Modified Williamson-Hall Plot Research Articles

The modified Williamson-Hall plot and dislocation density evaluation from diffraction peaks

Diffraction peak profiles were calculated numerically for dislocation ensembles with different spatial arrangements and correlations between the Burgers vector signs. The latter property determines the stored elastic energy in the crystal and the width of the diffraction peaks. It is shown that within the approximation of the asymptotic line-profile theory the relationship between peak breadth and the magnitude of the diffraction vector in the modified Williamson-Hall (mWH) plot is linear. The slope of the line is proportional to the arrangement parameter M0.3 and to the square root of the dislocation density. The only rigorous way for determining M is the asymptotic Fourier method. Therefore, the evaluation of the dislocation density from the mWH-plot alone is impossible and should be avoided. The mWH plot however, is very useful in practice. Its linearity indicates a consistent asymptotic line-profile analysis.

Effect of Reduction Rate on the Recrystallization Behavior in AA3003 Aluminum Alloy Fabricated by DC Casting

The recrystallization behavior of the cold-rolled AA3003 aluminum alloy with the reduction rate of 20%, 50% and 90% during annealing at the temperature ranging from 300°C to 400°C was investigated. As increasing reduction rate, the cold rolled specimens exhibit deformation bands with elongated grain microstructure consisting of straight grain boundary parallel to rolling direction. Therefore, large density of nucleation sites for recrystallization would be expected with increase of strain energy. The grain size of the cold-rolled specimens decreased with increase of reduction rate, c.f., as the rolling reduction increased to 90%, grain size along the direction normal to the sheet decreased to about 8μm in thick. When the sample annealed at 350°C for 5s, the first recrystallized grains were observed in the vicinity of the grain boundary. The relaxation and recrystallization kinetics under different annealing conditions were characterized in terms of the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model. The apparent activation energies of recrystallization for the cold-rolled specimens with reduction rate of 20%, 50% and 90% were determined as 332 kJ/mol, 239 kJ/mol and 115 kJ/mol, respectively. XRD analysis by using modified Williamson–Hall plots revealed that the tendency of the change in dislocation density is varied depending on reduction rate. These results indicate that the apparent activation energy for recrystallization and the crystallites size decrease with increase of the reduction rate, which leads to a decrease in the size of the recrystallized grains.

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.

A New Explanation for the Effect of Dynamic Strain Aging on Negative Strain Rate Sensitivity in Fe-30Mn-9Al-1C Steel.

In this study, the evolution of the mechanical properties of Fe–30Mn–9Al–1C steel has been determined in tensile tests at strain rates of 10−4 to 102 s−1. The results show that the strain rate sensitivity becomes a negative value when the strain rate exceeds 100 s−1 and this abnormal evolution is attributed to the occurrence of dynamic strain aging. Due to the presence of intergranular κ-carbides, the fracture modes of steel include ductile fracture and intergranular fracture. The values of dislocation arrangement parameter M were obtained using a modified Williamson–Hall plot. It has been found that once the strain rate sensitivity becomes negative, the interaction of dislocations in the steel is weakened and the free movement of dislocation is enhanced. Adiabatic heating promotes the dynamic recovery of steel at a high strain rate.

Study of vacancy defects and their thermal stability in MeV Fe ion irradiated RAFM steel using positron beam Doppler broadening spectroscopy

ABSTRACTIndian reduced activation ferritic-martensitic steel was irradiated with 1.1 MeV Fe ions to various doses from 1 to100 dpa at room temperature. The depth profiling of irradiation-induced vacancy-type defects and the defect-recovery under post-irradiation annealing was studied using variable low-energy positron beam Doppler broadening spectroscopy. The influence of irradiation-induced defects on the microstructural properties was studied by glancing incidence x-ray diffraction (GIXRD) and nanoindentation technique. Positron annihilation study showed the signatures of reduced vacancy concentration at the peak damage region due to injected interstitial effect from 30 to 100 dpa and the widening of vacancy-interstitial recombination-rich region towards the end of ion range with the increase in dose. The GIXRD results were analysed by modified Williamson–Hall plot method, and the variation of coherent domain size and micro-strain with irradiation dose was studied. Irradiation-induced hardening was observed in the nanoindentation study. The features observed in the GIXRD and nanoindentation study are correlated with the depth-resolved defect distribution observed in the positron annihilation study.

Understanding the deformation mechanism of individual phases of a dual-phase beta type titanium alloy using in situ diffraction method

An in situ tensile X-ray diffraction (XRD) set-up with an area detector was employed to characterize deformation behaviors of individual phases in a commercial dual-phase β-Ti alloy. A developed analytical approach based on the modified Williamson-Hall plot accounting for dislocation evolution was proposed to elucidate the deformation mechanism of each phase from the in situ XRD data. A commercial purity titanium (alpha type, α-Ti) alloy was examined as a comparison to assist identifying the influence of inter-phase interaction on the deformation behavior of the β-Ti alloy. We found that the small amount of the fine lamella shaped hcp (α) precipitates, which is only 5% in volume, has great effects on the deformation mechanism of the bcc (β) matrix in the β-Ti alloy due to the Burger's orientation relationship (BOR) between the two phases. Due to the reason that slip on the coherent plane of (211)β of the β phase (i.e. (10 1̅0)α plane of the α phase) is more predominant than that of (110)β plane (i.e. (0002)α plane) in a hcp ploycrystal, slip on (211)β plane is easier than that on (110)β plane in the β-Ti alloy (cf. {110} < 111 > is the typical slip system in single phase bcc polycrystals). Although slip on (211)β plane is the most facile, lattice strain on (211)β plane is not the smallest, manifesting that stress/strain redistribution between α precipitates and β matrix occurred to accommodate the inter-phase interaction.

Processing of fine grained AISI 304L austenitic stainless steel by cold rolling and high-temperature short-term annealing

An advanced thermomechanical process based on the formation and reversion of deformation-induced martensite was used to refine the grain size and enhance the hardness of an AISI 304L austenitic stainless steel. Both low and high reversion annealing temperatures and also the repetition of the whole thermomechanical cycle were considered. While a microstructure with average austenite grain size of a few micrometers was achieved based on cold rolling and high-temperature short-term annealing, an extreme grain refinement up to submicrometer regime was obtained by cold rolling followed by low-temperature long-term annealing. However, the required annealing time was found to be much longer, which negates its appropriateness for industrial production. While a magnificent grain refinement was achieved by one pass of the high-temperature thermomechanical process, the reduction in grain size was negligible by the repetition of the whole cycle. It was found that the hardness of the thermomechanically processed material is much higher than that of the as-received material. The results of the present work were shown to be compatible with the general trend of grain size dependence of hardness for AISI 304L stainless steel based on the Hall-Petch relationship. The results were also discussed based on the X-ray evaluation of dislocation density by modified Williamson-Hall plots.

Effect of size and shape of crystallites on the optical properties of nanostructured ZnS films

The nanoparticles of ZnS is grown on the glass slide substrates using the thermal evaporation technique. The films are annealed in a vacuum ambient at temperatures between 300 and 550°C. The origin of anisotropic diffraction line broadening is studied using the modified Williamson-Hall plot. The shape and size of crystallites as well as the mean value of strain are studied by applying one of the powerful method of X-ray diffraction analysis i.e. Rietveld refinement procedure. It is found that, with the rise of annealing temperature, not only the size of crystallites increases, but also the shape of them changes from sphere to ellipsoid. The optical band gap are also studied from the transmittance and reflectance spectra of the films. The correlation between the microstructure and optical band gap are reported.

Quantitative analysis of the microstructure in NiTi wires by Synchrotron X-ray diffraction: An approach to the cause of the Two Way Shape Memory Effect

Abstract To understand the complex behaviour of the NiTi shape memory alloys, the use of advanced characterization techniques as Synchrotron X-ray diffraction, becomes more and more necessary. In this paper, this technique was performed in heat-treated, thermally cycled at zero stress and two-way memory trained NiTi wires to evaluate through microstrain and retained martensite which is the predominant micro-mechanism that cause the Two Way Shape Memory Effect. The microstructural effects in the structure of the Austenite by thermal and training methods were quantified separately for each NiTi sample, allowing us to calculate how much of the accumulated microstrain in the Austenite phase is due to the increment in density of dislocations and how much is consequence of the decrease in crystallite size. To achieve this, two different methodologies were used. The mean microstrain and shift index were calculated by analysing the whole diffractogram with the Rietveld method and the Double-Voigt Approach. The individual peak shift and the peak broadening of the Austenite phase were evaluated by the modified Williamson-Hall plot. The results show that as higher is the increase in microstrain by thermal and training procedures, higher is the two-way memory strain of the NiTi sample. The micromechanical results pointed out that there is a certain formation of retained martensite during two-way memory training, but is not the main cause of the two-way shape memory effect. What is more, it seems that an early formation of retained martensite during training may decrease the generation of two-way shape memory effect. Pre-training thermal procedures that minimize the formation of retained martensite and maximize the increase in microstrain are fundamental to improve the generation of the NiTi two-way memory strain by subsequent training.

A Size‐Dependent Analysis of the Structural, Surface, Colloidal, and Thermal Properties of Ti1–xB2 (x = 0.03–0.08) Nanoparticles

We report the size‐dependent structural, surface, colloidal, and thermal properties of the well‐known refractory material titanium diboride prepared at the nanoscale by a size‐controlled inorganic molten‐salt technique. A combined analysis of the powder X‐ray diffraction data through a modified Williamson–Hall plot, a size–strain plot, and Rietveld fitting methods indicates that TiB2 nanocrystals with average crystallite sizes smaller than D ≈ 22 nm prefer to form defects at the titanium site rather than experience strain. The resulting composition is Ti1–xB2 [x = 0.03(1)–0.08(1)]. The size‐induced defect formation is accompanied by anisotropic lattice contraction that decreases primarily the cell parameter c. Transmission electron microscopy revealed that the nanocrystals are embedded in an amorphous matrix. A comparison between the electron spin resonance spectra of bulk and nanosized samples indicated that only the nanosized samples yield observable signals. This signal is associated with unpaired electrons trapped in the boron–oxygen species that surround the Ti1–xB2 nanocrystals. These species provide stability to the Ti1–xB2 nanocrystals in aqueous dispersions, as evidenced by electrokinetic measurements. Upon heating under an Ar atmosphere, the boron–oxygen species evaporate from ca. 1000 °C, and the Ti vacancies in the interior nanocrystalline core vanish. TiB2 nanocrystals show excellent chemical stability against decomposition up to 1500 °C.

Enhancement effect of inter-pass annealing during equal channel angular pressing on grain refinement and ductility of 9Cr1Mo steel

To obtain enhanced mechanical property in both the strength and the ductility, 9Cr1Mo steel (T91) was severely deformed by equal channel angular pressing (ECAP) combined with an additional inter-pass annealing. Tensile results show that the additional inter-pass annealing can significantly improve the ductility (i.e. 18% of the total elongation after four-pass extrusion with the inter-pass annealing) but slightly decrease the tensile strength comparing with the case without the inter-pass annealing (i.e. 10% of the total elongation after four-pass ECAP processing). The average grain size of the two passes ECAP-processed materials with the inter-pass annealing (~0.8µm) is smaller than that of the sample without inter-pass annealing (~2µm), and the fraction of the high angle grain boundaries in the samples with the inter-pass annealing (~40%) is higher than that of ~34% (two-pass ECAP) without the inter-pass annealing based on electron backscattering diffraction analysis. The crystallite size and dislocation density were evaluated by means of the modified Williamson-Hall plot based on X-ray diffraction analysis. The microstructural analysis indicates that the enhanced ductility of the ECAP processed and inter-pass annealed materials can be attributed to the relatively smaller grain sizes, larger crystallite sizes and lower dislocation densities.

X-ray Diffraction Analysis of Severely Cold Deformed Hypereutectoid Steel Wire

&lt;p&gt;Hypereutectoid steel wire rod of diameter 6.40 mm is lead patented in lead bath of an electric powered furnace and then it is cold drawn through converging conical dies in a die sequence up to 2.50 mm diameter. The drawn wires subjected to different true strain are analysed using line profile X-ray diffraction methods. The classical Williamson-Hall plot as well as modified Williamson-Hall plot of drawn wire specimens of different true strain is plotted. The theoretical as well as experimental value of q is evaluated. The q is a parameter which depends up on elastic constant of the crystal and type of dislocations. The changes in nature of dislocations from edge dislocations to screw dislocations are calculated against true strain and are verified by scanned electron microscopy’s micrograph of drawn wire.&lt;/p&gt;

Influence of boron and nitrogen on microstructure and hardness of heat-affected zone of modified 9Cr–1Mo steel—Gleeble simulation study

Microstructural evolution in three different boron-added modified 9Cr-1Mo (P91) steels has been studied after subjecting them to in different peak simulation conditions. Optical microscopy, scanning electron microscopy, and X-ray diffraction tools have been used to characterize the microstructure. Prior austenite grain boundaries are found to be present after heat treatments at 950–1200 °C, suggesting thereby that these boundaries are stable and that the “memory effect” exists in these steels. Analysis based on the modified Williamson–Hall plot shows that while the crystallite size remains similar irrespective of the peak simulation temperature, the highest peak simulation temperature results in lower dislocation density. The measured hardness values remain similar irrespective of the peak simulation temperature, except for marginal variations among the three different heats.

The effect of magnetic annealing on crystallographic texture and magnetic properties of Fe-2.6% Si

Abstract The effect of magnetic annealing on crystallographic texture, microstructure, defects density and magnetic properties of a Fe-2.6% Si steel has been analyzed. After two stage cold rolling (75% and 60% cold rolled) with intermediate annealing process at (600 °C/1 h) the sample annealed at 600 °C for one hour during which different magnetic field of 0, 7 and 14 T were applied has been investigated. The effect of defects density after cold rolling process on the recrystallization texture and magnetic properties was characterized. Heat treatments under a high external field of 14 T show a drastic improvement of the magnetic properties such as significantly increased permeability. Neutron diffraction measurements were preferred for measurement of the bulk sample texture so that sufficient grain statistics were obtained. Because of its small wavelength (0.05–0.2 A) Synchrotron diffraction with high photon energy was used to evaluate the defects density by a modified Williamson–Hall plot.

Investigation of deformation and microstructural evolution in Grade 91 ferritic–martensitic steel by in situ high-energy X-rays

In situ wide- and small-angle X-ray scattering (WAXS/SAXS) were used to characterize microstructural evolution in Grade 91 ferritic–martensitic steel during tensile tests at room temperature (RT) and 650°C. Elastic lattice strains in the Fe matrix, M23C6 and MX precipitates were measured from peak shifts in WAXS patterns. Load transfer, as evidenced by precipitates developing much higher lattice strain than the Fe matrix in the plastic regime, was found for the RT test but was not obvious at 650°C. Detailed peak-broadening analysis as a function of strain, using modified Williamson–Hall plots, indicates strong dislocation activity in the Fe matrix during the RT test which can be divided into two stages: (i) dislocation multiplication (from 0 to 4.0% strain) and (ii) formation of dislocation walls and cells (after 4.0% strain). This framework is consistent with the observed precipitate strain response and can describe the macroscopic flow stress behavior. At 650°C, Fe peaks broadened much less with increasing strain, indicating a low dislocation density and providing an explanation for the low precipitate strains and macroscopic flow stress at this temperature. Changes in SAXS intensity were used to infer nanoscale void formation, which occurred immediately after necking at RT but long after necking at 650°C. Most voids were concentrated at the necking center, and the RT specimen developed more voids than the 650°C specimen.

Structural and Wear Characterization of Heat Treated En24 Steel

Ni–Cr–Mo steels such as En24 steel are widely used in machine part members, gears and shafts. En24 steel is generally used in the hardened and tempered condition to achieve an optimum combination of hardness and ductility. In the present study, heat treatment response of En24 steel was investigated by variation of hardening and tempering temperature in relation to microstructure and hardness. The microstructures were studied through a combination of scanning electron microscopy (SEM) and X-ray diffraction (XRD). The hardness decreased with the increase in hardening temperature from 1123 to 1273 K, whereas it increased slightly with the increase in hardening temperature after tempering at 823 K. The martensitic microstructure (laths) became coarser with increase in hardening temperature. The hardness results were well supplemented by XRD results (Williamson-Hall (WH) & modified WH plots and qualitatively by dislocation density). The specimens tempered at different temperatures (in the range 473–823 K) exhibited decreasing hardness with increase in tempering temperature. The abrasive wear tests were carried out on hardened and tempered specimens. The abrasive wear volume loss decreased with increase in tempering temperature, which was attributed to coarsening of martensite. The worn out specimens were observed under SEM, which revealed micro ploughing and cutting as important mechanisms of material removal during abrasive wear.

Electronic-grade GaN(0001)/Al2O3(0001) grown by reactive DC-magnetron sputter epitaxy using a liquid Ga target

Electronic-grade GaN (0001) epilayers have been grown directly on Al2O3 (0001) substrates by reactive direct-current-magnetron sputter epitaxy (MSE) using a liquid Ga sputtering target in an Ar/N2 atmosphere. The as-grown GaN epitaxial films exhibit low threading dislocation density on the order of ≤1010 cm−2 determined by transmission electron microscopy and modified Williamson–Hall plot. X-ray rocking curve shows narrow full-width at half maximum (FWHM) of 1054 arc sec of the 0002 reflection. A sharp 4 K photoluminescence peak at 3.474 eV with a FWHM of 6.3 meV is attributed to intrinsic GaN band edge emission. The high structural and optical qualities indicate that MSE-grown GaN epilayers can be used for fabricating high-performance devices without the need of any buffer layer.

Structural analysis of chemically deposited nanocrystalline PbS films

Nanocrystalline PbS films are deposited on glass substrates by chemical bath deposition technique at room temperature. The structural parameters of PbS nanoparticles are studied by X-ray line profile analysis using Williamson-Hall and modified Williamson-Hall plot. The values of average crystallite sizes are found to vary from 12 to 18 nm having very high dislocation density of the order of 10 17 m −2.

Resolving ensembled microstructural information of bulk-metallic-glass-matrix composites using synchrotron x-ray diffraction

The microstructural characterization of the Zr60.0Ti14.7Nb5.3Cu5.6Ni4.4Be10.0 bulk-metallic-glass-matrix composites is investigated using high-energy synchrotron x-ray diffraction. The convoluted diffraction-intensity distribution in the azimuthal direction is naturally yielded from the spatial arrangements of the crystalline dendrites and their amorphous matrix. We facilitate the area selection and the intensity integration of the diffraction collected from a two-dimensional detector to characterize the diffraction intensity of the amorphous matrix. The results enable us to apply the modified Williamson–Hall plots for using the peak width to study the microstrain and micromechanism of the deformation of the crystalline phase.

X-ray studies of structure defects in nanostructured FeAl alloy

The evolution of the microstructure of the mixture iron and aluminium powders during the high energy mechanical alloying process was investigated by X-ray line profile analysis. Analysis of line breadths was carried out to get an insight into the interrelated effects of grain size, lattice strain and dislocations. The final product of the MA process was the nanocrystalline Fe(Al) solid solution with a mean crystallite of 10 nm. On the basic on the modified Williamson–Hall plots, the root-mean squared strains were explained by the presence of dislocations, with a dislocation density of about 6 × 10 16 m − 2 . The identified steady-state saturation values of these parameters can be related to accumulate strain hardening of the powder material during longer milling times.