis is shown to be an illusion. Balancing the partly contradictory requirements, an optimum standard specimen for a parafocusing diffractometer is developed. To obtain the optimum standard specimen, a 5–10 μm particle size fraction is taken from the NIST certified Si powder SRM640a, about 1.5 mg/cm2 of this powder is uniformly deposited on a (510) oriented Si single-crystal wafer and the assembly is heat treated for 2 h at 1273 K to remove lattice imperfections. All procedures necessary are precisely given, easily applicable, and reproducing. For the present standard specimens, the random errors due to crystal statistics are quantified and shown to be acceptable for spinning specimens; the systematic errors due to residual size and transparency broadening are determined semi-empirically and can be eliminated, if desired. Thus the proposed optimum standard specimen allows the determination of instrumental line profiles free from systematic errors and with random errors in the line width of the order of 0.001 °2θ, allowing a full use of the capacities of modern diffractometers and data evaluation procedures.

An orthorhombic fully ordered structural model is proposed for vaterite [space group Ama2, a=8.4721(5) Å, b=7.1575(7) Å, c=4.1265(4) Å, Z=4, and V=250.23(4) Å3]. It is based on a microtwinning hypothesis, with three domains rotated by 120° along the orthorhombic a axis, regenerating a pseudohexagonal habit. The solution came from direct space ab initio calculations applied to the powder diffraction data. However, five weak superstructure reflections seen in single-crystal and powder diffraction experiments, leading to a six times larger unit cell, are still unexplained.

Measurements of X-ray diffraction patterns of high-Tc superconductor and tungsten–carbide powder samples using a Bragg–Brentano diffractometer showed systematic variations of the intensities for different preparation conditions. For specimens with high surface roughness, an angle-dependent decrease of the intensities is observed which is caused by the microabsorption of the X-rays due to the microstructure of the powder sample. In Rietveld analysis, the thermal parameters are strongly influenced by this effect and may tend to negative values. A realistic description of the surface structure of flat powder samples is proposed. Using an analytical approximation for the microabsorption effect and its dependence on the microstructural parameters the Rietveld refinement yields reasonable values for the thermal parameters.

So-called alite is a solid solution of tricalcium silicate Ca3SiO5 with a few percent of impurities. It constitutes the major phase of anhydrous Portland cement. In industrial compounds, alite crystallizes into two monoclinic forms designated M1 and M3. The possibility of correlation between the crystallographic structure of the clinker and its reactivity is still an open question. The answer of such a question involves a proper quantitative analysis of the various phases—including the exact alite polymorph—of the industrial product. The rather similar structure of the two alites makes it difficult to distinguish them from their XRD patterns. This paper shows that five angular windows in the X-ray diffraction patterns can be used with synthetic alites as well as industrial compounds, to identify the nature of the actual polymorph (M1 or M3) present and the structural model to be used (with or without superstructure) in subsequent Rietveld analysis of the data.

Rietveld refinement using synchrotron powder X-ray diffraction data revealed that the crystal structure of synthetic Na-birnessite is triclinic (C1), not monoclinic as was previously reported. The Mn–O octahedra have elongated axial bonds, consistent with Jahn–Teller distortion resulting from partial occupancy by Mn3+. Mean Mn–O distances indicate that Mn sites are ∼2/3 Mn4+ and ∼1/3 Mn3+. The interlayer Na cations and H2O molecules occupy a split site that shows evidence of considerable disorder.

Synthesis of high-purity, single-phase gallium nitride (GaN) powder has been achieved by reacting molten Ga with flowing ammonia (NH3) in a hot wall tube furnace. The optimum temperature, NH3 flow rate, and position of the boat in the hot wall tube furnace relative to the NH3 inlet for the complete reaction to pure GaN for our system were 975 °C, 400 standard cubic centimeters per minute (seem) and 50 cm, respectively. The X-ray diffraction (XRD) data revealed the GaN to be single phase with a = 3.1891 Å, c = 5.1855 Å, in space group P63mc, Z=2 and Dx =6.089 g cm−3. Scanning electron microscopy revealed a particle size distribution in the crushed material between 1 and 5 μm with most of the particles being ≍1 μm.

The existence of glass or amorphous component in Portland cement clinker has been questioned for a long time. However, besides the crystalline phases, there are reports in the literature of noncrystalline material in cement clinker, which is considered to be the residue of the melt that has failed to crystallize. Absolute phase abundances were determined in this study by Rietveld refinements with laboratory X-ray data, using both internal and external phase composition standards. The results clearly demonstrate the existence of an amorphous component in Portland cement clinker. The presence of an amorphous component was also apparent from diffraction data for clinker from which the silicate phases had been chemically removed, using both laboratory X-ray and synchrotron radiation patterns.

M2(dhtp)·nH2O (M = Mn, Co, Ni, Zn; dhtp = 2,5-dihydroxyterephthalate), known as MOF74, is a family of excellent sorbent materials for CO2 that contains coordinatively unsaturated metal sites and a honeycomb-like structure featuring a broad one-dimensional channel. This paper describes the structural feature and provides reference X-ray powder diffraction patterns of these four isostructural compounds. The structures were determined using synchrotron diffraction data obtained at beam line 11-BM at the Advanced Photon Source (APS) in the Argonne National Laboratory. The samples were confirmed to be hexagonal R 3 (No. 148). From M = Mn, Co, Ni, to Zn, the lattice parameter a of MOF74 ranges from 26.131 73(4) Å to 26.5738(2) Å, c from 6.651 97(5) to 6.808 83(8) Å, and V ranges from 3948.08 Å3 to 4163.99 Å3, respectively. The four reference X-ray powder diffraction patterns have been submitted for inclusion in the Powder Diffraction File (PDF).

The following sixteen reference patterns of boride, silicide, nitride and oxide ceramics represent the second group of reference patterns measured at the National Bureau of Standards under the project “High Quality Reference Patterns and Total Digital Powder Patterns of Technologically Important Ceramic Phases”. Included in the sixteen reference patterns are data for two high Tc superconducting oxide phases (CuSr0.2La1.8O4 and Ba2Cu3YO7) plus one related phase (BaCuY2O5). In addition to these new phases, five other patterns represent phases previously not contained in the PDF and eight represent major corrections to data in the file. The general methods of producing these X-ray powder diffraction reference patterns are described in this journal, Vol. 1, No. 1, pg. 40 (1986).

Silver sulfide, Ag2S, is most commonly known as the tarnish that forms on silver surfaces due to the exposure of silver to hydrogen sulfide. The mineral acanthite is a monoclinic crystalline form of Ag2S that is stable to 176°C. Upon heating above 176°C, there is a phase conversion to a body-centered cubic (bcc) form referred to as argentite. Further heating above 586°C results in conversion of the bcc phase to a face-centered cubic (fcc) phase polymorph. Both high-temperature cubic phases are solid-state silver ion conductors. In situ high-temperature X-ray diffraction was used to better understand the polymorphs of Ag2S on heating. The existing powder diffraction file (PDF) entries for the high-temperature fcc polymorph are of questionable reliability, prompting a full Rietveld structure refinement of the bcc and fcc polymorphs. Rietveld analysis was useful to show that the silver atoms are largely disordered and can only be described by unreasonably large isotropic displacement parameters or split site models.

A time-resolved powder diffraction study of the crystallisation of porous metal organic framework materials with the CPO-27 structure ([M2(dhtp)(H2O)2]·8H2O where, dhtp=2,5-dioxoterephthalate) using the energy dispersive X-ray diffraction method is described. Crystallisation under solvothermal conditions is performed between 70 - 110 °C from clear solutions of metal salts (M=Co2+ or Ni2+) and 2,5-dihydroxyterephthalic acid in a mixture of THF-water in sealed reaction vessels, using both conventional and microwave heating. Integration of Bragg peak areas with time provides accurate crystallisation curves, which are modelled using the method of Gualtieri to determine rate constants for nucleation and for growth and then, by Arrhenius analysis, activation energies. Crystallisation is determined to be one-dimensional, consistent with the elongated morphology of the crystals produced in these reactions. With conventional heating the Co-containing CPO-27 crystallises more rapidly than the isostructural Ni-containing analogue and analysis of the kinetic parameters would suggest a complex multi-step crystallisation process. The effect of microwave heating is upon activation energies: the values for both nucleation and for crystal growth are lowered compared to reactions using conventional heating.

The Rietveld method is increasingly used for amorphous portion determination. This article describes the quantification of amorphous portions using an internal standard in a formal mathematical way. From a set of basic assumptions and postulations, equations for the amorphous portion quantification, the optimum amount of internal standard, and the slope of the amorphous portion calculation formula were derived. With this tool set, the influence of the method principle on the analytical uncertainty is discussed. It is shown that the amount of internal standard has a strong influence on the precision of the amorphous portion determination. A poor choice can make the determination impossible, while a clever choice can enhance the precision compared to the precision of the Rietveld refinement.

A detailed neutron powder diffraction study of the atomic structure of α-Bi2O3 at high temperatures using the Rietveld method was performed to clarify the nature of the unusual magnetic behavior and the origin of the high temperature dielectric anomalies of α-Bi2O3 in the temperature interval 300–700 K. Analysis of obtained experimental data shows that there are no evidence of a structural phase transition in α-Bi2O3 between 295 and 660 K. The observed high temperature dielectric anomalies in α-Bi2O3 are evidently governed by changes in the electron subsystem of the bismuth oxide.

Materials in the Ti–Al–C ternary system commonly contain three coexisting phases, Ti3AlC2, Ti2AlC, and TiC. Quantitative phase analysis in this ternary system was investigated using X-ray diffraction. First, nonoverlap diffraction peaks were selected: the (002) peak at 2θ=9.5° for Ti3AlC2 (I∕I0=26.5), the (002) peak at 2θ=13.0° for Ti2AlC (I∕I0=39), and the (111) peak at 2θ=35.9° for TiC (I∕I0=78), respectively. Then, based on the mixing-sample method without internal standards, a set of equations was derived for determining the amounts of Ti3AlC2, Ti2AlC, and TiC in a sample using the intensities of the selected diffraction peaks. Finally, the applicability and error sources for this method were investigated. The method is simple and straightforward, and is applicable to the entire Ti–Al–C ternary system, since the derivation of this equation group is self-checking.

Phases of general formula (RE, A)2M3O7 (RE=lanthanide, A=Ca, Sr, Ba; M=Ga, Al) are of interest for their nonlinear optical properties and have potential as solid state lasers. Their structures have been refined using X-ray and neutron diffraction data and are related to gehlenite, Ca2Al2SiO7, with M cations occupying Al and Si sites and RE and A cations sharing the Ca site with no evidence for ordering, although they occur in the ratio 1:1 because of stoichiometry; the M cations are tetrahedrally coordinated. (RE, Ba)2M3O7 compounds cannot be synthesized for M=Al or for RE cations smaller than Sm; this limitation is believed to be due to size mismatch between cations within the structure.

Single crystals of gypsum were studied in a diffractometer equipped with a CCD two-dimensional detector. The microstructure of the crystal gave wide poorly shaped spots showing sometimes curved streaks around the spots, which made the integration process very difficult, yielding a low quality structure. The crystal structure and microstructure of gypsum has been studied by high-resolution synchrotron powder diffraction of a ground single crystal. The intensities in the synchrotron powder pattern can be reliably fitted although the peak shape displays anisotropic peak broadening. The Rietveld results for gypsum were a=6.522 91(3) Å, b=15.197 63(9) Å, c=6.522 91(3) Å, β=118.479(1)°, V=494.536(5) Å3 and Z=4 (s.g. I2/c) with RWP=5.39% and RF=1.64%. We have also studied the influence of the structural description used for gypsum in a synchrotron Rietveld quantitative phase analysis of a standard mixture containing 50 wt % of CaSO4⋅2H2O and Al2O3. Finally, the effects of the type of preferred orientation correction for laboratory X-ray powder data are also discussed. © 2004 International Centre for Diffraction Data.

Polycapillary optics are utilized in a wide variety of applications and are integral components in many state of the art instruments. Polycapillary optics operate by collecting X-rays and efficiently propagating them by total external reflection to form focused and parallel beams. We discuss the general parameters for designing these optics and provide specific examples on balancing the interrelations of beam flux, source size, focal spot-size, and beam divergence. The development of compact X-ray sources with characteristics tailored to match the requirements of polycapillary optics allows substantial reduction in size, weight, and power of complete X-ray systems. These compact systems have enabled the development of portable, remote, and in-line sensors for applications in industry, science and medicine. We present examples of the utility and potential of these optics for enhancing a wide variety of X-ray analyses.

The aim of this work was to design, construct, install, and commission an on-line, X-ray diffraction (XRD) analyzer capable of continuously monitoring phase abundances for use in process plant control. This has been achieved through a joint project between CSIRO Minerals and Fuel & Combustion Technology Pty. Ltd. with an instrument designed for use in a Portland cement manufacturing plant. Key factors in tailoring such an instrument to the cement industry were (i) the handling and presentation of a dry sample and (ii) the development of an analytical method suitable for the complex suite of phases contained within Portland cement. The instrument incorporates continuous flow of sample through the diffractometer using a purpose-built sample presentation stage. The XRD data are collected simultaneously using a wide range (120° 2θ) position sensitive detector, thus enabling rapid collection of the full diffraction pattern. The data are then analyzed using a Rietveld analysis method to obtain a quantitative estimate of each of the phases present. The instrument is controlled by a PC linked to the diffractometer through a purpose built interface. The phase abundance information is then transmitted to the central computer in the cement plant where it can be used for the control of mill parameters such as temperature and retention times as well as gypsum feed rate.