X-ray Line-broadening Research Articles

A common theory of line broadening and rocking curves

X-ray diffraction peak broadening is discussed in terms of line broadening and rocking-curve broadening in a novel theoretical description. The nonlocal strain tensor is factorized by using the method of polar decomposition instead of the more conventional separation into symmetrical and antisymmetrical components. A number of X-ray line-broadening and rocking-curve experiments on the same single crystals or individual grains in bulk polycrystals prove that plastic deformation produces strained subgrains mutually rotated by rigid-body rotations. The novel theoretical description appropriately accounts for the rigid-body rotation and strain at the same time and provides straightforward separation of the two effects of line and rocking-curve broadening in the radial and normal directions of the diffraction vector. The mathematical results are discussed in terms of experiments of X-ray diffraction, Laue asterism and electron backscatter diffraction. From the experimental results it is shown that the simultaneous evaluation of line and rocking-curve broadening provides qualitative information about the redundant and geometrically necessary character of dislocations, not available if only one or the other is accessible.

Strain Induced X-Ray Line Broadening and Morphological Investigation on Silver Nanoparticles

Strain Induced X-Ray Line Broadening and Morphological Investigation on Silver Nanoparticles

Microstrain and Defects in Polycrystalline Zn1-xMgxO (0 ¡? x ¡? 0.15) Studied by X-ray Diffraction and Optical and Raman Spectroscopies

The properties of polycrystalline wurtzite Zn_{1-x}Mg_{x}O (0 <= x <= 0.15) have been studied, by powder X-ray diffraction, including an analysis of the X-ray line-broadening, and by luminescence, absorption, and Raman spectroscopies. We have previously established from synchrotron X-ray difffraction that with increasing Mg-concentration, the c-axis compresses, and the off-center cation displacement within each tetrahedral (Zn,Mg)O_{4} unit decreases. Here we perform a size-strain line-broadening analysis of the XRD peaks, which reveals that the Mg-substitution reduces the coherent crystallite size and also develops the lattice microstrain. The optical properties of the samples have been characterized by diffuse-reflectance spectroscopy and fluorimetry. Both the optical band gap and the band-edge emission energies gradually increase with the Mg-concentration in Zn_{1-x}Mg_{x}O. The Mg-substituted samples show broader band tails near the absorption edge, due to the increase of crystal imperfections. The peak broadening of the E_{2}{high} Raman mode, upon the Mg-substitution, is also ascribed to the phonon shortening lifetime mechanism via crystal defects.

Structural Characterization of Nanostructured Nickel Coated Carbon Fibers by X-Ray Line Broadening

Structural Characterization of Nanostructured Nickel Coated Carbon Fibers by X-Ray Line Broadening

Characterization of Dislocation Structures in Hexagonal Close-Packed Metals by X-ray Line-Broadening Analysis

Characterization of Dislocation Structures in Hexagonal Close-Packed Metals by X-ray Line-Broadening Analysis

Reduction of MgO-supported iron oxide: formation and characterization of Fe/MgO catalysts

Fe-oxide MgO (5–30 mol% Fe) was prepared by calcination of coprecipitated precursors. Reducibility in H 2 at 693 K was measured gravimetrically and volumetrically. All samples yielded metallic iron (Fe o) suitable for catalytic use but much unreduced Fe 2+ remained, stabilized by the MgO. The mean particle size of the supported metallic iron was determined by X-ray line-broadening and its surface area by CO chemisorption. Mössbauer spectroscopy confirmed the presence of Fe o, Fe 2+ and Fe 3+ in the reduced material.

Dislocation Density and Long Range Internal Stresses in Heavily Cold Worked Cu Measured by X-ray Line Broadening

A well proven method of high resolution X-ray line profile analysis is applied to large-strain straight rolled samples of polycrystalline copper. Both the obtained dislocation densities and long-range internal stresses show a monotonous increase within the strain stage IV, and then a levelling off in stage V. The local stresses of cell walls and cell interiors are found to increase within stage IV even in relation to the macroscopic stress. Together with the measured values of volume fraction of cell walls, the strengthening in stage IV turns out to arise mainly from the cell interior, although it is clearly related to the increase of total dislocation density and not so much to dislocation rearrangements which enhance the stress field.

A Monte Carlo Estimate of Crystallite-Size and Microstrain Distribution Functions from X-ray Line Broadening

A method of X-ray line-broadening analysis is presented whereby the coherence length and microstrain contributions can be calculated using a Monte Carlo interference-function-fitting algorithm. The method is based on the `column-like' crystal model and can be applied to both single and multiple-order reflections. Examples on simulated diffraction peaks, deformed face-centred-cubic palladium powder and heavily textured deformed body-centred-cubic low-carbon-steel sheets are presented and comparisons are made with currently applied methods.

Internal Stresses and Microstructure in Plastically Deformed Metals and Alloys as Revealed by Asymmetric X-Ray Line Broadening

Internal Stresses and Microstructure in Plastically Deformed Metals and Alloys as Revealed by Asymmetric X-Ray Line Broadening

Characteristically Asymmetric X-Ray Line Broadening, an Indication of Residual Long-Range internal Stresses

Characteristically Asymmetric X-Ray Line Broadening, an Indication of Residual Long-Range internal Stresses

Long-range internal stresses and asymmetric X-ray line-broadening in tensile-deformed [001]-oriented copper single crystals: The correction of an erratum

Long-range internal stresses and asymmetric X-ray line-broadening in tensile-deformed [001]-oriented copper single crystals: The correction of an erratum

Selective X-Ray Line Broadening in the Goethite-derivedhematite Phase

La transition goethite-hematite au cours d'une deshydroxylation thermique passe a travers une sequence de changements encore inexpliques. On etudie un grand nombre de specimens de goethite synthetises par differentes methodes pour demontrer l'independance de certaines caracteristiques de phase hematite avec leurs caracteristiques initiales. On analyse les taux des facteurs de structure pour etablir une correlation entre ces valeurs

Characterization of barium titanate fine powders formed from hydrothermal crystallization

A detailed evaluation of size, shape and microstrains of BaTiO 3 crystallites produced by hydrothermal crystallization at 90 – 180 °C and 0.1 – 1.2 MPa, from amorphous TiO 2· xH 2O (3 < × < 8) gel and aqueous Ba(OH) 2 is presented, using X-ray line-broadening and TEM studies. Whereas the concentration of Ba(OH) 2 and the acceptor impurities affect the crystallite shape, the stoichimetry with respect to Ba/Ti, donor as well as acceptor impurities, and the temperature of crystallization influence the microstrains. It is shown that strains in the crystallites are related to the point defects in the lattice. Compensation of the residually present hydroxyl ions in the oxygen sublattice by cation vacancies results in strains leading to metastable presence of the cubic phase at room temperature. Studies on the diffuse phase transition behaviour of these submicron powders show that the stable tetragonal phase is produced only on annealing at high temperatures where the mobility of cations vacancies are larger. Heat-treatment reduces anisotropy and strain in undoped samples, whereas annealing is less effective in doped materials. Comparison of the crystillite size by TEM showed better agreement with the Warren—Averbach method.

Preparation and characterization of stable copper/zinc oxide/alumina catalysts for methanol systhesis

A series of Cu/ZnO/Al 2O 3 catalysts for the low pressure methanol synthesis has been prepared by coprecipitation with a sodium carbonate solution from solutions of a mixture of the corresponding metal nitrates, followed by drying, calcination and reduction. The catalysts and their precursors were analyzed by techniques like X-ray diffraction (XRD), X-ray line broadening (XLB), differential thermal analysis (DTA), chemical analysis, adsorptive decomposition of N 2O and B.E.T.-measurements. The catalytic activity for the methanol synthesis was determined in a flow reactor under industrial conditions. Depending on the metal ion ratio in the initial metal nitrate solutions different compounds were formed during coprecipitation, like rosasite (Cu, Zn) 2(OH) 2CO 3, malachite, Cu 2(OH) 2CO 3, Cu, Zn-hydrotalcite, (Cu, Zn) 6Al 2CO 3(OH) 16.4H 2O and a ternary compound which we called roderite. Its structure is unknown and it contains, besides Zn 2+, up to 28 at % Cu 2+ and up to 17 at % Al 3+. Addition of 7 at % Mg 2+ stabilizes the Cu, Zn-hydrotalcite structure but leads to a drastic decrease in catalytic activity. The rate of methanol production depends on the phase composition of the precursors. Rosasite containing precursors give the highest activity; hydrotalcite proves to be an excellent catalyst stabilizer which evokes the formation of small Cu and ZnO particles. Mg 2+ inhibits methanol production.

Long-range internal stresses and asymmetric X-ray line-broadening in tensile-deformed [001]-orientated copper single crystals

Abstract Copper single crystals oriented for multiple slip with [001] axes have been deformed in tension and investigated by X-ray line-broadening measurements using {002} Bragg reflections. The intensity distributions of the broadened line profiles of the deformed crystals exhibit an asymmetry whose ‘sign’ depends on the particular reflection used. It is shown that the asymmetric line profiles are due to the superposition of two mutually displaced symmetrically broadened line profiles. These two sub-profiles can be ascribed to the material located in the cell walls and in the cell interiors of the dislocation cell structure, respectively. The mutual displacements of the sub-profiles are evaluated quantitatively in terms of deformation-induced long-range internal stresses, which aid the applied stress in the cell walls and oppose it in the cell interiors. It is shown by a simple model that the long-range internal stresses are a necessary consequence of the plastic strain mismatch between the soft cell int...

Metal-support interactions between iron and titania for catalysts prepared by thermal decomposition of iron pentacarbonyl and by impregnation

Metallic iron particles supported on titania were prepared by aqueous incipient wetness impregnation, nonaqueous impregnation, and thermal decomposition of iron pentacarbonyl. For iron loadings between 1 and 5 wt%, only the last technique produced metallic iron particles smaller than 10 nm, as judged by X-ray line-broadening and CO chemisorption measurements. During the decomposition of iron pentacarbonyl at 380 K, Mössbauer spectroscopy showed that Fe 2+ and zero-valent iron (e.g., subcarbonyl species) were formed on titania, presumably due to the interaction of iron carbonyl with hydroxyl groups on the support surface; however, these iron species were reduced to metallic iron particles in hydrogen at ca. 700 K. The ammonia synthesis apparent activation energy, E A, and ammonia partial pressure dependence, m, for all Fe TiO 2 catalysts reduced at ca. 700 K were similar to those values for metallic iron supported on silica or magnesia. Upon increasing the reduction temperature to ca. 800 K, the values of E A and m increased for Fe TiO 2 catalysts with iron particles are large as 20 nm. Room temperature Mössbauer spectra of the Fe TiO 2 catalysts after reduction at either 700 or 800 K indicated that the majority or the iron was present as α-Fe, with Mössbauer parameters essentially identical to bulk metallic iron. Accordingly, the metal-support interaction between iron and titania, which is initiated by reduction at 800 K and is responsible for the changes in ammonia synthesis kinetics, is due to titanium species at the surface of the metallic iron particles. This interaction, which also suppresses CO chemisorption, can be partially destroyed by exposure of the sample to air at room temperature. Possible modes of transport of titanium species during catalyst preparation, reduction, and oxidation are discussed.

Decomposition of formic acid on copper, nickel, and copper-nickel alloys: I. Preparation and characterization of catalysts

Copper-nickel powders were prepared and shown to be monophasic, homogeneous alloys. Their surface composition was determined by strong hydrogen chemisorption with an assumed surface stoichiometry of 1:1 hydrogen to Ni. The surface analysis agrees with previous experimental and theoretical estimates. Nickel particles supported on silica were prepared. The metal dispersion was calculated from the uptake of strongly adsorbed hydrogen with a 1:1 stoichiometry of hydrogen to Ni surface atoms. The extent of Ni reduction, determined from dioxygen uptake measurements, was in excess of 80%. The titration of Cu surface atoms with oxygen from nitrous oxide on powders and alumina-supported Cu agrees with results of BET N 2 physisorption and X-ray line-broadening, respectively, when a surface stoichiometry of 2:1 Cu to O is assumed.

中央構造線に近接する花崗岩類の変形

The deformation of quartz in granitic rocks up to 5km from the Median Tectonic Line (MTL) was investigated by X-ray diffraction. The X-ray line broadening of the pulverized quartz grains (5-20μm) is related to the strain distribution arond dislocation in quartz grains. In order to determine dislocation densities, a relation has been derived between X-ray line broadenings and dislocation densities. Using the relation, the magnitude of the differential stress level has been found to vary from 50 to 150 MPa(the corresponding dislocation density ranges in 5.9x107 to 5.1x108 cm-2). The differential stress near MTL(less than 500m from the MTL) was about 130 MPa, but that away more than 2km from MTL was about 60 MPa. This change of the differential stress as a function of distance from MTL reflects the stress state of the last tectonic event.

Magnetite surface area titration using nitric oxide, II. Pretreatment effects and silica-supported samples

The use of NO adsorption for determination of Fe3O4 surface areas has been examined and extended, from earlier work on unsupported samples, to silica-supported Fe3O4. Gravimetric studies confirm earlier suggestions that the irreversible NO adsorption uptake on unsupported Fe3O4 is dependent upon sample pretreatment. Long (ca. 24 h) vacuum treatment at 650 K leads to increased apparent NO adsorption uptakes due to reduction of the surface. Magnetite particle size estimates were made using irreversible NO adsorption uptakes on silica-supported Fe3O4 samples that had received a “standard” 1 h vacuum pretreatment at 650 K. These estimates agreed well with average particle sizes calculated using x-ray line-broadening and magnetization measurements, indicating that NO adsorption can, in fact, be used to measure magnetite surface areas on silica-supported samples.

The Influence of the Grain Shape on X-Ray Line Broadening

Abstract The analysis of X-ray reflections allows for the determination of the grain dimension in the direction of the bisector of the incident and scattered radiation. It is shown that correct results will be obtained only as long as the grain dimensions perpendicular to this direction are sufficiently large. The possible errors are estimated. The conditions for the determination of the shape anisotropy are discussed.