<b>Structural and Microstructural Characterization of Cu-Doped NiFe<sub>2</sub>O<sub>4</sub> Nanoparticles Using Williamson-Hall Method</b>

Microstructural parameters from X-ray peak profile analysis by Williamson-Hall models; A review

This research paper dealt with the synthesis and characterization of pure and metal-doped hydroxyapatite covering an in-depth crystallographic analysis. The Scherrer equation, Linear Straight-Line Model, Munshi Scherrer Model, Uniform Deformation Model, Uniform Stress Deformation Model, Uniform Deformation Energy Density Model, Size Strain Model, Halder Wagner Model, and Sahadat Scherrer Model were engaged to estimate crystallite size as well as strain, stress, and energy density from few models. All the models were evaluated with their merits and demerits along with usefulness. All the mentioned models showed acceptable results as the crystallite size ranges were from 22 to 77 nm except Linear Straight-Line Model (revealed invalid results for all the synthesized samples). The modified Williamson-Hall model (Uniform Deformation Model, Uniform Stress Deformation Model, Uniform Deformation Energy Density Model) exerted strain, stress and energy density positive and negative. But Size Strain Model, and Halder Wagner Model resulted in only positive values.

ABSTRACTCoAl2O4 nanoparticles were prepared by a Pechini method using chelating agent citric acid. CoAl2O4 nanoparticles were synthesized at different calcination temperatures of 600–900°C. The crystalline spinel cubic phase was confirmed by X-ray diffraction results. High-resolution scanning electron microscopy (HRSEM) revealed that nanoparticles of CoAl2O4 morphology showed spherical forms with a certain degree of agglomeration. The Williamson–Hall (W–H) method and size–strain method to evaluate the size of crystallites and strain in the CoAl2O4 nanoparticles’ peak broadening were applied. Physical parameters such as strain and stress values were calculated for all XRD reflection peaks corresponding to the cubic spinel phase of CoAl2O4 in the range of 20–70° from the modified plot shape by the W–H plot assuming a uniform deformation model (UDM), uniform stress deformation model (USDM), uniform deformation energy density model (UDEDM), and by the size–strain plot (SSP) method. The crystal size of the CoAl2O4 NPs calculated on the W–H plots and the SSP method are in good agreement with the HRSEM and Scherrer method.

ZnO doped with different concentrations of Al2O3 (2, 4, 6, 8 and 10 wt%) is prepared by conventional solid-state reaction method. X-ray diffraction results revealed that the samples were crystalline with a hexagonal wurtzite phase. As the concentration of alumina (Al2O3) increases in ZnO, the X-ray diffraction peaks shifts towards higher angle. This shifting in peak position and decrease in intensity reflect that Al is successfully replaced Zn in ZnO matrix. X-ray peak broadening analysis was used to evaluate the crystallite size and lattice strain by the Williamson–Hall (W–H) method and size-strain plot (SSP) method. The physical parameters such as strain, stress, and energy density values were also calculated using W–H method with different models namely uniform deformation model, uniform stress deformation model and uniform deformation energy density model. The surface morphology and elemental analysis of the prepared samples were characterized by field emission scanning electron microscopy and energy dispersive spectra.

We report on a comparison of methods based on XRD patterns for calculating crystal size. In this case, XRD peaks were extracted from hydroxyapatite obtained from cow, pig, and chicken bones. Hydroxyapatite was synthesized through the thermal treatment of natural bones at 950 °C. XRD patterns were selected by adjustment of X-Pert software for each method and for calculating the size of the crystals. Methods consisted of Scherrer (three models), Monshi–Scherrer, three models of Williamson–Hall (namely the Uniform Deformation Model (UDM), the Uniform Stress Deformation Model (USDM), and the Uniform Deformation Energy Density Model (UDEDM)), Halder–Wanger (H-W), and the Size Strain Plot Method (SSP). These methods have been used and compared together. The sizes of crystallites obtained by the XRD patterns in each method for hydroxyapatite from cow, pig, and chicken were 1371, 457, and 196 nm in the Scherrer method when considering all of the available peaks together (straight line model). A new model (straight line passing the origin) gave 60, 60, and 53 nm, which shows much improvement. The average model gave 56, 58, and 52 nm, for each of the three approaches, respectively, for cow, pig, and chicken. The Monshi–Scherrer method gave 60, 60, and 57 nm. Values of 56, 62, and 65 nm were given by the UDM method. The values calculated by the USDM method were 60, 62, and 62 nm. The values of 62, 62, and 65 nm were given by the UDEDM method for cow, pig, and chicken, respectively. Furthermore, the crystal size value was 4 nm for all samples in the H-W method. Values were also calculated as 43, 62, and 57 nm in the SSP method for cow, pig, and chicken tandemly. According to the comparison of values in each method, the Scherrer method (straight line model) for considering all peaks led to unreasonable values. Nevertheless, other values were in the acceptable range, similar to the reported values in the literature. Experimental analyses, such as specific surface area by gas adsorption (Brunauer–Emmett–Teller (BET)) and Transmission Electron Microscopy (TEM), were utilized. In the final comparison, parameters of accuracy, ease of calculations, having a check point for the researcher, and difference between the obtained values and experimental analysis by BET and TEM were considered. The Monshi–Scherrer method provided ease of calculation and a decrease in errors by applying least squares to the linear plot. There is a check point for this line that the slope must not be far from one. Then, the intercept gives the most accurate crystal size. In this study, the setup of values for BET (56, 52, and 49 nm) was also similar to the Monshi–Scherrer method and the use of it in research studies of nanotechnology is advised.

CoAl2O4nanoparticles were prepared by a sol-gel process using citric acid as chelating agent with different calcination temperatures of 600 to 900 °C. The crystalline spinel cubic phase was confirmed by X-ray diffraction results. High-resolution scanning electron microscopy (HRSEM) revealed that nanoparticles of CoAl2O4morphology showed spherical forms with a certain degree of agglomeration. The Williamson-Hall (W-H) method and size-strain method to evaluate the size of crystallites and strain in the CoAl2O4nanoparticles peak broadening were applied. Physical parameters such as strain and stress values were calculated for all XRD reflection peaks corresponding to the cubic spinel phase of CoAl2O4in the range of 20 to 70° from the modified plot shape by W-H plot assuming a uniform deformation model (UDM), uniform stress deformation model (USDM), uniform deformation energy density model (UDEDM) and by the size-strain plot method (SSP). The CoAl2O4NPs crystal size calculated on the W-H plots and the SSP method are in good agreement with the HRSEM Scherrer method.

<abstract> In the present paper, nanometer scale hydroxyapatite powders with a rod-like shape, were prepared using a combined ultrasonic and microwave heating-based method. Subsequent annealing of as-synthesized powders at 800 ℃ for 2 h produced nanoparticles with a rectangular and granular morphology. The hydroxyapatite particles were characterized using X-ray diffraction and Fourier transform infrared spectroscopy methods. Also, nanoparticle size and morphology were investigated using transmission electron microscopy and field emission scanning electron microscopy. A comparable selected area electron diffraction (SAED) analysis also showed results in line with X-ray powder diffraction patterns. The resulting X-ray diffraction peaks indicated that the powders were highly crystalline in nature and no impure phases were present. The X-ray diffraction data, was also used to study the effects of peak broadening by using the Williamson–Hall (W–H) analysis technique. The analysis used the uniform deformation model (UDM), uniform stress deformation model (USDM) and uniform deformation energy density model (UDEDM) to determine physical parameters like crystallite size, lattice strain, stress and energy density. The results of the W-H analysis were found to be comparable to the results obtained from microscopy studies. Importantly, the studies confirmed the synthesized nano- hydroxyapatite powders had morphologies similar to those found in dental hard tissues. </abstract>

ZnO nanoparticles and Cu-doped ZnO nanoparticles were prepared by co-precipitation method. Also, a part of the pure ZnO nanoparticles were annealed at 750 °C for 3, 6, and 9 h. X-ray diffraction studies were carried out and the lattice parameters, unit cell volume, interplanar spacing, and Young’s modulus were calculated for all the samples, and also the crystallite size was found using the Scherrer method. X-ray peak broadening analysis was used to estimate the crystallite sizes and the strain using the Williamson–Hall (W–H) method and the size–strain plot (SSP) method. Stress and the energy density were calculated using the W–H method assuming different models such as uniform deformation model, uniform strain deformation model, uniform deformation energy density model, and the SSP method. Optical absorption properties of the samples were understood from their UV–visible spectra. Photocatalytic activities of ZnO and 5 % Cu-doped ZnO were observed by the degradation of methylene blue dye in aqueous medium under the irradiation of 20-W compact fluorescent lamp for an hour.

Hexagonal structure of pure and Al doped ZnO nanocrystals were synthesized by co-precipitation technique. The average crystallite size determined from XRD data using Debye Sherrer’s formula was found to be 16.8 nm for pure 19.3 nm for 4% Al Doped ZnO. High-resolution transmission electron microscopy (HR-TEM) showed single-crystal ZnO nanocrystals with nearly spherical shapes. The W-H analysis and size-strain plot were used to study the individual contributions of crystallite sizes and lattice strain “ε” on the peak broadening of pure and Al doped ZnO nanocrystals. The physical parameters namely strain, stress and anisotropic energy density were calculated considering uniform deformation model (UDM), uniform stress deformation model (USDM) and uniform deformation energy density model (UDEDM) of modified form of W-H analysis. Texture coefficient was estimated using XRD data. The average crystallite size of pure and Al doped ZnO samples estimated from W-H model. It is also revealed from the TEM the diameters of as synthesized samples are in good agreement with the W-H model analysis.

ABSTRACTYttrium oxide (Y2O3) particles were synthesised from a yttrium nitrate solution via ultrasonic spray pyrolysis (USP) method. The effects of temperature and precursor concentration on morphology and microstructural parameters were investigated. Y2O3 particles were characterised by scanning-electron-microscope energy-dispersive spectroscopy, Raman spectroscopy and X-ray diffraction analysis. Based on X-ray peak broadening, the crystallite size was calculated using the modified Debye–Scherrer (MDS) method. Furthermore, the crystallite size, crystal strain and the energy density of the crystal were evaluated using the Williamson–Hall (W–H) analysis integrated with the uniform deformation model, the uniform stress deformation model and the uniform deformation energy density model. A comparative evaluation of Y2O3 crystallite size using the MDS and W–H methods was carried out.This is part of a thematic issue on Nanoscale Materials Characterisation and Modeling by Advances Microscopy Methods - EUROMAT.

X-ray diffraction analysis of nanocomposite [formula omitted]/activated carbon by Williamson–Hall and size-strain plot methods

In this study, five periodic InGaN / GaN LED (light emitting diode) structures grown by the Metal Organic Vapor Deposition (MOCVD) at different active layer growth temperatures were studied. These structures were grown as InGaN / GaN multiple quantum wells (MQW) between c-oriented sapphire substrate and n-GaN and p-AlGaN + GaN contacts. These constructions were characterized by the high-resolution X-ray diffraction (HR-XRD) system. HRXRD patterns obtained by X-ray diffraction and Reciprocal space maps were performed from the same data. One of the most effective ways of studying the crystal lattice is reciprocal space mapping with HR-XRD technique. This technique does not damage the sample. Information can be obtained from the internal system of the sample or from the intermediate layer including substrate. Using the FWHM (β hkl ) values and the elastic coefficients of the structures obtained for each of the three samples separately with the inverse mesh technique, D (nm) particle size, σ (GPa) uniform stress, e strain, u (kJm -3 ) anisotropic energy density parameters were calculated. These calculations were done in a Scherrer method and Uniform Deformation Model (UDM) which is the Williamson Hall method, modified uniform Williamson stresses model (USDM) and Uniform Deformation Energy Density Model (UDEDM). The results show that the stretching in the crystal size is very little. Line expansion in HR-XRD is due to small crystal size and lattice strain. UDEDM, one of the W-H methods, has emerged as the most suitable model for stretching..

Al2O3 with 10 wt.% of SiC ceramic composite is synthesized at 1500°C by electrical resistance heating sintering with a holding time of 5 hours and microwave sintering methods with a holding time of 15 minutes. The samples generated by the two methods are characterized using powder X‐ray diffraction and field emission scanning electron microscopy (FESEM). Experiments with both samples showed that the existence of the α‐Al2O3 and β‐SiC phases in both samples was verified by the findings of XRD pattern on both samples. Microstructure study illustrates that the Al2O3 matrix particles have spherical‐like shape and their average matrix particle size is 67 ± 5 nm for electrical resistance heating sintered sample and 38 ± 5 nm for microwave sintered sample. The lattice strain and crystallite size of Al2O3 matrix were measured using Williamson–Hall (W‐H) methods, which were achieved via the use of XRD peak broadening, based on a diffraction pattern. Three modified W‐H models were used to compute other parameters, including strain (ε) and stress (σ), as well as energy density (u). These models were the uniform deformation model (UDM), the uniform deformation energy density model (UDEDM), and the uniform deformation stress model (UDSM). The average crystallite sizes of α‐Al2O3 attained from these three models of Williamson–Hall (W–H) methods and FESEM analysis are correlated and found very close to each other. In all three models of the W‐H technique, X‐ray diffraction peak profile examination of electrical resistance heating‐sintered and microwave‐sintered Al2O3/10 wt. % SiC ceramic composite reveals that the microwave‐sintered sample has finer crystallite size with less strain.

X-ray diffraction analysis of orthorhombic SnSe nanoparticles by Williamson–Hall, Halder–Wagner and Size–Strain plot methods

Cadmium sulfide (CdS) nanoparticles were prepared by hydrothermal method at 150 °C under different reaction times. It was found that hydrothermal method is an effective, quick, and eco-friendly method to synthesis CdS nanoparticles of hexagonal structure at lower temperature. X-ray peak profile analysis by Williamson–Hall analysis and size–strain plot was employed to estimate the crystallite size and lattice strain of the synthesized CdS nanoparticles and to investigate their effects on the peak broadening. The values of strain, stress and energy density were determined for all XRD peaks of wurtzite hexagonal phase of CdS, by applying various forms of Williamson–Hall procedure, such as UDM (uniform deformation model), USDM (uniform stress deformation model) and UDEDM (uniform deformation energy density model). The obtained results indicate that the crystallite size of CdS nanoparticles estimated from Scherrer equation, Williamson–Hall plots and size–strain plot, are nearly similar and in the range of 14–37 nm. CdS nanoparticles were also investigated using high-resolution transmission electron microscopy (HR-TEM), Fourier transform infra-red spectroscopy (FT-IR), and UV–visible and fluorescence spectroscopy. A dependence of the band gap and the nanoparticle size on the reaction time was reported.