X-ray Diffraction Peak Profile Research Articles

Dislocation structure and crystallite size distribution in hexagonal nanomaterials from X-ray peak profile analysis

The microstructure of three different nanocrystalline materials with hexagonal crystal structure are studied by X-ray diffraction peak profile analysis. The crystallite size distribution and the dislocation structure are determined in plasmathermal silicon nitride powder, sintered tungsten carbide and severely deformed titanium, and are compared with transmission electron microscopy (TEM) results. In the case of the silicon nitride powder, the particle size determined by TEM is in good correlation with the coherently scattering domain size provided by X-rays. In the case of bulk titanium, the crystallite size, given by X-rays, correlates well with the dislocation cell size obtained by TEM. It is found that in tungsten carbide the dominant dislocation slip system is basal, whereas in plastically deformed titanium the basal slip is practically absent with the dominance of pyramidal dislocations, in good correlation with other investigations of the literature.

Structure of Milled Galena (PbS) Particles as a Result of Grinding: Observations by Electron Microscopy

We have examined galena powders with the aim of providing information about the preparation mode of such powders from ancient Egyptian burial objects. Two extreme conditions of milling have been used to prepare galena powders in the laboratory, and the resulting products have been examined using scanning electron microscopy and transmission electron microscopy (TEM). The microstructure of hand-crushed coarse particles consists mainly of dislocation tangles. Annealing at 300 °C promotes a substantial recovery of the dislocation structure with the formation of subboundaries. Energetic ball milling produces a large variety of particle sizes, from 10 nm to several micrometers, with grains containing very high dislocation densities. Although PbS is a soft plastic compound, its fragmentation occurs down to very small sizes along various fracture regimes like in many brittle materials. Comparisons are made between TEM observations and the data obtained from x-ray diffraction peak profile analysis.

Microstructure of carbon blacks determined by X-ray diffraction profile analysis

The microstructure of carbon blacks is investigated by X-ray diffraction peak profile analysis. Strain anisotropy is accounted for by the dislocation model of the mean square strain in terms of average dislocation contrast factors. Crystallite shape anisotropy is modeled by ellipsoids incorporated into the size profile function. Different grades of carbon blacks, N990, N774 and N134, untreated, heat-treated and compressed at 2.5 GPa have been investigated. The microstructure is characterized in terms of crystallite size-distribution, dislocation density and crystallite shape anisotropy. Heat treatment results in increased vertical and lateral sizes of graphitic crystallites. Postproduction pressure treatment has little effect on the average sizes of the crystallites, however, it affects the crystallite size distribution function. The average sizes of the crystallites obtained by X-ray diffraction agree with those estimated from Raman spectra. Applied pressure affects the magnitude of strain within the crystallites.

Revealing the powdering methods of black makeup in Ancient Egypt by fitting microstructure based Fourier coefficients to the whole x-ray diffraction profiles of galena

Galena (PbS) is a major ingredient in ancient Egyptian eye makeup. The microstructure of PbS in Egyptian cosmetic powders is used as a fingerprint and is matched with the microstructures produced artificially in geological galena minerals. The microstructure of PbS is determined by x-ray diffraction peak profile analysis in terms of dislocation density, crystallite size, and size distribution. High-resolution powder diffractograms were measured at the ESRF Grenoble synchrotron source with high resolution and high peak-to-background ratios. The Fourier coefficients of the first nine measured reflections of galena are fitted using physically based Fourier coefficients of strain and size functions. Strain anisotropy is accounted for by the dislocation model of the mean square strain. The x-ray data are supplemented by scanning electron microscopy (SEM) and transmission electron microscopy (TEM) micrographs, and are compared with archæological documents. It enables us to describe the procedures of eye makeup manufacturing in the Middle and New Kingdoms of Egypt some 2000 years before Christ.

Large strain work hardening in the alloy Al–1Mg–1Mn at low and intermediate deformation temperatures: experiments and modelling

Samples of the commercial alloy Al–1 wt.%Mg–1 wt.%Mn (AA3004) have been subjected to deformation by compression at different temperatures T=0.3–0.5 T m ( T m is the melting temperature in K) and equivalent strain rates from 10 −3 to 10 s −1. Dislocation densities and volume fractions of cell interior areas have been measured by means of X-ray diffraction peak profile analysis. Clearly, the hardening characteristics exhibited stages IV and V of deformation. The hardening curves have been fitted by two different models basing on the composite ansatz by Mughrabi, i.e. that by Mülders and that by Zehetbauer and Les. Fit results from both models are in good agreement with the measured dislocation densities and volume fractions of cell interior areas. The fits also give strong hints to the participation of deformation-induced vacancies in the deformation process. In contrast to pure Al, the actual alloy exhibits only a weak dependence of the dislocation density and vacancy concentration on the deformation temperature, which seems to be a consequence of the presence of alloy atoms restricting diffusion and dislocation movement.

Characterization of self-similar dislocation structures by X-ray diffraction

The development of the statistical parameters of the dislocation structure during plastic deformation of copper single crystals (average dislocation density, and average dislocation density fluctuation) was investigated by the method of X-ray diffraction peak profile analysis. It is found that during the deformation process, while the dislocation density increases monotonically, the average fluctuation exhibits a maximum corresponding to the transition from stage II to stage III of work hardening. The fractal dimension of the dislocation structure was also investigated. A strong correlation was found between the fractal dimension and the relative dislocation density fluctuation.

Stored energy and its role in recrystallization process

Abstract The stored energy, present in a material after deformation in the form of dislocation density, plays a crucial role in the recrystallizaton process. It can be evaluated directly using electron diffraction or indirectly using X-ray and neutron diffraction (peak profile study). The stored energy can be also calculated, using deformation models. Knowledge of the stored energy distribution is necessary in quantitative studies of recrystallization. The distribution of stored energy can explain the highly oriented nucleation (case of most of b.c.c. metals) as well as the highly oriented growth (case of most of f.c.c metals).

Dislocation densities, arrangements and character from X-ray diffraction experiments

X-ray diffraction peak profile analysis has become a powerful tool during the last two decades for the characterisation of microstructure either in the bulk or in loose powder materials. The evaluation and modelling procedures have developed together with the experimental techniques. It will be shown that the different features of diffraction peak profiles such as (i) broadening, (ii) asymmetric peak shape, (iii) peak shifts and (iv) anisotropic broadening provide a variety of microstructural parameters by modelling crystallite size and strain. Modelling strain by assuming dislocations will be more extensive. Two different procedures will be considered: (1) evaluation by using characteristic parameters of individual peak profiles, especially the FWHM, the integral breadths and the Fourier coefficients and (2) multiple whole profile fitting (MWPF) procedure using ab initio size and strain functions scaled by the contrast factors of dislocations. The two procedures will be discussed and illustrated by different case studies.

Dislocation Structure and Crystallite Size Distribution in Plastically Deformed Metals Determined by Diffraction Peak Profile Analysis

The dislocation densities and arrangement parameters and the crystallite size and size-distributions are determined in tensile or cyclically deformed polycrystalline copper specimens by X-ray diffraction peak profile analysis. The Fourier coefficients of profiles measured by a special high resolution X-ray diffractometer with negligible instrumental broadening have been fitted by the Fourier transforms of ab-initio size and strain profiles. It is found that in the fatigued samples the dislocations are mainly of edge type with strong dipole character. In the fatigued specimens the dislocation densities are found to be larger than in the tensile deformed samples when the saturation and flow stress levels are the same.

Composition fluctuations in the demixed supercooled liquid state of Zr41Ti14Cu12.5Ni10Be22.5: a combined ASAXS and SANS study

This chapter contains basic concepts and applications of wide-angle X-ray diffraction (XRD) and small-angle X-ray scattering (SAXS) to studies of nanostructured materials. The first part includes an introduction to the technique of X-ray powder diffraction (XPD), which is commonly applied to phase identification of powdered materials, characterization of unit cells, determinations of lattice parameters and, in some cases, also coordinates of atoms inside the unit cells. The main aspect described here is the analysis of the shape of X-ray diffraction peak profiles, which allows one to determine additional and also valuable structural information of nanomaterials, such as average crystallite sizes and crystallite microstrains. Detailed deductions of the equations used for different applications of X-ray diffraction and basic concepts of crystallography (such as those related to symmetries, Bravais and reciprocal lattices, etc.) are not described. The second part presents the basic equations related to the SAXS method and their applications to several biological systems (proteins in solution). Classical SAXS is an experimental procedure that is employed in transmission mode and is also applied to the study of many nanostructured inorganic materials. The third part includes two variants of the classical SAXS procedure, namely grazing incidence small-angle X-ray scattering (GISAXS) and anomalous small-angle X-ray scattering (ASAXS). The basic concepts of the GISAXS method and several applications to studies of nanostructured materials deposited on flat substrates and buried nanostructures are presented. The basic concepts of the ASAXS method are described, together with its applications to complex materials that cannot be properly studied using the classical SAXS technique, such as, for example, materials modeled by three phases with different electron densities. Most of the experiments described in this chapter were performed by the authors using X-ray beam lines of the National Synchrotron Light Laboratory (LNLS), Campinas, Brazil.

Residual Strain in Mechanically Ground Powders of Al-Ti Base Ternary and Quaternary Compounds with L1<SUB>2</SUB> Single-Phase at 1450 K

We examined the microstructural characters of L1 2 -type (Al, X, Y) 3 Ti (X, Y=Mn, Cr, Ag, Fe) phase alloys, with compositions selected from the regions connecting ternary L1 2 -type (Al, X) 3 Ti and (Al, Y) 3 Ti single-phase regions in the quaternary phase diagrams using laser microscopy, scanning electron microscopy and electron probe microanalysis. The residual strain, which was induced during milling of the alloys, was measured by examining the X-ray diffraction peak profile of the alloy powders. Most of the (Al, X, Y) 3 Ti alloys heat-treated at 1450 K for 24 h exhibited the L1 2 single-phase structure, while a few alloys containing Ag showed two-phase structures consisting of L1 2 and Ag-rich phases. The lattice parameters of (Al, Mn, Ag) 3 Ti and (Al, Cr, Ag) 3 Ti increased remarkably with increasing Ag content, while those of (Al, Mn, Cr) 3 Ti, (Al, Mn, Fe) 3 Ti and (Al, Cr, Fe) 3 Ti decreased gradually with increasing Cr or Fe content. The change of the lattice parameter with the contents of ternary and/or quaternary elements could be explained by the atomic size effect. The size and fraction of porosity, which were formed during heat treatment at 1450K for 24 h, depended on the composition of the alloys. The changes of the size and fraction can be explained by the Kirkendall effect, irrespective of alloy systems. The increase of the residual strain by variation of the composition in the Al-Ti-Mn-Ag and Al-Ti-Cr-Ag systems may be explained by the fact that the decrease of size and fraction of the porosity increased the residual strain. However, in the Al-Ti-Mn-Cr, Al-Ti-Mn-Fe and Al-Ti-Cr-Fe systems, the change could he explained by the fact that the residual strain increased as the sum of the contents of Al and Ti decreased.

Dislocations in Submicron Grain Size and Nanocrystalline Copper

ABSTRACTUsing the dislocation model of strain anisotropy in X-ray diffraction peak profile analysis it is shown that in nanocrystalline copper produced by inert gas condensation dislocations are present, at least, down to average grain sizes of the order of 20 nm. Based on the analysis of the dislocation contrast factors it is suggested that with decreasing grain size the proportion of Lomer-Cottrell type dislocations increases.

A relationship between the stress distribution and the peak profile broadening of meridional X-Ray diffraction from poly-p-phenylenebenzobisoxazole (PBO) fiber

Poly-p-phenylenebenzobisoxazole (PBO) is one of the rigid-rod polymers, the fiber of which shows high modulus and high strength. For these high mechanical properties to be understood, an analysis of the deformation process occurring in the fiber under stress was inevitable. For this purpose, X-ray diffraction measurements were carried out for the fiber under stress. The diffraction peak broadened as the degree of applied stress was increased. According to a Hosemann analysis, in the PBO fiber only the crystalline order was changed along the fiber axis in the crystal structure under deformation, whereas a change in the crystallite size was not detected. The external stress induced heterogeneous stress distribution to the molecule in the crystal; this distorted the X-ray diffraction peak profile, which followed Hosemann's theory. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2937–2942, 2000

X-ray diffraction study of crystallite size-distribution and strain in carbon blacks

ABSTRACTThe crystallite size and size-distribution in carbon blacks in the presence of strain are determined by recently developed procedure of X-ray diffraction peak profile analysis. The Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well established ab initio functions of size and strain peak profiles. Strain anisotropy is accounted for by expressing the mean square strain in terms of average dislocation contrast factors. Crystallite shape anisotropy is modelled by ellipsoids incorporated into the size profile function. To make the fitting procedure faster, the Fourier transform of the size profile is given as an analitical function. The method is applied to carbon blacks treated at different preassures and temperatures. The microstructure is characterised in terms of crystallite size distribution, dislocation density, and crystallite shape anisotropy.

Determination of Mean Crystallite Dimensions from X-Ray Diffraction Peak Profiles: A Comparative Analysis of Synthetic Hematites

AbstractX-ray diffraction (XRD) profile analysis of eight synthetic hematite samples was performed to identify the best parameters for determining the apparent mean crystallite dimension (D) and, consequently, surface area, The samples are comparable to soil hematite with respect to crystallinity. The procedure included: a) deconvolution of the XRD peaks to Gauss and Cauchy components and subtraction of the instrumental profile, b) determination of D from full-width at half-maximum, integral breadth, and integral breadth measurements of the Cauchy component, and c) comparison of deduced surface areas with those obtained by the N2-BET adsorption method. As expected, D values are strongly influenced by the broadening parameters. An appropriate selection of peaks is required to obtain size values along the crystallographic axes a (hkl: 110,300) and c (hkl: 104, 116) and to calculate reliable surface areas. Using the Cauchy component of the above peaks, the calculated surface areas compared well with those measured by the N2-BET adsorption method.

Martensite formation during heat treatments of AISI 304 steel with biphasic structure

Abstract X-ray diffraction (XRD) and Mossbauer spectroscopy (MS) measurements were used to evaluate the content of α′ ferromagnetic phase in AISI 304 steel cold rolled and then heat treated for increasing times (up to 7.2×104 s) at 673 K. Both analytical techniques show the same trend of α′ content versus annealing time, characterized by two maxima. The first maximum has been attributed to the growth of preexisting martensitic zones due a different microstress relaxation in the two phases, which induces a stress gradient through the α′/γ interface forcing it to move. The second maximum was explained assuming that local composition variations were induced by carbide precipitation and that a new martensitic phase may form during cooling to room temperature. MS data, i.e. the increase of average hyperfine field of magnetic fraction and the constancy of austenite isomer shift, and the analysis of precision XRD peak profiles support this assumption. Furthermore, MS measurements evidenced in cold rolled samples the presence of layers with decreasing martensite content towards the inside.

Scanning X-ray diffraction peak profile analysis in deformed Cu-polycrystals by synchrotron radiation

Densities and arrangements of dislocations and mesoscopic long-range internal stresses in cold-rolled polycrystalline copper were determined in scanning mode by X-ray peak profile analysis with synchrotron radiation. The high brilliance enabled the use of a focal spot of less than 50 μm. The diffraction profiles of the 200 reflections were measured by scanning the specimen step by step in front of the beam. In this way, the heterogeneities of the deformation-induced microstructure within single grains were obtained. At small deformations including stage III, the dislocation densities and the internal stresses were uniform within the grain interior, but larger near the grain boundaries where the dislocations showed a tendency to form stress-intensive arrangements. At higher deformations towards and in stage IV, the dislocation density and the internal stresses increasingly fluctuated within the whole grain. The fluctuations were interpreted as the transformations of polarized dipolar dislocation walls (PDW) into polarized tilt walls (PTW) observed recently by macroscopic diffraction experiments on highly deformed specimens. These results are important for the current research of strengthening processes in stage IV.

Estimating grain-size distributions in nanocrystalline materials from X-ray diffraction profile analysis

Abstract It is well known that the Fourier analysis of X-ray diffraction peak profiles (as implemented by Warren and Averbach) can accurately determine the areaweighted average grain size of a fine-grained sample. Less well known is the fact that this method simultaneously yields a volume-weighted average grain size. Under certain circumstances, knowledge of these two weighted average grain sizes is sufficient to permit reliable estimation of the grain-size distribution, even when the distribution cannot be calculated directly from the Fourier coefficients, as is usually the case. We demonstrate this for a nanocrystalline Pd sample prepared by inert-gas condensation; average grain sizes and the grain-size distribution are estimated by X-ray diffraction profile analysis and compared with the same quantities measured directly by transmission electron microscopy (TEM). Very good agreement between the resulting average grain sizes is achieved only after compensating for the fact that diffraction profile analy...

Elaboration and compressibility behavior of nanostructured SiC

Nanostructured SiC has been elaborated from coarse grained SiC by mechanical attrition. Milling time ranged from 1 h to 14 h. Crystallites sizes and microstrains have been determined from X-ray diffraction peak profile analysis using a “one peak method”. According to this method, the average crystallite size calculated from the (11.0) and (10.4) 6H-SiC reflections is less than 50 nm with a milling time of one hour. Up to 6 h milling time, crystallite sizes determined from these two peaks are very close, indicating that crystallite size evolution versus milling time is nearly identical for these two crystallographic directions. We observe a strong decrease of the crystallite size up to 3 h milling time. A saturation value is reached after 6 h milling time, associated with a strong increase of microstrains. From density-pressure measurements performed in uniaxial compression, the powder's compressibility behavior appears to be strongly related to changes in powder morphology and granularity during ball milling. The evolution of the powder morphology was followed by scanning electron microscopy. The iron contamination level by the steel vial and balls was controlled by X-ray microanalysis.

X-ray diffraction peak profiles from heteroepitaxial structures with misfit dislocations

X-ray diffraction peak profiles of relaxed heteroepitaxial layers with randomly distributed misfit dislocations are simulated and compared with the experimental data for two systems, LPE-grown SiGe/Si and MBE-grown AlSb/GaAs heterostructures. Different types of correlations in the spatial distribution of misfit dislocations are considered. For relatively small dislocation densities in the SiGe/Si system, the observed peaks are broader than the calculated ones for uncorrelated distributions of 60° dislocations. This broadening is explained as a result of a non-uniform tilt of the layer due to variations in the densities of dislocations with different Burgers vectors. In the AlSb/GaAs system possessing a high density of misfit dislocations, the peak of the relaxed AlSb buffer layer is found to be essentially narrower than expected from the model of uncorrelated dislocations. This effect can be explained by the short-range spatial correlations in the positions of the dislocations.