Most synchrotron radiation X-ray diffraction (XRD) beamlines have been primarily designed for studying conventional materials, whereas a modern approach to nanomaterials requires a complete control of the diffracted signal, and therefore of the optics and general setup of the beamline. This requirement is especially relevant when Line Profile Analysis is pushed to the limits of large domain sizes, small deformations, or low defects concentration, which is a driving force to use synchrotron radiation XRD. We combine the SHADOW ray-tracing optical simulation with the calculation of powder diffraction profile from standard materials, into a high-level workflow environment based on the ORANGE software. Algorithms are developed to reproduce optical elements in a realistic form, so to evaluate the effects of aberrations, with the final purpose of reconstructing the Instrumental Profile Function of the beamline, with the possibility of investigating the role of each separate element. The results of this work can be of interest to most beamlines as a powerful tool for the design of setups of existing as well as new beamlines.

A powder obtained by ball milling a commercial FeMo alloy has been identified and investigated as possible reference material for powder diffraction line profile analysis. Ball milling yields micrometer-scale agglomerate particles made of rounded nanocrystalline domains with extensive lattice defects, so as to produce both size and strain contributions to the line profiles. The capability of a modern whole-powder pattern modeling to accurately quantify those aspects and the stability of the powder over a decade are shown and discussed.

Atomistic copper nanocrystals were investigated via Molecular Dynamics (MD) under hydrostatic pressure to probe the relationship between applied load and structure deformation. The corresponding X-ray powder diffraction patterns were generated from the atomic coordinates. The analysis followed both the traditional Williamson-Hall approach based on pseudo-Voigt fitting and an alternative, more accurate method able to derive the integral breadths without applying a fitting. The Williamson-Hall results show discrepancies not fully associated with an issue of fitting.

A NIST SRM certified to address the issue of crystallite size measurement through a line profile analysis has been under development for several years. In order to prepare the feedstock for the SRM, nano-crystalline zinc oxide was produced from thermal decomposition of zinc oxalate. The thermal processing parameters were chosen to yield particles in two size ranges, one with a distribution centered at approximately 15 nm and another centered at 60 nm. Certification data were collected on a NIST-built diffractometer equipped with a Johansson incident beam monochromator and scintillation detector. Data were analyzed using whole powder pattern modeling to determine microstructural data. The analysis shows domains to be in the form of discs of a fairly small aspect ratio. While both materials exhibit the effects of stacking faults through broadening of specific hkl reflections, their presence in the 60 nm is more difficult to discern. Images of the crystallites obtained with transmission electron microscopy are consistent with the results from the X-ray diffraction analyses.

The employment of the Debye function to model line profiles in the powder diffraction pattern from small crystallites is briefly reviewed. It is also demonstrated that for the case of very small spherical particles, it is necessary to average patterns from multiple constructions of the particle to have complete agreement with reciprocal space models. In doing so it is demonstrated that the technique of Debye function analysis is best suited for systems with only a few possible atomic arrangements.

The growth kinetics of Cu2ZnSnS4 thin films and powders was studied using in-situ synchrotron data. Isothermal and isochronal measurements were performed at the MCX beamline of the Elettra synchrotron (Trieste, Italy). Diffraction line profile analysis was used to follow the changes in the domain size distribution during isothermal measurements, and the change in the mean volume of the domains was studied using the Johnson-Mehl-Avrami equation. The growth was found to be diffusion controlled from small dimensions while the nucleation rate is temperature dependent. An activation energy of 210 kJ/mol could be estimated. In case of the isochronal data, the evolution of inverse of the integral breadth of the diffraction peaks in dependence on temperature was studied using the Ozawa and Šatava equations. The activation energy determined for the growth process is between 112(2) and 145(5) kJ/mol.

An experimental investigation has been carried out to determine the extent to which axial divergence in a conventional powder diffractometer influences the measurement of peak profile parameters. A Siemens D5000 θ–2θ diffractometer was used for this study along with the LaB6 line profile standard SRM 660. Eight unique levels of axial divergence were investigated either by removing one or more of the Soller slits, or by introducing different combinations of Soller slits in the incident and diffracted beams. The measure of axial divergence used throughout is based on the maximum axial divergences of the incident and diffracted beams, Ψi and Ψd. Axial divergence produces a small and almost constant shift δ2θp in the peak angle which in a typical diffractometer would amount to a zero offset 2θ≈0.005°. The integrated intensity of a profile increases almost linearly with the product Ψi*Ψd. The increase in breadth in profiles in the angular region 2θ<120° arises mainly from the change in asymmetry DH=Hlo−Hhi in which one side of the profile broadens (i.e., either the high angle or low angle side) without any significant broadening of the other side. Moreover, the asymmetry DH is linearly dependent on 2θ for a fixed level of axial divergence, and linearly dependent on the total axial divergence Ψi+Ψd at fixed 2θ.

As part of a study by high-resolution X-ray diffraction of chrome ores from the Great Dyke, Zimbabwe, powder data are reported for a well-crystallized ferroan magnesiochromite spinel, in which some Cr had been replaced by Al. Data were obtained by using CuKα1 radiation, with an incident beam focusing monochromator to eliminate the Kα2 component. The cell parameter is a0=8.3123(2) Å, the figures of merit are M17=383 and F17=182 (0.0055, 17) and the calculated density is 4.50(5) Mgm−3. A small amount of sample broadening was observed and this was attributed to a mean crystallite size of 259(1) nm. © 1997 International Center for Diffraction Data.

The diffraction pattern of nanocrystalline Ce0.9Zr0.1O2 was analyzed by whole powder pattern modeling, a recently proposed method for the study of line broadening. The main result in this typical case of study—the crystalline domain size distribution—matches closely the corresponding information obtained by transmission electron microscopy. Further information on nature and content of lattice defects is also discussed.

From 1967 to 2000 Daniel Louër of the Department of Crystal Chemistry, University of Rennes, and J. Ian Langford of the Department of Physics, University of Birmingham, collaborated in studying structural imperfections by means of high-resolution X-ray powder diffractometry. They contributed to the theory and practice of line profile analysis and investigated the microstructure of a variety of nanocrystalline materials. Although many of the projects undertaken were part of the research programme at Rennes to investigate the mechanisms of solid-state reactions, the work is relevant in other fields of materials science.

A general expression is proposed for the peak profile produced by a system of simple-shape crystalline domains (sphere, cube, tetrahedron, octahedron) whose size is dispersed according to a gamma distribution. The analytical expression obtained is particularly suited to “on the fly” pattern simulation or profile fitting for nanocrystalline materials. An advantage of using the proposed profile expression is that it always corresponds to a physically meaningful, though a priori fixed, size distribution, whereas the traditionally employed Voigtian profiles can produce unphysical negative size distributions for certain combinations of profile parameters. The peak profile depends on the distribution mean and variance instead of the more common empirical parameters of peak width and shape.

Four sol-gel TiO2 powders have been prepared from titanium tetraisopropoxide. The calcined powders are then characterized by X-ray diffraction. Cell parameters are extracted using two Rietveld refinement programs (FULLPROF and MAUD) leading to close values and indicating a contraction of the a (or b) cell parameter and an expansion of the c cell parameter of the anatase phase with temperature. Crystallite size and microstrain are highly dependent not only on the sol synthesis but also on the diffraction line profile analysis (LPA) models (i.e., Williamson-Hall, Thomson-Cox-Hastings, Dehlez et al., and log-normal size distribution) employed. Discrepancies are then observed for the phase transformation critical size, the activation energy of grain growth, and the microstrain stored potential energy according to the LPA approach used to calculate the microstructural parameters.

Shot peening was conducted on [100]- and [111]-oriented monocrystalline nickel-based superalloy samples to study the effect of crystal orientation on the distributions of the residual stress and evolution of microstructures in the deformation layers on the sample surfaces as a function of the coverage up to 400%. The XRD results show that the orientation randomizations and the values of compressive residual stress in the [111]-oriented samples are relatively higher than those in the [001]-oriented samples. Moreover, the residual-stress distribution in each sample is anisotropic, and the residual stress is maximum along the 〈110〉 direction. This phenomenon can be explained by the anisotropic properties of a single-crystal alloy and mechanism of the dislocation slip in the plastic deformation layers. Line profile analysis was also used to obtain microstructural information of the samples.