Diffraction Line Profile Research Articles

Correlative image learning of chemo-mechanics in phase-transforming solids.

Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (for example, due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. Here we developed a generalizable, physically constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on LiXFePO4, a technologically relevant battery positive electrode material. We uncovered the functional form of the composition-eigenstrain relation in this two-phase binary solid across the entire composition range (0 ≤ X ≤ 1), including inside the thermodynamically unstable miscibility gap. The learned relation directly validates Vegard's law of linear response at the nanoscale. Our physics-constrained data-driven approach directly visualizes the residual strain field (by removing the compositional and coherency strain), which is otherwise impossible to quantify. Heterogeneities in the residual strain arise from misfit dislocations and were independently verified by X-ray diffraction line profile analysis. Our work provides the means to simultaneously quantify chemical expansion, coherency strain and dislocations in battery electrodes, which has implications on rate capabilities and lifetime. Broadly, this work also highlights the potential of integrating correlative microscopy and image learning for extracting material properties and physics.

Characterization of irradiation effect on 5251 Al-alloy using rietveld x-ray diffraction analysis

This work aims to study irradiation doses (0, 100, 200, 400, 600 and 1000 kGy of Co60 γ-source doses) effect on 5251 Al-alloy samples using XRD analysis. The main structures of the x-ray diffraction patterns are the same, a considerable difference in the peak intensities is observed due to the grain growth associated with increasing of irradiation doses. The intensity ratio of higher reflections declares that nearly 600 kGy irradiation dose is the preferred orientation or threshold point. Microstructure characterization has been studied using x-ray Diffraction Line Profile (XDLP) analysis. Minimum crystallite size of about 0.106 μm is measured for non-irradiated sample, maximum value is observed at 600 kGy. Micro-strain decreases exponentially with increasing irradiation dose, in addition the cell parameter seems to be constant. The dislocation and defect densities reveal the same behavior as the micro-strain. The defect and dislocation density decrease exponentially with increasing of irradiation doses with maximum values of about 1.10 × 1019 cm−3 and 3.15 × 1010 cm−2 respectively obtained for non-irradiation. The variation of the stored dislocation energy due to irradiation doses reveal maximum stored dislocation energy of about 334.95 kJ m−3 for non-irradiated sample, then it is approximately kept constant with increasing of irradiation dose up to 1000 kGy.

Formation of Dislocations and Stacking Faults in Embedded Individual Grains during In Situ Tensile Loading of an Austenitic Stainless Steel.

The formation of stacking faults and dislocations in individual austenite (fcc) grains embedded in a polycrystalline bulk Fe-18Cr-10.5Ni (wt.%) steel was investigated by non-destructive high-energy diffraction microscopy (HEDM) and line profile analysis. The broadening and position of intensity, diffracted from individual grains, were followed during in situ tensile loading up to 0.09 strain. Furthermore, the predominant deformation mechanism of the individual grains as a function of grain orientation was investigated, and the formation of stacking faults was quantified. Grains oriented with [100] along the tensile axis form dislocations at low strains, whilst at higher strains, the formation of stacking faults becomes the dominant deformation mechanism. In contrast, grains oriented with [111] along the tensile axis deform mainly through the formation and slip of dislocations at all strain states. However, the present study also reveals that grain orientation is not sufficient to predict the deformation characteristics of single grains in polycrystalline bulk materials. This is witnessed specifically within one grain oriented with [111] along the tensile axis that deforms through the generation of stacking faults. The reason for this behavior is due to other grain-specific parameters, such as size and local neighborhood.

A novel approach to analyse combined pre and post strain rate dependent phase transformation in uniaxially deformed AISI 304 stainless steel using XRD and EBSD

ABSTRACT The effect of pre-strain, pre-strain rate and post-strain rates on the deformation-induced austenite to martensite phase transformation have been studied in AISI 304 stainless steel. The martensite content obtained from the X-ray diffraction analysis and complemented by the magnetisation measurements showed that the phase transformation is enhanced for a unique combination of pre-strain, pre-strain rate and post-strain rate. The microstructural characterisation using detailed X-ray diffraction line profile analysis in terms of the size of the coherently scattering region and the dislocations that cause the microstrain within this region could give evidence of the enhanced/reduced martensite formation. The results of the electron backscattered diffraction in terms of the angular distribution of the lattice correlation boundaries and the orientation relationship boundaries of the austenite-martensite phase substantiated this finding. Considering that the multiple combinations of deformation parameters control the mechanism of martensitic transformation, this study will also contribute to the understanding of deformation-induced phase transformation of other materials with improved plasticity.

Assessment of Dislocation Density by Various Techniques in Cold Rolled 1050 Aluminum Alloy

This study examines the evolution of dislocation density in cold rolled 1050 Al alloy. Various techniques such as numerical approaches, indentation techniques, X-ray diffraction line profile analysis, and electron backscattering diffraction were employed for the characterization of the deformed state. These methods allowed us to determine the nature of the evolution of the dislocation substructure during cold rolling. The investigated material was subjected to thickness reductions varying from 5% to 47%, which resulted in a continuous increase in hardness while the estimated dislocation density showed a tendency towards a less intense increase after a ~30% straining level. The numerical approaches employed, such as the Kubin–Estrin and a modified version of this model, are capable of ensuring a reasonable estimation of dislocation density at low and moderate deformation levels (~5–30%), while the discrepancy between the measured and simulated data is negligible when the material has been exposed to more severe rolling reductions.

Influence of prior deformation temperature on strain induced martensite formation and its effect on the tensile strengthening behaviour of type 304 SS studied by XRDLPA

Type 304 stainless steel is a metastable austenitic stainless steel that undergoes strain induced transformation from austenite to α′ martensite during deformation at room temperature. Role of prior deformation, by rolling at room temperature and at 200 °C (a temperature at which the strain induced martensitic transformation does not occur), on the subsequent room temperature tensile deformation behaviour of the austenite phase is investigated. The changes in dislocation density of the parent phase and the volume fraction of the martensite formed due to deformation were estimated by X-ray diffraction line profile analysis of data obtained from Beam Line - 12 of the Indus 2 synchrotron. The contrast caused by dislocations in the austenite phase has been addressed using the modified Williamson-Hall method. The character of dislocations changes from screw to edge above a critical equivalent strain of ~0.14. The influence of martensite formation on the increase in dislocation density in the austenite phase is confirmed from XRDLPA. An alternative approach to determine dislocation density is proposed which is independent of elastic constants of the material and is found to correlate well with the values determined by the Williamson-Smallman approach. The results obtained from XRDLPA are corroborated with EBSD analysis. It is also seen that the composite strength of the steel, which has undergone different levels of deformation, is related to the changes in dislocation density of austenite and volume fraction of martensite based on Taylor's equation enabling correlation of structure-property.

Microstructure, Hardness, and Elastic Modulus of a Multibeam-Sputtered Nanocrystalline Co-Cr-Fe-Ni Compositional Complex Alloy Film

A nanocrystalline Co-Cr-Ni-Fe compositional complex alloy (CCA) film with a thickness of about 1 micron was produced by a multiple-beam-sputtering physical vapor deposition (PVD) technique. The main advantage of this novel method is that it does not require alloy targets, but rather uses commercially pure metal sources. Another benefit of the application of this technique is that it produces compositional gradient samples on a disk surface with a wide range of elemental concentrations, enabling combinatorial analysis of CCA films. In this study, the variation of the phase composition, the microstructure (crystallite size and defect density), and the mechanical performance (hardness and elastic modulus) as a function of the chemical composition was studied in a combinatorial Co-Cr-Ni-Fe thin film sample that was produced on a surface of a disk with a diameter of about 10 cm. The spatial variation of the crystallite size and the density of lattice defects (e.g., dislocations and twin faults) were investigated by X-ray diffraction line profile analysis performed on the patterns taken by synchrotron radiation. The hardness and the elastic modulus were measured by the nanoindentation technique. It was found that a single-phase face-centered cubic (fcc) structure was formed for a wide range of chemical compositions. The microstructure was nanocrystalline with a crystallite size of 10–27 nm and contained a high lattice defect density. The hardness and the elastic modulus values measured for very different compositions were in the ranges of 8.4–11.8 and 182–239 GPa, respectively.

In situ diffraction characterization on microstructure evolution in austenitic stainless steel during cyclic plastic deformation and its relation to the mechanical response

Diffraction line profile analysis was performed to qualitatively evaluate the change in the microstructure of austenitic stainless steel during 250 cycles of plastic deformation. The dislocation density increased with increasing number of cycles until 50 cycles but thereafter decreased. The cycle number corresponding to this maximum point differed depending on whether it was evaluated as the total dislocation density or was deconvoluted into edge and screw dislocation densities. At the initial state, edge dislocations were predominant; however, screw dislocations greatly increased at the first stage of cyclic loading. Afterwards, edge dislocations formed cell walls and screw dislocations annihilated. The cycle number at which the singularity was reached depended on the development of the dislocation structure. When the cell structure developed and the cell wall became sharp, the arrangement of dislocations on average decreased and the crystallite size increased. The flow stress of the austenite phase increased and decreased, reflecting the dislocation density during cyclic loading. However, after αʹ-martensite was generated as the number of cycles increased, the contribution of the transformed martensite to the total flow stress could increase.

Microstructural characterisation of 160 MeV oxygen irradiated niobium

ABSTRACT Microstructural changes due to 160 MeV oxygen ion irradiation on pure Nb have been characterised using X-ray Diffraction Line Profile Analyses. Microstructural parameters such as coherent domain size, microstrain within the domain and dislocation density are evaluated from the homogeneously damaged region. It is observed that the domain size decreases along with an increase in microstrain and dislocation density as a function of dose. The local changes in the microstructure have also been evaluated in terms of band contrast, mean angular deviation and local misorientation from electron backscattered diffraction data at the surface and an intermediate depth in the homogenously damaged region of selected irradiated samples and in the unirradiated sample. An increase in mean angular deviation and local misorientation is observed in the highest dose sample, which may be an indication of dislocation loop formation. Defect clusters and dislocation loops are observed using transmission electron microscopy in the highest dose sample. Microhardness measurement has also been carried out on the unirradiated and irradiated samples to correlate the microstructural changes with the mechanical property as a function of dose. It is observed that the hardness of the material increases as a function of dose due to the formation of defect clusters and dislocation loops that pin the movement of dislocations. Finally, a comparison of the microstructures in proton and heavy ion irradiated samples at approximately similar dpa-rate has been carried out to understand the effect of the ion species on the defect morphology.

Depth-profiling of residual stress and microstructure for austenitic stainless steel surface treated by cavitation, shot and laser peening

While the general characteristics of various peening techniques have been established, there have been few comparative studies. Here we compare the variation of the residual stresses and microstructural characteristics with depth for 316L austenitic stainless steel treated by cavitation peening (CP), shot peening (SP) and laser peening (LP) all peened to similar intensity levels. While the plastically affected depths were similar in all cases (~400 μm), the SP specimen showed the most extensive near surface plastic deformation, deformation twinning, dislocation density and compressive residual stress. To counterbalance this, the compressive residual stresses extended deeper for the LP and CP. Across the three treatments, a similar dependency was found between diffraction peak broadening and hardness. The dislocation density at the surface determined by the diffraction line profile analysis (LPA) for the SP specimen (4.9 × 10 15 m −2 ) was approximately 2.5 times that for the CP and LP specimens (2.0 × 10 15 and 2.1 × 10 15 m −2 ). Electron backscatter diffraction (EBSD) shows that the extensive work introduced by the SP had generated planar defects near to the surface. The increase in yield stress estimated from the hardness corresponded with the increase in dislocation density obtained by the LPA. • Shot peening (SP) introduces larger near-surface stresses while cavitation peening and laser peening penetrate deeper. • SP gives the highest nearsurface hardness of the three treatments. • SP also introduces a larger number of dislocations and planar defects than the others. • The hardness at a given FWHM is broadly the same regardless of the kind of the peening treatment. • The increase in yield stress estimated from the hardness correlates with the increase in dislocation density.

Microstructural evolution of proton irradiated Fe-2.25Cr–1Mo characterized using synchrotron XRD (SXRD)

Synchrotron X-ray diffraction data (SXRD) has been used to characterize the microstructural changes in 3.5 MeV proton irradiated 2.25Cr–1Mo (T22) steel samples as a function of dose through different techniques of X-ray diffraction line profile analysis (XRDLPA). Williamson-Hall (W–H) method, modified Rietveld method and convolutional multiple whole profile (CMWP) fitting technique have been used to evaluate the coherent domain size, r.m.s microstrain, dislocation density and dislocation character from SXRD data. It is demonstrated that XRDLPA from SXRD data is a powerful tool for extracting the microstructural parameters of irradiated samples in a reliable manner. Transmission Electron Microscopy (TEM) investigation has been carried out on unirradiated and irradiated samples to corroborate the results of XRDLPA. It is observed that dislocation density increases with dose and forms dislocation loops at highest dose. Vickers microhardness measurement has also been carried out to get the information on the mechanical property changes with dose. The variation in Vickers microhardness as a function of dose has been explained using the results from XRDLPA and TEM analysis.

Line profile analysis of synchrotron X-ray diffraction data of iron powder with bimodal microstructural profile parameters

Room-temperature synchrotron X-ray diffraction and subsequent detailed line profile analysis of Fe powder were performed for microstructural characterization. The peak shapes of the diffraction pattern of Fe were found to be super-Lorentzian in nature and the peak widths were anisotropically broadened. These peak profile features of the diffraction pattern are related to the microstructural parameters of the material. In order to elucidate these features of the diffraction pattern, detailed line (peak) profile analyses were performed using the Rietveld method, modified Williamson–Hall plots and whole powder pattern modelling (WPPM), and related microstructural parameters were determined. Profile fitting using the Rietveld and WPPM methods with a single microstructural (unimodal) model shows systematic deviation from the experimentally observed diffraction pattern. On the basis of Rietveld analysis and microstructural modelling it is revealed that the microstructure of Fe consists of two components (bimodal profile). The microstructural parameters of crystallite/domain size distribution, dislocation density, nature of dislocations and phase fraction were evaluated for both components. The results obtained using different methods are compared, and it is shown that diffraction peak profile analysis is capable of modelling such inhomogeneous bimodal microstructures.

Effect of dislocation characteristics on electrical conductivity and mechanical properties of AA 6201 wires

Abstract Aluminum 6201 alloys (AA 6201) exhibit high electrical conductivity and are lightweight, thus suitable for substituting Cu alloys. However, studies on the mechanical properties of and texture evolution in these alloys are few. To determine the relationship between the mechanical and electrical properties of these alloys, their properties and drawing processes were analyzed at room temperature; for this purpose, annealing was performed at 350 °C. The dislocation behavior caused by annealing was investigated by electron backscattered diffraction (EBSD) and X-ray diffraction line profile analysis. EBSD was also used for observing the texture evolution caused by deformation and annealing. An increase in the strain led to the formation of an ideal shear texture, in line with the drawing processes. It is well known that hardness is inversely proportional to electrical conductivity. However, when the hardness of the deformed alloy with a strain of 1.38 was maintained even after annealing for a long time, the electrical conductivity gradually decreased. In other words, as the recrystallized grains were coarsened by reducing the dislocation density, the dislocations were more randomly arranged, resulting in a decrease in the electrical conductivity. Furthermore, a highly strained alloy has more randomly oriented grains, and thus, the evolution of texture changes. The direct relationship between texture evolution and electrical properties could not be determined, but it seems to be a composite effect of dislocation characteristics, texture evolution, and grain size. As noted, the dislocation characteristics and texture evolution affect the mechanical properties.

Effect of ball milling on the sintering performance of indium-gallium-zinc oxide ceramics: The diffusion mechanism and lattice distortion of milled powders

The mechanisms inducing lattice distortion and grain boundary diffusion in mixed In2O3–Ga2O3-ZnO (IGZO) powders were investigated during ball-milling treatment at different rotation speeds. After sintering, the highest relative densities for the sintered IGZO compacts were 92.87%, 98.72%, and 99.12% at rotation speeds of 100 rpm, 200 rpm, and 300 rpm, respectively, and the corresponding grain growth activation energies were 78.78, 67.17, and 49.52 kJ/mol. The sintering process of InGaZnO4 ceramics was shown to be dominated by grain boundary diffusion. X-ray diffraction line profile analysis indicated that the highest average lattice distortion of IGZO powders milled at 200 rpm and 300 rpm was 2.85 and 10.27 times higher, respectively, than that of IGZO powder milled at 100 rpm. The enhancements of the sintering properties of the IGZO powders induced by the faster milling speeds were attributed to the higher lattice distortion energies and shorter diffusion distances of the elements. This elucidated the mechanism behind the high-energy ball-milling process for achieving enhanced sintering performances in ceramic powders.

Quantitative Analysis of the Recovery Process in Pure Iron Using X-ray Diffraction Line Profile Analysis.

We conducted quantitative analysis of the recovery process during pure iron annealing using the modified Williamson-Hall and Warren-Averbach methods. We prepared four types of specimens with different dislocation substructures. By increasing the annealing temperature, we confirmed a decrease in dislocation density. In particular, screw-dislocation density substantially decreased in the early stage of the recovery process, while edge-dislocation density gradually decreased as annealing temperature increased. Moreover, changes in hardness during the recovery process mainly depended on edge-dislocation density. Increases in annealing temperature weakly affected the dislocation arrangement parameter and crystallite size. Recovery-process modeling demonstrated that the decrease in screw-dislocation density during the recovery process was mainly dominated by glide and/or cross-slip with dislocation core diffusion. In contrast, the decrease in edge-dislocation density during the recovery process was governed by a climbing motion with both dislocation core diffusion and lattice self-diffusion. From the above results, we succeeded in quantitatively distinguishing between edge- and screw-dislocation density during the recovery process, which are difficult to distinguish using transmission electron microscope and electron backscatter diffraction.

A microstructure study of colloidal gold nanoparticles by X-ray diffraction line profile analysis

We present the colloidal synthesis of gold nanoparticles (Au NPs) using the chemical reduction of gold precursors by changing the reducing agent (Na3C6H5O7) volume. We aimed at achieving different particle sizes, morphologies, and defect structures. The modified process impacted the overall synthesis time and nanoparticles' microstructures. We used X-ray diffraction profile analysis (XPA) and transmission electron microscopy (TEM) to follow the nanoparticles’ size and lattice strain details. The NPs' size distributions agree well between the indirect XPA and TEM direct measures. Nanocrystal shapes change from triangular, octahedral, and decahedral to hexagonal plate-like; it shows how the NPs minimize their energy formation by creating defects and well-defined crystallographic directions, including crystal fusion. The combined effects of dislocations, twin boundaries, and surface tension add together to broaden the diffracted line profiles. In particular, the density of dislocation and twin boundaries increase toward the smaller NPs.

High-Resolution Strain/Stress Measurements by Three-Axis Neutron Diffractometer.

Resolution properties of the unconventional high-resolution neutron diffraction three-axis setup for strain/stress measurements of large bulk polycrystalline samples are presented. Contrary to the conventional two-axis setups, in this case, the strain measurement on a sample situated on the second axis is carried out by rocking the bent perfect crystal (BPC) analyzer situated on the third axis of the diffractometer. Thus, the so-called rocking curve provides the sample diffraction profile. The neutron signal coming from the analyzer is registered by a point detector. This new setup provides a considerably higher resolution (at least by a factor of 5), which however, requires a much longer measurement time. The high-resolution neutron diffraction setting can be effectively used, namely, for bulk gauge volumes up to several cubic centimeters, and for plastic deformation studies on the basis of the analysis of diffraction line profiles, thus providing average values of microstructure characteristics over the irradiated gauge volume.

Quantifying the dislocation structures of additively manufactured Ti–6Al–4V alloys using X-ray diffraction line profile analysis

Abstract Ti–6Al–4V alloy is widely used in aerospace and biomedical industries, and its preparation using additive manufacturing techniques has recently attracted considerable attention. Herein, the dislocation structures developed during electron beam and laser beam powder-bed fusion (EB-PBF and LB-PBF, respectively) of the Ti–6Al–4V alloy were quantitatively examined via X-ray diffraction (XRD) line profile analysis. The microstructures of both as-built samples were characterized, revealing fine acicular microstructures attributable to a β → α' martensitic transformation. While a fully α'-martensite matrix with a high dislocation density was formed and preserved during the LB-PBF process, the decomposition of the α'-martensite toward the thermodynamically stable α + β microstructure occurred during EB-PBF as a result of post-solidification exposure to high temperatures. Accordingly, a higher dislocation density and finer crystallite size were observed at the top cross-section from the XRD line profile analysis, suggesting that the extent of phase decomposition depended on the duration of the exposure to the elevated temperature. Nonetheless, the saturated dislocation density was as high as 1014 m−2, where dislocation strengthening affected the overall strength of the EB-PBF specimen. Diffraction peaks of sufficient intensity that enabled the analysis of the dislocation structures in both the α (α')-matrix and the nanosized β-phase precipitates at the α (α')-laths were obtained under high-energy synchrotron radiation; this revealed that the β-phase had a much higher dislocation density than the surrounding α (α')-matrix. The enhanced dislocation accumulation in the nanosized β-phase precipitates probably reflects the elemental partitioning that occurred during post-solidification cooling. The valuable insights provided in this study are expected to promote further development of alloy preparation using additive manufacturing processes.

Diffraction Line Profiles in the Rietveld Method

The present work traces the evolution of the modeling of the diffraction line profiles in the Rietveld method, starting from the early and most schematic description with Gaussian curves to the mos...

Effect of Mg content on microstructure, texture and strength of severely equal channel angular pressed aluminium-magnesium alloys

Equal channel angular pressing was carried out on Al–Mg alloys to study the effect of Mg addition on the microstructure, texture and strength after severe plastic deformation by 8 passes of equal channel angular pressing (ECAP) through route Bc. The increase in Mg content enhanced the propensity of continuous dynamic recrystallization and simultaneously decreased the average grain size of the alloy. The microstructure and local texture was heterogeneous across the billet thickness for all the samples, irrespective of composition. All the samples showed a shear-type bulk texture generally observed in face-centred cubic metals with strong BE/‾BE components. The weakening of the texture with increase in Mg content is attributed to the substructure evolution during the ECAP process. The grain size and dislocation density have been determined by X-ray diffraction line profile analysis. The experimentally determined yield strength of the ultrafine grained samples can be explained by a combination of solid solution, dislocation and grain size strengthening, the latter being predominant.