X-ray Powder Diffraction Line Profiles Research Articles

A capillary specimen aberration for describing X-ray powder diffraction line profiles for convergent, divergent and parallel beam geometries

X-ray powder diffraction patterns of cylindrical capillary specimens have substantially different peak positions, shapes and intensities relative to patterns from flat specimens. These aberrations vary in a complex manner with diffraction angle and instrument geometry. This paper describes a fast numerical procedure that accurately describes the capillary aberration in the equatorial plane for convergent focusing, divergent and parallel beam instrument geometries. Axial divergence effects are ignored and only a cross section of the capillary, a disc, is considered; it is assumed that axial divergence effects can be described using an additional correction that is independent of the disc correction. Significantly, the present implementation uses theTOPAS-Academicaberration approximation technique of averaging nearby aberrations in 2θ space to approximate in-between aberrations, which results in no more than ∼30 disc aberrations calculated over the entire 2θ range, even when the diffraction pattern comprises thousands of peaks. Finally, the disc aberration is convoluted with the emission profile and other instrument and specimen aberrations in a Rietveld refinement sense, allowing for refinement on the specimen's absorption coefficient and capillary diameter, as well as the instrument focal length. Large differences between refined and expected values give insight into instrument alignment.

Effects of limestone petrography and calcite microstructure on OPC clinker raw meals burnability

Limestone represents the main raw material for ordinary Portland cement clinker production. In this study eight natural limestones from different geological environments were chosen to prepare raw meals for clinker manufacturing, aiming to define a parameter controlling the burnability. First, limestones were characterized by X-Ray Fluorescence, X-Ray Powder Diffraction and Optical Microscopy to assess their suitability for clinker production and their petrographic features. The average domains size and the microstrain of calcite were also determined by X-Ray Powder Diffraction line profile analysis. Then, each limestone was admixed with clay minerals to achieve the adequate chemical composition for clinker production. Raw meals were thermally threated at seven different temperatures, from 1000 to 1450 °C, to evaluate their behaviour on heating by ex situ X-Ray Powder Diffraction and to observe the final clinker morphology by Scanning Electron Microscopy. Results indicate the calcite microstrain is a reliable parameter to predict the burnability of the raw meals, in terms of calcium silicates growth and lime consumption. In particular, mixtures prepared starting from high-strained calcite exhibit a better burnability. Later, when the melt appears this correlation vanishes; however differences in the early burnability still reflect on the final clinker composition and texture.

An Implementation of the Fundamental Parameters Approach for Analysis of X-ray Powder Diffraction Line Profiles.

This work presents an open implementation of the Fundamental Parameters Approach (FPA) models for analysis of X-ray powder diffraction line profiles. The original literature describing these models was examined and code was developed to allow for their use within a Python based least squares refinement algorithm. The NIST interest in the FPA method is specific to its ability to account for the optical aberrations of the powder diffraction experiment allowing for an accurate assessment of lattice parameter values. Lattice parameters are one of the primary certified measurands of NIST Standard Reference Materials (SRMs) for powder diffraction. Lattice parameter values obtained from analysis of data from SRMs 640e and 660c using both the NIST FPA Python code and the proprietary, commercial code Topas, that constitutes the only other actively supported, complete implementation of FPA models within a least-squares data analysis environment, agreed to within 2 fm. This level of agreement demonstrates that both the NIST code and Topas constitute an accurate implementation of published FPA models.

Structure and morphology of shape-controlled Pd nanocrystals

Pd nanocrystals were produced with uniform truncated-cube shape and a narrow size distribution, yielding controlled surface area fractions from low Miller index ({100}, {110}, {111}) crystalline facets. Details on the structure and morphology of the nanocrystals were obtained by combining X-ray powder diffraction line profile analysis, high-resolution transmission electron microscopy and surface electrochemistry based on Cu underpotential deposition.

X-ray powder diffraction line profile analysis of mechanically alloyed Cu–Cr powder

Four different compositions of Cu–Cr system (Cu0·90Cr0·10, Cu0·75Cr0·25, Cu0·60Cr0·40 and Cu0·50Cr0·50) were mechanically alloyed using different milling parameters. Samples collected from the milled powder of 24 batches after different time intervals were studied by X-ray diffraction. The diffraction data were analysed by three different line profile analysis methods, namely, Williamson–Hall method, integral breadth method and peak fitting method to calculate the crystallite size and microstrain in the materials. Peak fitting and integral breadth methods were found to be more suitable for the systems under study. Logarithmic relationships between the milling time and crystallite size or microstrain are proposed. The model was further validated by time interpolated data from two of the present batches and two composition extrapolated batches (Cu0·25Cr0·75 and Cu0·10Cr0·90).

Microstructural studies on variation of defect parameters in Zr-Sn alloys and their transition with interchange of solvent and solute in Zr-Ti and Ti-Zr alloy systems by modified Rietveld method and Warren-Averbach method

The effects of deformation and the transition of microstructural defect states with the interchange of solvent and solute in Ti-Zr and Zr-Ti alloys of six different compositions and Zr-Sn alloys in three different compositions have been investigated by X-ray diffraction line profile analysis. The detailed analysis of the X-ray powder diffraction line profiles was interpreted by Fourier line shape analysis using modified Rietveld method and Warren-Averbach method taking silicon as standard. Finally the microstructural parameters such as coherent domain size, microstrains within domains, faulting probability and dislocation density were evaluated from the analysis of X-ray powder diffraction data of Zr base Sn, Ti and Ti base Zr alloys by modified Rietveld powder structure refinement. This analysis confirms that the growth fault, β, is totally absent or negligibly present in Zr-Ti, Ti-Zr and Zr-Sn alloy systems, because the growth fault, β, has been observed to be either negative or very small for these alloy systems. This analysis also revealed that the deformation fault, α, has significant presence in titanium-base zirconium alloy systems but when zirconium content in the matrix goes on increasing beyond 50%, this faulting behaviour suffers a drastic transition and faulting tendency abruptly drops to a level of negligible presence or zero. This tendency has also been observed in Zr-Sn alloys signifying high stacking fault energy. Therefore, Zr and Zr-base alloys having high stacking fault energy can be used as hard alloys in nuclear technology at high temperature.

Effect of compression force on the crystal properties of erythromycin acistrate tablets

The crystal properties of compressed and powdered erythromycin acistrate tablets were studied by the X-ray powder diffraction (XRPD) method. Detailed analysis of X-ray powder diffraction line profiles was performed. Diffraction peak intensities and full width at half maximum (FWHM) values of the peaks corresponding to three different crystal lattice directions were determined. Crystallite size was calculated by Scherrer's equation using the data of integral breadth of the peaks. The preferred orientation of the crystallites is also discussed. According to the results, the crystallite size increased on the tablet surface after a small compression force (4 kN) in all crystal lattice directions studied. Even small compression forces caused recrystallization. With higher compression forces (8–18 kN) the crystallite size and the FWHM values remained rather constant. After the compression force of 18 kN the peaks in different crystal lattice directions behaved differently. In the lattice directions of diffraction maxima 2 and 3, the effect was the same with the small (4 kN) and the high compression force (22 kN). Further recrystallization occurred with 22 kN. However, in the crystal lattice direction of diffraction maximum 1 at the compression force of 8 kN the crystallite broke and crystallinity decreased. These were not seen in the powdered tablet samples. It could be concluded that the effect of compression force on the crystal properties of erythromycin acistrate tablets was seen on the tablet surface but not in the powdered tablets. Compression force also affected the preferred orientation of crystallites on the tablet surface and especially in the lattice direction of diffraction maximum 3. This was not seen in the powdered tablets.

00/00378 Solar collectors versus lamps—a comparison of the energy demand of industrial photochemical processes as exemplified by the production of ε-caprolactam

The effects of annealing on the hysteresis of pressure-composition isotherms for the LaNi5H2 system were examined. It was found that the higher was the annealing temperature before absorption, the higher was the pressure of the subsequent absorption isotherm and eventually the larger was the hysteresis. The dehydrided samples, which were annealed at various temperatures, were subjected to X-ray powder diffraction line profile analysis using the Warren-Averbach method. It was concluded from the results obtained for the crystallite domain size and the lattice strain that the predominant factor affecting the hysteresis is the microstrain in the direction perpendicular to the hexagonal c axis.

An Analysis of the Effect of Different Instrumental Conditions on the Shapes of X-ray Powder Line Profiles

Abstract In this investigation we have examined how the full width at half maximum intensity (FWHM) and asymmetry of x-ray powder diffraction line profiles are influenced by the instrumental conditions adopted. Experimental x-ray data has been collected for a matrix of instrumental conditions by systematically varying the divergence slit angle (and the corresponding anti-scatter slit) over the range 0.25° to 1.25°, by using either a 0.05mm or 0.2mm receiving slit, or by removing the diffracted beam Soller slit. The line profile Standard Reference Material, SRM, 660 (LaB6) was used as the powder specimen in that it imparts minimal specimen induced broadening to the diffraction profiles. X-ray data were collected on a conventional, divergent beam, x-ray diffractometer using CuKα radiation. The FWHM of the CuKα1 component can be as low as 0.035°2θ for high resolution conditions, but is normally ∼0.1°2θ at 2θ ≈ 30° for the instrumental conditions adopted in routine diffractometry. Below 2θ = 50°, the divergence slit has a significant effect on the FWHM and is the major cause of the increase in FWHM with decreasing 2θ. Results are presented of the 2θ dependence of FWHM values for each of the instrumental conditions recorded. A general relationship for the 2θ dependence of the FWHM and the asymmetry has been investigated to supersede the inappropriate Cagliotti expression frequently used in x-ray Rietvcld refinement.

X-ray powder diffraction line profiles by Fourier synthesis

This work presents a new method of synthesizing the reflection profile, based on the calculation of Fourier coefficients of instrumental functions. The classification and construction of Fourier coefficients are effected, in a general way, from the analysis of the possible paths of beams in the diffractometer. Relationships were obtained which made it possible to synthesize the line profiles in different experimental conditions. The possibility of calculating the reflection profiles of a standard (annealed BaF2) without introducing varying profile parameters is shown. Better results in describing the reflection profiles have been obtained than by applying the Pearson VII function with varying profile parameters.

Effects of lattice strain on the hysteresis of pressure-composition isotherms for the LaNi 5H 2 system

The effects of annealing on the hysteresis of pressure-composition isotherms for the LaNi 5H 2 system were examined. It was found that the higher was the annealing temperature before absorption, the higher was the pressure of the subsequent absorption isotherm and eventually the larger was the hysteresis. The dehydrided samples, which were annealed at various temperatures, were subjected to X-ray powder diffraction line profile analysis using the Warren-Averbach method. It was concluded from the results obtained for the crystallite domain size and the lattice strain that the predominant factor affecting the hysteresis is the microstrain in the direction perpendicular to the hexagonal c axis.

Stacking fault probability determinations in HCP Ti−Al alloys

X-ray powder diffraction line profile studies have been made from hcp Ti−Al alloys. A Fourier analysis of the profiles has been used to separate the total broadening into that caused by domain size, mean-square (ms) microstrains, and stacking faults. The stacking fault probability and the ms microstrains of the Ti−Al alloys decrease with increasing aluminum content, whereas the domain size remains relatively constant. This change in stacking fault probability is used to explain the corresponding changes in dislocation structures.

Méthode directe de correction des profils de raies de diffraction des rayons X. I. Méthode numérique de déconvolution

A new method of correction of X-ray powder diffraction line profiles by deconvolution is being developed. The convolution equation, representing the phenomenon of deformation of a true diffraction line profile, is approached with the help of a quadrature formula by a system of linear equations. The bad conditioning of this system has led to the use of a stabilization method enabling one to obtain a result converging to the true solution which satisfies the physical phenomenon. The quadrature formulae which are used are described. This method has been programmed in Fortran II for the IBM 1620.

X-ray diffraction studies of the effects of deformation on niobium alloys containing titanium, vanadium and zirconium

The effects of deformation by filing on the body-centred cubic niobium-based alloys have been investigated. The broadening of the x-ray powder diffraction line profiles was interpreted by Fourier analysis, and the results are reported in terms of particle size, strain, faulting probability and dislocation density. The results were derived using two calculation procedures for the application of Warren's method. It is concluded that faulting is not of major importance in the deformation process in these alloys. The particle size and dislocation density show systematic variation with composition.

Computer programmes for Fourier analysis of broadening of X-ray powder diffraction line profiles

A computer programming procedure is described for the correction of X-ray powder diffraction line profiles using Stokes' numerical Fourier analysis method. The programme provides results in a suitable form for analysis of the line broadening in terms of particle size and strain using the Warren and Averbach method, and a further programme is described to perform this analysis.

Stacking fault densities in hexagonal silver alloys

X-ray powder diffraction line profile studies have been made of filings from hexagonal close-packed silver-tin and silver-indium alloys. The profiles have been analysed by Fourier and line breadth methods to separate the total line broadening into that caused by particle size, lattice strain and the presence of stacking faults. The stacking fault probabilities of the silver-tin alloys are greater than those of the silver-indium alloys. In each alloy system, those alloys whose composition is nearer to the composition of the face-centred cubic phase boundary have the greatest stacking fault density. The stacking fault density is thus dependent upon the relative free energies of the hexagonal and face-centred cubic phases and is not a function of electron concentration.