Showing papers on "Rietveld refinement published in 1988"

Quantitative phase analysis using the Rietveld method

Abstract: Quantitative phase analysis of multicomponent mixtures using X-ray powder diffraction data has been approached with a modified version of the Rietveld computer program of Wiles & Young [J. Appl. Cryst. (1981), 14, 149–151]. This new method does not require measurement of calibration data nor the use of an internal standard; however, the approximate crystal structure of each phase of interest in a mixture is necessary. The use of an internal standard will allow the determination of total amorphous phase content in a mixture. Analysis of synthetic mixtures yielded high-precision results, with errors generally less than 1.0% absolute. Since this technique fits the complete diffraction pattern, it is less susceptible to primary extinction effects and minor amounts of preferred orientation. Additional benefits of this technique over traditional quantitative analysis methods include the determination of precise cell parameters and approximate chemical compositions, and the potential for the correction of preferred orientation and microabsorption effects.

Application of the Rietveld Refinement Procedure in Assaying Powdered Mixtures

Abstract: Results are given of an assessment of a Rietveld-type X-ray powder diffraction pattern fitting structure refinement technique for assaying powdered mixtures as an alternative to conventional discrete peak empirical methods of the type described by Klug and Alexander (1974) and Chung (1974). The values obtained for a mixture of corundum and α-quartz, following calibration of the instrument with a profile of the former, indicate that this technique has excellent potential as an analytical tool.

Rietveld refinement of the todorokite structure

Abstract: Affinements utilisant des donnees RX sur poudre obtenus sur des echantillons d'Afrique du Sud et de Cuba. Confirmation de la structure tunnel fondamendale [3×3] et, pour la premiere fois, obtention d'informations sur les positions des cations tunnel et des molecules d'eau

X-Ray Diffraction Study on the Crystal Structure of Nd1+xBa2-xCu3O7-δ

Abstract: Crystal structures in the Nd1+xBa2-xCu3O7-δ system have been investigated by X-ray powder diffraction combined with Rietveld analysis The compound NdBa2Cu3O7-δ is isomorphic with orthorhombic YBa2Cu3O7-δ With the increase of x the orthorhombic distortion decreases, and the compound becomes tetragonal at x=02 The tetragonal structure is isomorphic with the tetragonal form of YBa2Cu3O7-δ Tc of the compounds with x=0 and 005 is above 90 K, which decreases monotonically with x and the compound becomes semiconducting at x=04

Rietveld analysis of Tl2Ba2Can−1CunO4+2n (n=1, 2 and 3) by powder x-ray diffraction

Abstract: Crystal structures of the phases in the Tl-Ba-Ca-Cu-O system determined by powder X-ray diffraction were refined using Rietveld analysis. Three samples having the general composition Tl 2 Ba 2 Ca n −1 Cu n O 4+2 n where synthesized. These were Tl 2 Ba 2 Ca 2 Cu 3 O 10 ( n =3,2223 phase ) with a T c of 116 K, Tl 2 Ba 2 CaCu 2 O 8 ( n =2,2212 phase ) with a T c of 85 K, and Tl 2 Ba 2 CuO 6 ( n =1,2201 phase ) which did not exhibit superconductivity. The results of the Rietveld analysis revealed that as n increased the lattice parameter, a , and the interatomic distance Cu-O(2) became shorter, and the Tl-O and Ba-O layers showed a tendency to become flatter. Possible substitution of about 10% of the Ca-sites with Tl ions in the 2212 and 2223 phases was also suggested.

Acquisition of power diffraction data with synchrotron radiation

Abstract: During the past year, a dedicated triple-axis powder diffractometer has been in routine operation at the Brookhaven National Synchrotron Light Source as a user-oriented facility. The diffractometer is designed to allow easy interchange between energy-dispersive and monochromatic beam experiments. In the latter mode of operation, high resolution data have been collected for a variety of samples with the use of the crystal-analyser technique, and in several cases these data sets have been used successfully for structure solution and Rietveld refinement. Several aspects of data acquisition at a synchrotron beam-line are described, and some of the different types of scattering geometry which have been used are discussed. Simple expressions are given for the instrumental resolution function expressed as the angular variation of peak widths for each of these. The peak shapes observed for a reference sample of Si on the present triple-axis instrument are well described by the convolution of Gaussian and Lorentzian functions, and the angular dependence of the Gaussian component is in excellent agreement with the corresponding calculated instrumental function. One of the most important considerations for each type of experiment is the necessary compromise between intensity Ilnd resolution over a wide range of scattering angles, and some of the available options are discussed. In particular, the use of Ge(440) and LiF(400) analyser crystals gives a focussing minimum at relatively high angles (28 ::::: 50· at 1·54 A), a highly desirable feature for Rietveld analysis of complex structures. Absolute intensities from reference samples of Si and Ce02 are calculated for these and several other scattering configurations involving both fiat-plate and capillary geometry to illustrate this compromise.

Hole concentration compensation effect and superconducting properties of Nd1+xBa2−xCu3O7−δ

Abstract: The superconducting transition temperature Tc and normal-state resistivity have been investigated as a function of x for the Nd1+xBa2-xCu3O7-? system, whose crystal structures have been determined at room temperature by X-ray powder diffraction combined with the Rietveld method. Tc of the samples with x=0 and 0.05 is above 90 K, which decreases monotonically with x except for around x=0.25?0.30 (Tc?35 K) and the sample becomes semiconducting at x=0.40. The orthorhombic distortion of the compounds decreases with x and the compound becomes tetragonal at x=0.20. The variation of Tc with x is insensitive to the orthorhombic-tetragonal phase transition. A correlation of Tc with hole concentration in copper-oxide-type superconductors is discussed based on a possible hole concentration compensation effect of excess Nd.

Neutron-powder-diffraction study of nuclear and magnetic structure in YBa2Cu3-xCoxO7+y with x=0.84 and y=0.32.

Abstract: Neutron powder diffraction has been used to study the crystal structure and magnetic ordering of YBa/sub 2/Cu/sub 3-//sub x/Co/sub x/O/sub 7+//sub y/ with x = 0.84 and y = 0.32. Rietveld refinement of the crystal structure was carried out at 295 K (space group P4/mmm,a = 3.888 A,c = 11.636 A) and showed in particular that Co substitutes in the Cu(1) position of YBa/sub 2/Cu/sub 3/O/sub 7-//sub y/. Long-range, three-dimensional antiferromagnetism was observed up to a Neel temperature of about 405 K. All five detected magnetic peaks could be indexed on a wave vector ((1/2 1) / 2( 1/2) with h,k,l all odd, indicating a body-centered tetragonal magnetic unit cell with a/sub mag/ = a ..sqrt..2, c/sub mag/ = 2c. At 9 K the proposed magnetic structure has moments parallel to c antiferromagnetic ordering within both Cu and Co layers. Adjacent moments in neighboring Cu layers are antiparallel whereas the small moments found in the Co layers are parallel to their adjacent moments in the neighboring Cu layers. The ordered moment was 0.87..mu../sub B/ for the Cu layers and 0.16..mu../sub B/ in the Co layers, respectively. With increased temperature the ordered moments in the Co layers decrease faster than thosemore » in the Cu layer. At room temperature the ordered moment was (0.65(7))..mu../sub B/ for the Cu layers with no detectable ordered moment in the Co layers.« less

The structure and Si,Al distribution of the ultramarines

Abstract: The structure and Si,A1 distributions of various ultramarine pigments have been investigated using X-ray and neutron powder diffraction with Rietveld refinement, and magic-angle-spinning NMR (MAS NMR). The basic structures of the ultramarines studied are found to be very similar: refinement proceeds far better in space group I713m than in PT~3n which indicates that Si and A1 in the framework of ultramarines are disordered. This conclusion is supported by 29Si MAS NMR spectra which contain five signals, rather than a single signal which would be present if AI-O-AI linkages were forbidden. The intensities of the five peaks are consistent with the presence of Si-O-Si, Si-O-A1 and A1-O-AI linkages in the structure. Such disordered Si,A1 distributions in pyrolytically formed ultramarines are in striking contrast to the ordered distributions found in both the naturally formed counterpart lazurite and in hydrothermally synthesized zeolites.

Crystal Substructure of the Bi-Sr-Cu-O System

Abstract: A substructure with a pseudotetragonal unit cell is proposed for a low-Tc superconducting oxide Bi-Sr-Cu-O system on the basis of Rietveld analysis of powder X-ray diffraction data. It is a layered structure having the composition Bi2Sr2CuOy. The relationship between the crystal structure of the Bi-Sr-Ca-Cu-O system and that of Bi-Sr-Cu-O system was discussed.

Crystal Substructure of the Bi-Sr-Cu-O System : Electrical Properties of Condensed Matter

Abstract: A substructure with a pseudotetragonal unit cell is proposed for a low-Tc superconducting oxide Bi-Sr-Cu-O system on the basis of Rietveld analysis of powder X-ray diffraction data. It is a layered structure having the composition Bi2Sr2CuOy. The relationship between the crystal structure of the Bi-Sr-Ca-Cu-O system and that of Bi-Sr-Cu-O system was discussed.

The rietveld method—a historical perspective

Abstract: differences between observed and calculated values was already well established in crystallography. From there it was, in retrospect, only a small step to refrain from using the integrated intensities as observed values but to use the actual measured profile intensities obtained by step scanning the powder diagram. The Rietveld method was first reported at the I.U.Cr. congress in Moscow in 1966. However, it was not until 1975, when it was also applied to X-ray diffraction, that it became widely accepted. Nowadays its use is no longer confined to elastic neutron powder diffraction, but to all diffraction techniques producing complex diffraction diagrams.

Crystal Structure and Superconductivity in Ba2Y1-xPrxCu3O7-y

Abstract: Crystal structures and superconductive properties of the solid solution Ba2Y1-xPrxCu3O7-y (0≤x≤1) are studied Although Ba2Y1-xPrxCu3O7-y has an orthorhombic structure which is isomorphic with Ba2YCu3O7-y, Tc decreases monotonically with increasing Pr concentration, and superconductivity disappears at around x=06 The Rietveld analysis of X-ray powder diffraction data shows that both Cu(1)-O(3) bond length and the structural asymmetry of the Cu(2)O2 planes increase by the substitution of Pr for Y Such structural changes induce the carrier density reduction and localization effects, which may cause the suppression of superconductivity in this system

Bimodal distributions of profile-broadening effects in Rietveld refinement

Abstract: It is demonstrated with computer simulations that a bimodal distribution (narrow and broad) of reflection profile broadening effects, such as crystallite size and microstrain, can lead to several spurious results when the profiles are modeled by single pseudo-Voigt functions in Rietveld refinement (RR), e.g. mixing parameter η > 1 (`super-Lorentzian'), a few observed data points lying consistently above the calculated peak maxima for some reflections, misrepresentation of the background level and shape, and in special cases well defined small observed peaks not seen in the calculated pattern as though they belonged to an additional minor phase. With a bimodal model (two pseudo-Voigt functions) the RR's accurately returned the profile, mixing, and background parameters used in the data synthesis both without and with counting statistical fluctuations simulated in the data. The RR method thus demonstrates remarkable ability to sort out complex specimen characteristics when accurate modeling functions are used.

Evidence for K-substitution in the Tl-sites of superconducting Tl2CaBa2Cu2Oχ: Neutron diffraction studies

Abstract: A comparison of the Rietveld profile refinement of neutron diffraction data of the superconducting compounds Tl-2122 (i.e. Tl 2 CaBa 2 Cu 2 O χ ) and Tl 1 K 1 Ca 1 Ba 2 Cu 2 O y provides evidence that nearly half of the Tl-sites belonging to the pure Tl-2122 structure get substituted by K-ions in Tl 1 K 1 Ca 1 Ba 2 Cu 2 O y . The consequence of this is reflected in a substantial movement of Ba-ions towards the plane of the O(2)-ions in the K-substituted compound.

Simultaneous Structure Refinement of Neutron, Synchrotron and X-ray Powder Diffraction Patterns

Abstract: A technique has been developed for the simultaneous analysis of several powder diffraction data on the basis of the Rietveld method. Counting rates from one specimen at a given temperature taken at neutron, synchrotron or X-ray powder diffractometers are joined to one single data set with weights given by the counting statistics. The structure is refined from this data set with a parameter field containing one structural model and individual zero points, scale factors and FWHM parameters for each of the methods and data sets. A new definition of the residuals is given. The residuals and goodness-of-fit values are calculated for all as well as for the individual data sets.

Determination of Space Group and Refinement of Structure Parameters for La2CuO4-δ Crystals

Abstract: The space group in the orthorhombic phase of La2CuO4-δ was confirmed to be Cmca for both as grown and deoxygenated crystals by using conventional and convergent beam electron diffraction together with high resolution neutron powder diffraction methods. The Rietveld refinements of neutron powder diffraction data determined the structural parameters. Slight differences in lattice constants, positional parameters and occupation factor for oxygen atoms were found between the two crystals.

Neutron Powder Diffraction from Polymorphs of BaPb0.75Bi0.25O3

Abstract: Crystal structures of three polymorphs of the superconducting oxide BaPb0.75Bi0.25O3 have been determined by high-resolution neutron powder diffraction. The compound has been confirmed to form both tetragonal (I4/mcm) and orthorhombic (Ibmm) structures at room temperature. The latter transforms to the monoclinic phase (P21/m) at low temperatures. The structural difference of the three polymorphs has been described by the rotation as well as the distortion of oxygen octahedra surrounding the Pb0.75Bi0.25 cations.

Synchrotron X-ray and neutron powder diffraction studies of the structure of α-CrPO4

Abstract: The crystal structure of α-CrPO4, previously solved from high-resolution synchrotron powder X-ray data, has been refined by the Rietveld method. The peak shape variation is well fitted by a convolution of Gaussian and Lorentzian terms, which incorporate both instrumental and sample-broadening contributions. The structure has also been refined using medium-resolution neutron diffraction data, and the results of the two experiments are compared with a reported single-crystal study. The three sets of coordinates are found to be in good agreement, demonstrating the potential of structure determination and refinement using powder data.

Hexagonal lithium molybdate, LiMoO2: a close-packed layered structure with infinite molybdenum-molybdenum-bonded sheets

Abstract: A new compound, LiMoO/sub 2/, with hexagonal layered structure has been prepared by reaction of Li/sub 2/MoO/sub 4/ with Mo metal at 900/degree/C for 21 days. Neutron powder diffraction Rietveld analysis shows that LiMoO/sub 2/ is isomorphous with /alpha/-NaFeO/sub 2/; space group /bar R/3m, a = 2.8663 (1) /angstrom/, c = 15.4743 (5) /angstrom/, Z = 3. The structure consists of cubic close-packed oxide layers with Mo and Li atoms occupying octahedral sites between alternate layers. Each Mo atom is thus bonded to six other Mo atoms in a hexagonal sheet with d(Mo-Mo) = 2.8663 (1) /angstrom/. The Mo-O and Li-O distances are 2.0520 (9) and 2.146 (1) /angstrom/, respectively. DOS and COOP curves from extended Hueckel band calculations indicate that all Mo-Mo bonding states are filled within the O-Mo-O slabs. 20 refs., 5 figs., 1 tab.

X-RAY DIFFRACTION STUDY ON THE CRYSTAL STRUCTURE OF Sm1+xBa2−xCu3O7−y

Abstract: Crystal structures in solid solution of Sm1+xBa2−xCu3O7−y (X = 0 - 0.4) have been investigated by Rietveld analysis of X-ray powder diffraction data. The structure changes from orthorhombic to tetragonal at x=0.2. With the increase of x, Tc decreases monotonically from 90 K and the compound becomes semiconducting at x=0.4.

Variation of superconducting properties with hole concentration in the solid solution systems of Sm1+xBa2−xCu3O7−δ and Eu1+xBa2−xCu3O7−δ

Abstract: Superconducting transition temperatute Tc and the normal state resistivity of Sm1+xBa2-xCu3O7-δ and Eu1+xBa2-xCu3O7-δ are investigated by changing x in the range of 0~0.40. According to the X-ray powder diffraction at room temperature combined with the Rietveld method, all the samples are single phase. For both compound systems, Tc of the samples with x=0 and 0.05 is above 90 K and decreases monotonically with x, and the compounds become semiconducting at x=0.40. The variation of Tc with x is insensitive to orthorhombic-tetragonal phase transition at around x=0.20. These results are very similar to those of Nd1+xBa2-xCu3O7-δ reported in a series of recent papers by the present authors, where it has been proposed that Tc has a simple correlation with hole concentration. This also suggests that a hole concentration compensation effect by excess trivalent Ln ions substituted for divalent Ba ions commonly occurrs in Ln1+xBa2-xCu3O7-δ (Ln=Nd, Sm and Eu).

Neutron Diffraction Study of Nonstoichiometry in Ba1.5La1.5Cu3Oy

Abstract: The structure parameters of annealed and quenched samples of Ba1.5La1.5Cu3Oy were refined by the Rietveld analysis of TOF neutron powder diffraction data. Partial occupation of an oxygen site at (0, 1/2, 0) causes nonstoichiometry in the oxide. The y values calculated from the occupation factors of oxygen at this site are 7.20 (annealed) and 6.76 (quenched), which are in fair agreement with those determined by iodometry: 7.15 (annealed) and 6.74 (quenched).