Warren-Averbach Method Research Articles

Size-strain distribution analysis from XRD peak profile of (Mg, Fe) co-doped SnO2 nanoparticles fabricated using chemical co-precipitation route

In this study, we synthesize pristine and (Mg, Fe) co-doped SnO2 nanoparticles using the chemical co-precipitation method, where the Mg doping amount is fixed (2 mol%) and the amount of Fe is varied between 2 and 6 mol%. The narrow and sharp natures of intense XRD peaks notify that the crystallinity is pretty well. The formation of the single-phase tetragonal rutile type structure of all prepared compounds has been identified by Rietveld refinement, Fourier-transform infrared spectroscopy (FTIR), and Raman spectroscopy. Moreover, the well incorporation of Fe and Mg in SnO2 and absence of any other unexpected elements are confirmed by the energy dispersive X-ray spectroscopy. How the co-doping of Mg and Fe alter the crystallite size, microstrain, and dislocation density of the prepared samples have been investigated by Scherrer method with various modified version of it, Williamson-Hall method (W–H) in three factions (UDM, USDM, and UDEDM), Size strain plot (SSP) method, Halder-Wagner (H–W) method, Wagner-Aqua (W-A) method, and Warren-Averbach (WA) method. The obtained crystallite size using the WA method is smaller than the other methods and Scherrer-based methods show much comparable (except SLMSE) sizes. Additionally, the W–H, H–W, SSP, and W-A plots show almost similar tendency of decreasing crystal size, increasing dislocation density and lattice strain with increasing doping. The scanning electron microscopy (SEM) profiles revealed that the synthesized nanoparticles are agglomerated in nature, where the agglomeration increases with decreasing crystal size. The magnetic response of the prepared samples revealed a weak ferromagnetic (or soft magnetic) nature, where saturation magnetization increased due to doping, and a reducing trend of remanent magnetization and coercivity was explored which indicates the phase transition from ferromagnetic to paramagnetic. However, this soft magnetic nature was modified with the influence of defects like changes in lattice parameters, strain, and oxygen vacancy. This phase transition at higher doping concentration makes our nanomaterial as a suitable contender for memory devices, hyperthermia treatment, and photothermal effect.

Confirmation of the presence of edge dislocations in the prepared FCC ZnTe nanocrystals from the study of structural analysis through the MWH method with added Fourier analysis (W-A method) of diffraction peaks

Nanocrystalline ZnTe with cubic mono-phase has been synthesized by a wet-chemical synthesis process for the study of the presence of dislocations through X-ray diffraction peak profile analysis. The average size of the ZnTe nanocrystals has been determined from the High-Resolution Transmission Electron Microscopic (HRTEM) analysis as 21.9 nm. In the XRD pattern, (111), (200), (220), (311), and (400) diffraction planes have been observed, which confirms the formation of cubic mono-phase of ZnTe. For the extraction of microstructural details, the Rietveld refinement has been performed using Fullprof software and from this refinement, the lattice constant has been obtained as 6.17 Å under the space group of f-43. Here, X-ray diffraction peak has been analyzed through the Williamson-Hall (W–H) analysis method and the Warren-Averbach (W-A) analysis method. Williamson-Hall approach is based on the full-width at half-maxima analysis, whereas the Warren-Averbach method is related to the analysis of the Fourier transform of the broadened X-ray diffraction peaks. For considering and analyzing the anisotropic broadening of the peak, modified Williamson-Hall and modified Warren-Averbach methods have been used for the calculation of size, strain, and dislocation density. The presence of prominent edge dislocation of about 71 % has been confirmed from the anisotropic peak broadening study. In addition, the HRTEM image directly verifies the presence of edge dislocations in both the lattice planes of (111) and (220).

Dislocations and crystallite size distribution of cadmium oxide thin films synthesized by spray pyrolysis technique

Cadmium oxide (CdO) thin films have been successfully deposited on amorphous glass substrates by spray pyrolysis technique at a temperature, 573 °K using aqueous solution of cadmium nitrate 4-Hydrate powder with a concentration of 0.1 M. The X-ray diffraction (XRD) studies have revealed that the films exhibit cubic crystal structure. The modified Williamson–Hall and Warren–Averbach methods are used successfully for analyzing the XRD line profile for determining the crystallite size, dislocation densities and crystallite size distribution in CdO thin films. The crystallite size (D) and integral breadths (d) (D = 44.139 nm and d = 32.237 nm) are obtained by the modified Williamson Hall, while the area-weighted average grain sizes and volume-weighted obtained of modified Warren–Averbach method are xvol=46,06nm andxarea=29,7nm, respectively. The size parameter (Lo), dislocation density (ρ), effective outer cut-off radii (Re) and dislocation arrangement parameter (μ) gotten of Warren–Averbach are 35.53 nm, 2.0 × 1015 m−2, 7 nm and 0.31 nm, respectively. The particle size distribution (x) derived of XRD and estimated of size parameter is the size distribution function f(x) of log-normal.

X-ray diffraction analysis of kaolin M1 and M2 via the Williamson–Hall and Warren–Averbach methods

Kaolin M1 and M2 studied by X-ray diffraction focus on the mullite phase, which is the main phase present in both products. The Williamson–Hall and Warren–Averbach methods for determining the crystallite size and microstrains of integral breadth β are calculated by the FullProf program. The integral breadth ( β) is a mixture resulting from the microstrains and size effect, so this should be taken into account during the calculation. The Williamson–Hall chart determines whether the sample is affected by grain size or microstrain. It appears very clearly that the principal phase of the various sintered kaolins, mullite, is free from internal microstrains. It is the case of the mixtures fritted at low temperature (1200 °C) during 1 h and also the case of the mixtures of the type chamotte cooks with 1350 °C during very long times (several weeks). This result is very significant as it gives an element of explanation to a very significant quality of mullite: its mechanical resistance during uses at high temperature remains.

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.

Evolution of microscopic strains, stresses, and dislocation density during in-situ tensile loading of additively manufactured AlSi10Mg alloy

The AlSi10Mg alloy produced by laser powder bed fusion (LPBF) possesses a novel microstructure and higher mechanical properties compared with its casting counterpart. So far, the crystallographic orientation-dependent lattice strains, average phase stresses, and dislocation density during the tensile loading of the LPBF AlSi10Mg are not well understood. This fact is impeding further optimization of microstructure and mechanical properties. High energy synchrotron X-ray diffraction providing deep penetration capability and phase-specific measurements of various bulk properties of crystal materials is applied to investigate the LPBF AlSi10Mg under loading. The crystallographic orientation-dependent lattice strains and elastoplastic properties of the Al matrix are assessed. The average phase stresses are calculated to quantify load partitioning between the Al and Si phases. The nano-sized Si particles that bear high-stress are efficient strengthening particles. The maximum value of the average phase stress of Si reaches up to ~2 GPa. Based on the modified Williamson-Hall and the modified Warren-Averbach methods, the dislocation density and its evolution during the plastic deformation are determined. A multistage strain hardening behavior is detected in the Al matrix, which is associated with the interactions between the dislocations and the cell boundary network.

Internal Dislocation Density in Deformed GlidCop from X-Ray Line Profile Analysis

Dislocation densities of GLIDCOP®, dispersion-strengthened copper with ultra-fine particles of aluminum oxide, were evaluated by employing the X-ray line profile analysis using the modified Williamson-Hall and modified Warren-Averbach methods. X-ray diffraction profiles for GlidCop samples with compressive strains applied at 200oC were measured with synchrotron radiation. The dislocation densities of GlidCop with compressive strain ranging from 0.6 to 4.3% were in the order of 3.2 × 1014–5.8 × 1014 m-2. The dislocation density increased with increasing the compressive strain within the measured strain range.

Evaluation of Dislocation Densities in Various Microstructures of Additively Manufactured Ti6Al4V (Eli) by the Method of X-ray Diffraction.

Dislocations play a central role in determining strength and flow properties of metals and alloys. Diffusionless phase transformation of β→α in Ti6Al4V during the Direct Metal Laser Sintering (DMLS) process produces martensitic microstructures with high dislocation densities. However, heat treatment, such as stress relieving and annealing, can be applied to reduce the volume of these dislocations. In the present study, an analysis of the X-ray diffraction (XRD) profiles of the non-heat-treated and heat-treated microstructures of DMLS Ti6Al4V(ELI) was carried out to determine the level of defects in these microstructures. The modified Williamson–Hall and modified Warren–Averbach methods of analysis were used to evaluate the dislocation densities in these microstructures. The results obtained showed a 73% reduction of dislocation density in DMLS Ti6Al4V(ELI) upon stress relieving heat treatment. The density of dislocations further declined in microstructures that were annealed at elevated temperatures, with the microstructures that were heat-treated just below the β→α recording the lowest dislocation densities.

Rearrangements of dislocations during continuous heating of deformed β-TiNb alloy observed by in-situ synchrotron X-ray diffraction

Heating of deformed metals always causes changes in their structure and properties. These changes are related to annihilation of the crystallographic defects and rearrangement of the dislocation structure. The currently existing knowledge on structural transformations occurring during the heating of deformed metals is mainly based on ex-situ metallographic observation of samples after they have been cooled to room temperature. In this study we attempted to observe defect annihilation and dislocations rearrangement in β-titanium alloy during heating by using in-situ synchrotron X-ray diffraction (SXRD). For this reason, a thorough peak profile analysis using modified Williamson-Hall (mWH) and modified Warren-Averbach (mWA) methods was applied to several hundreds of diffraction patterns obtained during continuous heating of cold rolled Ti45Nb alloy. Several stages of dislocation structure evolution were distinguished based on observation of changes in dislocation density, type of dislocation, energy of dislocations and crystallite size. Such analysis revealed several phenomena which haven't been reported in the literature so far. The results of synchrotron XRD analysis were in excellent agreement with measurements of mechanical properties.

Structural Study of Novel Nanocrystalline fcc Ti-Ta-Sn Alloy

This report discussed the microstructural features of fcc Ti-13Ta-6Sn alloy synthesized using mechanical ball milling at 100 hours. The X-ray diffraction profile analysis was discussed using Rietveld, modified Williamson-Hall and Warren-Averbach methods. Two important conditions, high plastic deformation and nanocrystalline size range to satisfy the stable face-centered cubic (fcc) phase were achieved. The X-ray diffraction profile analysis and TEM images proved that the crystallite size and dislocation density of 6.6 nm and 1016 m−2, respectively.

Structure and microstructure characterization of the La2SrB10O19 glass-ceramics

The crystal structure of new lanthanum strontium borate glass-ceramics was refined by the Rietveld method. The results showed that La2SrB10O19 has the monoclinic crystal structure, space group C2 (No. 5) with a = 11.1170(6), b = 6.5667(3), c = 9.2363(3) ?, ? = 91.481?, V = 674.04(7) ?3, two formula units per unit-cell, and density 3.830 g cm?3. The main building units of the crystal structure are BO4 tetrahedra and BO3 triangles. Clusters composed of [B5O12] form an infinite double layer running perpendicular to the c-axis. Lanthanum atoms, situated in [B5O12]n layers, are coordinated with 10 oxygen atom in a form of LaO10 polyhedra, while Sr atoms, located between [B5O12]n layers, are coordinated with 8 oxygen atoms in a form of SrO8 polyhedra. Microstructural measurements contain both crystallite domain sizes and microstrain calculations obtained by the Warren-Averbach and the simplified integral-breadth methods.

X-ray diffraction line profile analysis: A microstructural study in polymorphic TiO2

Abstract The microstructural properties of polycrystalline materials can be indirectly analyzed through X-ray diffraction data. To this, the diffraction-line broadening phenomena is taking into account as a basis to develop theoretical approaches focusing on determinate defects into the crystal structure (e.g., dislocations, stacking and twin faults, lattice distortions, vacancies) as well as their concentrations and distributions. In this study, X-ray Line Profile Analysis (XLPA) from two pure samples of anatase and rutile TiO2 powders were conducted to look at their microstructural characterization using the classical Williamson Hall (WH) and Warren Averbach (WA) methods. WH microstructural analysis indicates that the calculated strain contribution at the upper limit is 1.89% and 1.31% for anatase and rutile, respectively, while the root mean-square of the variations in the strain was determined using the WA method to obtain percentages in about 0.23% and 0.30% for anatase and rutile, respectively. The area-weighted mean column length, t Area , was determine using WA obtaining 42 nm and 91 nm in anatase and rutile phases, respectively.

Onnanoscale phenomena inthe electroacoustic sputtering process

Introduction. The effect of variable parameters of the electroacoustic sputtering (ELAS) process on the characteristics of the crystalline structure of hardening coatings is studied. The ELAS parameter values providing nanostructured cover coatings for machine parts and cutting tools are determined. Hardening through using such coatings allows achieving a significant (5-10 times) increase in the life of hardenable machine parts and various tools designed for mechanical processing. To obtain coatings with the desired properties of the surface layer, nanocrystalline materials should be selected. In this case, a certain content of the amorphous phase is permissible.Materials and Methods. To carry out the X-ray structural analysis, the X-ray diffraction Russian-made device DRON-3M was used. The Scherrer-Wilson method was applied to determine the granularity of particle blocks from the value of the intrinsic broadening of the diffractogram peaks. The conclusions obtained in this paper are based on the method of separation of the affecting factor contributions into broadening the diffraction reflection peaks (the Warren-Averbach method).Research Results. Depending on the process conditions and the technique for obtaining nanostructured materials, a nonuniquely interpretable change in the indices of the diffraction peaks broadening occurs, which is generally characteristic of nanocrystalline metals. One of the possible explanations for this phenomenon is the presence of a nanosized effect in the hardened layer. The occurrence of the nanocrystalline structure in the sputtered layer verifies the calculated values of the dimensions of the coherent scattering regions (CSR). The occurrence of affecting values of the misorientation angle of the crystal structure is verified by the CSR value for the investigated 110 and 220 reflexes, which is supported by a high percentage of the amorphous phase.Discussion and Conclusions. The electroacoustic scattering method is promising for obtaining nanocrystalline structures in the surface and subsurface layers of the sprayed samples. The ELAS process variables variation leads to the parameter spread of the crystal lattice and coherent scattering areas. In this case, there is no definite trend. In the future it is expected to solve the given problem. First, experiments will be conducted to determine the optimal sputtering regimes that could stimulate the formation of nanocrystalline structures. Secondly, visual observation and evaluation of the sprayed layer structure using electron microscopy is planned.

Dislocation Densities in Dispersion-Strengthened Copper with Aluminum Oxide from X-Ray Line Profile Analysis

Dislocation densities of dispersion-strengthened copper with aluminum oxide, namely GlidCop were evaluated employing the X-ray line profile analysis using the modified Williamson-Hall and modified Warren-Averbach method. X-ray diffraction profiles for GldCop samples with compressive strains applied at ambient temperature were measured with synchrotron radiation. The dislocation densities of GlidCop with compressive strain ranging from 0 – 2.7 % were on the order of 1.5×1014 – 6.6×1014 m-2.

X-ray diffraction Warren–Averbach mullite analysis in whiteware porcelains: influence of kaolin raw material

ABSTRACTCompositional and microstructural analysis of mullites in porcelain whitewares obtained by the firing of two blends of identical triaxial composition using a kaolin B consisting of ‘higher-crystallinity’ kaolinite or a finer halloysitic kaolin M of lower crystal order was performed. No significant changes in the average Al2O3 contents (near the stoichiometric composition 3:2) of the mullites were observed. Fast and slow firing at the same temperature using B or M kaolin yielded different mullite contents. The Warren–Averbach method showed increase of the D110 mullite crystallite size and crystallite size distributions with small shifts to greater values with increasing firing temperature for the same type of firing (slow or fast) using the same kaolin, as well as significant differences between fast and slow firing of the same blend at different temperatures for each kaolin. The higher maximum frequency distribution of crystallite size observed at the same firing temperature using blends with M kaolin suggests a clearer crystallite growth of mullite in this blend. The agreement between thickening perpendicular to prism faces and mean crystallite sizes <D110> of mullite were not always observed because the direction perpendicular to 110 planes is not preferred for growth.

X-ray powder diffraction line broadening analysis of the nanocrystalline tin dioxide by the classical Warren-Averbach approach

In the present study, the X-ray diffraction line profile analysis technique has been applied to investigating the microstructure of nanocrystaline materials in terms of average crystallite sizes, size distributions and micro strains. We have calculated the size and strain Fourier coefficients by using classical Warren-Averbach method for the two (110) and (220) reflections. Assuming that the grain size distribution in the nanocrystaline SnO2 can be approximated by a log normal function, the area- and volume-weighted average grain size value were estimated as $ 16.14 \pm 0.23$ and $ 19.67 \pm 0.23$ nm, respectively. To validate the results obtained from Warren-Averbach analysis, the obtained size was compared by the SEM results reported in our previous work and the results are in good agreement. The behavior of strain indicates the extent of the inhomogeneous strain distribution which causes the broadening of X-ray line profile in the crystalline lattice of tin dioxide nanoparticles.

X-ray diffraction line broadening analysis of nanostructured nickel powder

X-ray diffraction peak profile analysis is a powerful method for investigation of the microstructural characteristics of nanocrystalline materials produced by severe plastic deformation. Williamson–Hall method, its modification, and Fourier transform methods like Warren–Averbach and its modification are used to extract microstructural information based on integral breadth and Fourier coefficients of the peak profiles. In this work, pure nickel powders were milled for 2, 5, 20, and 40 h to clarify the microstructural variations for this metal with FCC atomic structure. By using the Williamson–Hall and Warren–Averbach methods and their modifications, crystallite size, microstrain, dislocation density, and character of dislocation were extracted. It was obtained that the fraction of edge-type dislocation decreased with milling time (above 50%), while after prolonged milling, the fraction of screw-type dislocations decreased, so that 50%-edge-to 50%-screw ratio was obtained. It was also found that the values of the crystallite size obtained from classical Warren–Averbach and modified Warren–Averbach (area-average) were closed.

Dislocation Density of Plastically Deformed Oxygen-Free Copper

The dislocation density of plastically deformed oxygen free copper (OFC) was evaluated by X-ray diffraction profile analysis with synchrotron radiation. The modified Williamson-Hall and modified Warren-Averbach methods were applied to the analysis. The dislocation densities of OFC samples with compressive plastic strains of 1 % and 4 % were 5.1×1014 m-2 and 9.2×1014 m-2, respectively.

Characterization of Mn<sub>0.67</sub>Zn<sub>0.33</sub>Fe<sub>2</sub>O<sub>4</sub> Nanoparticles Synthesized under Different pH

Nanostructured Mn-Zn ferrites were synthesized using co-precipitation in alkaline solution with different pH. The samples were characterized using X-ray diffraction (XRD), X-ray fluorescence (XRF), thermal analysis (TG-DTA), dynamic light scattering (DLS) and scanning electron microscopy (SEM) techniques. Monophasic nanoparticles were formed when synthesized with pH 10.5. This sample was heat-treated and its XRD data was refined by the Rietveld method. Mean crystallite sizes and microstrains were determined from X-ray line profile analysis using Single-Line and Warren-Averbach methods, which revealed a mean crystallite size of approximately 10 nm and negligible microstrains. Zn content was estimated using refined cell parameters, giving a value of 33 at %, in accordance with XRF result. TG-DTA revealed that the incorporation of α-Fe2O3 occurs around 1130 °C and 1200 °C with recrystallization of the Mn-Zn ferrite spinel phase. DLS showed that mean particle size increase with temperature up to 1159 nm at 800 °C. SEM analysis showed the samples agglomerate and present similar morphology with negligible size changing when calcined between 280 °C and 800 °C. However, the sample calcined at 1200 °C presents larger agglomerates due to the sintering process.

XRDおよびEBSDを用いた23Cr-45Ni-7W合金溶接部のひずみ評価

The residual strain of 23Cr-45Ni-7W Alloy welds was estimated by the change in the dislocation density and the average misorientation within grains. X-ray diffraction was used to measure the dislocation density by the modified Williamson-Hall method and the modified Warren-Averbach method. EBSD technique was used to measure the orientation in order to calculate the grain orientation spread (GOS) as the average misorientation within grains. Tensile tests were conducted at room temperature and were interrupted to prepare a number of specimens with different residual strain. The changes in the dislocation density and GOS with the strain were investigated using the interrupted specimens and the heat-affected zone in 23Cr-45Ni-7W Alloy welds. The dislocation density and GOS increased approximately linearly with increase in the residual strain. The residual strain of the heat-affected zone in 23Cr-45Ni-7W Alloy welds was evaluated from the linear relationships. The residual strain near the bond line estimated by the dislocation density was 3.7%;the estimated residual strain decreased with increases in the distance from the bond line. At 10 mm away from the bond line, the residual strain became less than 1%. The change in the residual strain near the bond line estimated by GOS showed a similar tendency.