Uniform Deformation Energy Density Model Research Articles

A comparative approach for estimating microstructural characteristics of BaTi1−xZrxO3 (0.0 ≤ x ≤ 0.3) nanoparticles via X-ray diffraction patterns

AbstractBarium titanate materials are currently a special topic for scientific research due to their effective technological applications. The tetragonal BaTi1-xZrxO3 (0.0 ≤ x ≤ 0.3) nanoparticles (NPs) were synthesized using a modified citrate technique. The current work provides a comparative approach for the calculation of crystallite size, stress, strain, and elastic characteristics based on X-ray diffraction (XRD) patterns. Various models have been developed to analyze XRD data; these models differ in their assumptions, mathematical approaches, and the type of information they provide. The Scherrer model ignores lattice micro-structures that develop in nanostructures, such as intrinsic strain. To overcome such drawbacks, three Williamson-Hall models, (the uniform deformation model (UDM)), the uniform stress deformation model (USDM), and the uniform deformation energy density model (UDEDM) have been discussed. According to the USDM model, with increasing Zr ion concentrations, interplanar space increases, causing a drop in Young’s modulus. All the previous approaches take into account the diffraction angle (2θ)-dependent peak broadening, which is thought to represent a combination of size and strain-driven induced broadening. Graphical Abstract

Flexible photodetector for broadband detection using wurtzite phase CuFeS2 nanoparticles

In the realm of electronic devices, a rising demand for flexible and enhanced performance has emerged. Current research predominately centres on optoelectronics and sensors within the flexible devices’ domain. A flexible photodetector, utilizing CuFeS2 (CFS), is crafted on a cellulose paper substrate. Employing the hand printing method, a thin film of CFS on a graphene-based transporting layer is fabricated. The wurtzite phase of the material synthesized using microwave−assisted method is confirmed by X−ray diffraction (XRD) and Raman spectroscopy, with compositional details provided by energy dispersive X−ray analysis. Comprehensive XRD based calculations of size, stress, strain and energy density are conducted using three different models - Uniform Deformation Model, Uniform Stress Deformation Model and Uniform Deformation Energy Density Model. The average particle size, strain and stress from the three different models is found to be 9⋅73 nm, 1⋅35 × 10−3, 55⋅05 MPa along with calculated energy density value of 78⋅421 kJ m−3, respectively. Band gap calculations utilizing diffuse reflectance yielded an optical bandgap of 1⋅23 eV for the CFS thin film. The fabricated photodetector is studied for different illumination wavelengths, 450 nm, 520 nm, 570 nm, 620 nm and 940 nm, to determined device parameters. The optimum rise time, decay time, responsivity, and specific detectivity for wavelength of 520 nm are 6⋅43 s, 7⋅01 s, 0⋅0319 mA W−1 and 1⋅173 × 1010 Jones. The photoresponse of the fabricated device bended to 2⋅5− and 5−mm radii is studied to recognize suppleness. The photoresponse showed the photocurrent decreases with increase of bending. The observed traits under bending switched to initial on flattening the thin film.

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

SnSe nanoparticles were synthesized using the sonochemical exfoliation technique, employing SnSe single crystals. Various analysis, including Energy Dispersive Analysis of X-rays-Elemental mapping, X-ray Diffraction (XRD), High-Resolution Transmission Electron Microscopy, Ultra-Violet Diffused Reflectance Spectroscopy-Photoluminescence measurements, Raman spectroscopy, and X-ray Photoelectron Spectroscopy, were conducted to determine the chemical composition, crystalline phase, morphological characteristics, optical properties, vibrational modes, and oxidation states of the synthesized nanoparticles. The XRD peak broadening analysis, specifically employing Williamson–Hall (W-H), Size–Strain Plot (SSP), and Halder–Wagner Method (H-W), was employed to examine particle size and intrinsic strain. Additionally, three models within the W-H method, namely the uniform deformation model (UDM), uniform stress deformation model (USDM), and uniform deformation energy density model (UDEDM), were used to investigate physical and microstructural parameters such as strain, stress, and energy density. A comprehensive comparison of the average particle size results obtained from Williamson–Hall, Size–Strain, and Halder–Wagner Methods, along with results from HR-TEM and Particle Size Analysis, was carried out. The comprehensive comparison of results from different techniques adds credibility to the reported findings.

A comparative study in estimating of crystallite sizes of synthesized and natural hydroxyapatites using Scherrer Method, Williamson-Hall model, Size-Strain Plot and Halder-Wagner Method

In this study, an approach was made to create hydroxyapatite (HAp) crystals on nanoscale ranges from CaCO3 and H3PO4 utilizing a wet chemical process. Both fish and cow bones were used effectively for making bone powder as the natural sources of HAp. X-ray diffraction approach proved that powdered bone and HAp were in the crystalline phase. The determination of crystallite size in synthesized HAp crystals and bone powders was investigated using a range of techniques, including Linear Straight-Line Method (LSLM), Williamson-Hall Method (WHM), Size-Strain Plot (SSP), Halder-Wagner Method (HWM), and Sahadat-Scherrer Method (SSM). We also employed different Williamson-Hall models to quantify the stress and strain of the powdered materials for all diffraction peaks, including the Uniform Deformation Model (UDM), Uniform Stress Deformation Model (USDM), and Uniform Deformation Energy Density Model (UDEDM). Williamson-Hall is regarded as the best approach out of all of them since it was used to find the energy density, lattice stress, lattice strain, and crystallite size of the formed crystal. All the results from each model were compared to check the variation of analyzed data. The obtained results confirmed that there was an interrelation between the particle sizes of the Size Strain Plot and the Williamson-Hall method.

Microstructural, optical, and morphological investigations of SnO2 nanomaterials grown by microwave assisted sol gel method

Tin Oxide (SnO2) nanomaterials were grown using the microwave-assisted sol–gel method at different concentrations of tin precursor (namely 0.05, 0.1, 0.2, and 0.3 M). Stannous chloride is used as a Sn precursor. Liquid ammonia was used to maintain the pH in the range of 12–13. Synthesis was carried out in an aqueous medium using a Teflon container in a microwave oven for 1 hour. Precipitate was annealed in ambient air for 600oC. Structural, optical, and morphological investigations were done. XRD reveals the growth of the tetragonal phase of SnO2. The prominent presence of (110), (101), and (211) reflections was noticed at 26.6, 33.7, and 52 two-theta values. Tin oxide is transparent in the visible region of the electromagnetic spectrum. However, several attempts have been made to decrease the visible blindness of tin oxide. The band gap is a property of nanomaterials that can tailor their application in the optoelectronic field. Band gap and crystallite size show a prominent relationship in the nano-domain. Strain was not considered while calculating crystallite size using the Scherrer formula. In this investigation, we have measured the crystallite size and other structural features such as strain, stress, deformation energy, dislocation de\ sity, etc using the W-H plot method. All modified models of the W-H method have been utilized for this measurement. A comparative and comprehensive study of structural features was carried out using the Scherrer method, the Williamson–Hall method, and all its modified models. The crystallite size measured by the Scherrer method and various models of the W-H method shows a peak at 0.2 M concentration. Crystallite size plots of various modified W-H methods show similar trends, followed by the Scherrer plot. Strain calculated by Brag’s theory as well as all modified W-H depicts similar behaviour upon changing the concentration. Globular agglomerated morphology was revealed by scanning electron microscopy (SEM). The presence of tin (Sn) and oxygen (O) was confirmed by energy dispersive x-ray spectroscopy. The band gap was obtained using the Tauc theory, which portrays variation in the range of 3.4 to 3.6 eV.

Synthesis and mechanistic approach to investigate crystallite size of NbSe2 nanoparticles

Niobium diselenide (NbSe2) belongs to the class of transition metal dichalcogenides (TMDCs) and exhibits peculiar features such as charge density waves, superconductivity, and periodic crystal lattice distortion. The main focus of the article is the synthesis and characterisation of NbSe2 NPs utilising the wet chemical precursor solution route at room temperature, followed by in-depth x-ray diffraction (XRD) characterisation and analysis using the aforementioned techniques. The EDS result demonstrated that the NbSe2 NPs are devoid of impurities and close to stoichiometry. The sample has a crystalline hexagonal structure with the lattice constants a = b = 3.443Å, c = 12.576 Å, and α = β = 90°, γ = 120°, according to the XRD results. The work emphasises the need of comprehending how lattice strain and crystallite size affect physical attributes. x-ray peak broadening was used to study the epitaxial crystallisation of NbSe2 NPs. Various methods for determining crystallite size, such as the Williamson–Hall (W-H) method, Debye–Scherrer plots, uniform deformation model (UDM), uniform stress deformation model (USDM), uniform deformation energy density model (UDEDM), size strain plot (SSP) method, and Halder-Wagner (H-W) method, are employed to comprehensively analyse the nanoparticle characteristics, and additionally, high-resolution transmission electron microscopy (HRTEM) is employed to visualise the morphology and particle size distribution of the synthesised NbSe2 NPs. Physical parameters, including lattice stress, strain, and energy density, are also evaluated more precisely from the XRD pattern reflection peaks. The outcomes shed light on the interplay between crystallite size, lattice strain, and their effects on the material’s properties and showed excellent intercorrelation of the average crystallite sizes as estimated by employing various methods.

Green synthesis of Ag2O & facile synthesis of ZnO and characterization using FTIR, bandgap energy & XRD (Scherrer equation, Williamson-Hall, size-train plot, Monshi- Scherrer model)

A typical study has been performed for synthesizing Ag2O and ZnO nanoparticles. In our case, aloe vera extract was used as a reducing agent for synthesizing Ag2O. This green synthesis of silver oxide used silver nitrate (AgNO3) as a precursor material. On the other hand, the direct precipitation method was used for synthesizing zinc oxide nanoparticles, in which the precursor materials used were zinc nitrate hexahydrate (Zn(NO3)2·6H2O) and potassium hydroxide (KOH). Afterward, the characterization of these synthesized nanoparticles was done by the X-ray diffraction (XRD) method. Then, the crystal size, lattice strain, stress, and energy density of synthesized ZnO and Ag2O were determined by using XRD peak profile analysis. Among the various available models for determining these microstructural parameters, we explored the Scherrer model, the linear straight-line method of the Scherrer equation, the Monshi-Scherrer model, the Sahadat-Scherrer model, the Williamson-Hall model (including the uniform deformation model, the uniform stress deformation model, the uniform deformation energy density model), the size-strain plot method, the Halder-Wagner model, etc. By employing the crystal size values from these models, the accuracy and validity of crystals were also performed. The synthesized products were also characterized by the exploration of functional groups (by FTIR) and optical band gaps (by UV technique).

Calculation of crystallite sizes of pure and metals doped hydroxyapatite engaging Scherrer method, Halder-Wagner method, Williamson-Hall model, and size-strain plot

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.

Sustainable synthesis of nano CuO from electronic waste (E-waste) cable: Evaluation of crystallite size via Scherrer equation, Williamson-Hall plot, Halder- Wagner model, Monshi-Scherrer model, size-strain plot

Electronic waste (E-waste) is going to be one of the most hazardous materials for a sustainable environment in the technologically advanced era. In this research, waste electric cable was taken for efficient production of CuO using an easy and simple way. The synthesized product, CuO, was confirmed by the X-ray diffraction (XRD) data, and optical bandgap energy was also estimated. Various crystallographic parameters such as lattice parameters, the volume of unit cell, relative intensity, and preference growth were estimated from XRD data. Scherrer equation, Williamson-Hall plot (Uniform Deformation Model (UDM), Uniform Stress Deformation Model (USDM), Uniform Deformation Energy Density Model (UDEDM)), Halder-Wagner Model, Monshi-Scherrer Model, and Size- Strain plot were employed to calculate crystallite size and few models also exerted stress, strain and energy density. The estimated range of crystallite size was from 7 to 14 nm, strain from 5 × 10−4 to 1.5 × 10−3, stress of 1.0487 GPa, and energy density of 8.12 × 10−4 GPa using different model equations. The preference growth indicated that the (2 0 0) plane is the preferred direction for the synthesized conditions. FTIR spectrum and optical bandgap energy were also estimated for the synthesized products. The Rietveld refinement indicated that the synthesized product contained 99.524 % tenorite (CuO), and 0.476 % Cu2O phases.

Effect of cerium substitution on structural and optical properties of barium titanate ceramics

Barium titanate shows interesting behavior with little modification in synthesis route and variation in doping concentration. Barium titanate being perovskite material belongs to ABO3 family, shows tetragonal structure. In this present work, BaTiO3 with varying doping concentration of CeO2 (2 wt%) was fabricated by solid state reaction method. Structural and morphological study reveals a change in crystallite size and grain growth. X-ray powder diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), and a UV–VIS spectrophotometer were used to characterize the samples. Phases of the prepared samples were investigated by X-ray diffraction. The results of the investigation shows that pure barium titanate have no secondary phases. Pure form of barium titanate shows polycrystalline nature. Further, crystallite size, stress and strain for the doped sample were calculated using Scherrer method, Williamson-Hall analysis, Uniform deformation model (UDM), Uniform stress deformation model (USDM) and Uniform deformation energy density model (UDEDM) approaches. Crystallite size calculated by Scherrer method shows a variation with percentage doping. Doped sample shows reduce in crystallite size. Effect of size and strain induces X-ray peak broadening. In accordance with these findings, FE-SEM measurements demonstrate a shift in grain growth with Ce concentration with respect to pure barium titanate. X-ray diffraction results shows a good agreement with FE-SEM results. Peaks in the absorption are impacted by Ce ion doping concentration. An intriguing behavior of the ceramic is demonstrated by a considerable change in band gap with dopant. Cerium concentrations have a substantial impact on the physical and optical properties.

X-ray diffraction analysis of SrTiO3 nanoparticles by Williamson-Hall, size-strain plot and FullProf method

Strontium Titanate (SrTiO3) nanoparticles were synthesized using solid state method. Rietveld refinement using FullProf tool of x-ray diffraction data revealed the cubic structure with Pm-3 m space symmetry is present in SrTiO3-NPs. Williamson-Hall analysis with size-strain plot were used to examine the impact of crystallite size and lattice strain on the physical phenomenon of SrTiO3 nanoparticles. Different models like uniform density model (UDM), uniform stress deformation model (USDM), uniform deformation energy density model (UDEDM), and the size-strain plot (SSP) were used to estimate the strain, stress, and energy density parameters using shape profile of the X-ray diffraction peaks. FESEM microscopy is used to investigate the surface morphology as well as the particle size of the crystalline material. The particle size is obtained to be 66 nm.

Biomonitoring and risk assessment of naturally and chemically synthesized iron-oxide nanoparticles: A comparative approach

Nanostructured oxides and oxyhydroxides of iron are imperative constituents of the Earth's geological and biological processes i.e. biogeochemical cycles. So, the characteristic applications of iron oxide nanoparticles (FeONps) are closely linked to their surroundings and biological sinks. This work reports a low-cost green approach to promote ‘waste-to-wealth’ ideology by the direct and self-catalysis of iron rust into its nanoparticles (N-FeONps). A comparison is drawn based on the properties, morphologies, and applications after synthesizing FeONps by chemical precipitation method (C-FeONps). Spherical nanoparticles with vibrational properties are obtained in the size domain of 32 nm (N-FeONps) and 23 nm (C-FeONps). The application of Uniform deformation model, Uniform stress deformation model, Uniform deformation energy density model, and Size-strain plot models reveal comparatively greater defects in the crystal structures of C-FeONps. The biosafety profiling of natural and chemically designed nano-units performed on the species of bacteria, fungus, algae, and plants have shown enhanced safety terms associated with N-FeONps. The performance of N-FeONps has surpassed its chemical counterpart in medical applications such as antioxidant activity and anti-inflammatory activity with approximate percentages of 26 % and 51 % respectively. The findings of this piece of work favors the naturally obtained FeONps (N-FeONps), as they are economically viable, non-toxic, and have a greater antioxidant and anti-inflammatory arena. Hence, this waste-to-wealth ideology should be promoted for maintaining waste and designing solutions for the medical industries in one go.

Zn-based MOFs materials fabricated by mechanochemical ball milling and hydrothermal method and derived metal oxides

In the present work, the Zn-MOFs nanostructures from zinc sulfate and cyanoguanidine source precursors were successfully fabricated through two chemical and mechanical synthesis methods including hydrothermal and high energy ball milling methods. Then, the obtained Zn-MOFs were calcined at 550 °C for 110 min. The prepared nanostructures were determined by XRD, SEM and FTIR methods to gain insight about structure, morphology and functional groups properties. The findings confirm the fabrication of Zn-MOFs by using high energy ball milling methods. In addition, the obtained MOF and complex structures can be converted to porous zinc oxide by a simple thermal annealing in air. Then, the line broadening of ZnO calcined at 550 °C from MOFs structures from mechanochemical and hydrothermal methods due to the small crystallite size and lattice strain. The X-ray peak broadening analysis was investigated by the Scherrer formula and Williamson Hall method including uniform deformation model (UDM), uniform stress deformation model (USDM) and uniform deformation energy density model (UDEDM) and size-strain plot method.

A Very Low Temperature Growth of BaTiO3 Nanoparticles by Sol‐Hydrothermal Method

Low‐temperature intercessions are the most proficient technique to control the particle size in the nanometres range with low agglomeration. Herein, BaTiO3 (BT) nanoparticles (NPs) are prepared at low temperatures by using the sol‐hydrothermal technique. An X‐ray diffraction (XRD) pattern of the powder signifies the pure tetragonal phase, and the average crystallite size (43.2 nm) is calculated using different methods: Scherrer's, uniform deformation model (UDM), uniform stress deformation model (USDM), and uniform deformation energy density model (UDEDM) analysis, and the structure is refined by Rietveld refinement method with a good fit value (χ2 = 1.66). Spherical and uniform surface morphology is counted up for BT NPs. Under suitable conditions, BT NPs can be prepared with an average particle size of ≈115 ± 10 nm. However, after sintering, the average grain size (335 ± 10 nm) of the BaTiO3 nanopowder is found to increase with dense grain boundaries. The dielectric behavior of the sample is analyzed with the variation of frequency at different temperatures. The effect of grain and grain boundary on the electrical properties of the material is also investigated by using complex impedance spectroscopy (CIS).

Effect of annealing on chemically deposited Cu2Se thin films

Cu2Se is a promising candidate in the field of photovoltaic and thermoelectric devices. The pristine Cu2Se thin films are observed to be unstable under ambient conditions. One of the instabilities reported in this material is the formation of dendritic structures on the surface. The present work discusses the effect of post-deposition annealing on the dendritic growth formation. The pristine Cu2Se films were vacuum annealed at 60 °C, 80 °C, 100 °C, 150 °C, and 180 °C and the properties of the samples were investigated. The XRD peak profile analysis was done to evaluate the microstructural parameters like crystallite size, microstrain, stress and energy density. The various techniques used for this study include Scherrer method, Modified Scherrer Method, Williamson-Hall Plots, and Size Strain Plot. The modified variants of W–H Plots were employed which included Uniform Deformation Model, Uniform Stress Deformation Model and Uniform Deformation Energy Density Model. In all these cases, the crystallite size was found to increase on annealing. This is attributed to the reduction in defects and dislocations due to annealing of the sample. Microstrain is also observed to increase with the increase in annealing temperature. The calculation of crystallite size and lattice strain using UDM model deviates more from other models. This may be due to the incompatibility of its basic assumption of isotropic strain in UDM model. The W–H plots also suggest the presence of tensile strain in the lattice. The Cu ions in pristine Cu2Se thin films are in a disordered state due to their high mobility and diffusion coefficient. These mobile Cu ions form the centres of anisotropy and participate in dendritic growth formation with suitable stimulants. With an increase in annealing temperature, these ions get ordered due to strain hardening which in turn stabilizes the Cu2Se structure. The minimum temperature required to resist dendritic growth formation was found to be 150 °C. Thus annealing of pristine sample is suggested as a simple but effective method towards stabilization of the matrix. During the annealing process in the temperature range 60 °C–180 °C, it is observed that the optical band gap decreased from 2.2 eV to 1.9 eV.

Influence of L-cysteine engineering on structural and optical properties of nanocrystalline ZnS synthesized by the cost effective chemical co-precipitation method

Zinc Sulphide (ZnS) nanoparticles were successfully synthesized by the cost effective Chemical co-precipitation method at room temperature. The structural studies were carried out using X-ray diffraction (XRD),Dynamic Light Scattering (DLS) studies were used to analyze particle size, Functional group, optical properties and Morphological study were characterized by FTIR,UV-Vis, PL and Scanning Electron Microscope (SEM) .In this work also probe the crystallite development in nanostructure ZnS by X-ray peak broadening analysis. The individual contributions of small crystallite sizes and lattice strain to the peak broadening in Uncapped and L-Cysteine Capped ZnS nanoparticles were analyzed using Modified Williamson-Hall (W-H) analysis. The modified form of W-H plot assuming the uniform deformation model (UDM), uniform stress deformation model (USDM) and uniform deformation energy density model (UDEDM). The root mean square (RMS) lattice strain <εrms> calculated from the interplanar spacing and the strain estimated from USDM and UDEDM are different due to consideration of anisotropic crystal nature.

Biogenic synthesis of Cerium oxide nanoparticles using Justicia Adathoda leaves extract: Size-strain study by X-ray peak profile analysis and luminescence characteristics

Cerium Oxide (CeO2) nanoparticles were successfully synthesized by a facile bio-reduction technique using Justicia Adathoda leaves extract. The X-ray diffraction pattern and the Rietveld refinement analysis confirm that the prepared sample was crystallized in a cubic structure with space group Fm-3m. In the present work, X-ray peak profile analysis methods such as Williamson-Hall (W–H), Size-Strain Plot (SSP), and Halder-Wagner Method (H–W) have been used to investigate the crystalline development in the sample. Various physical parameters such as strain, stress, and energy density values were also calculated using the W–H method with different models namely Uniform Deformation Model (UDM), Uniform Stress Deformation Model (USDM), and Uniform Deformation Energy Density Model (UDEDM). The results obtained from the various methods used for the X-ray peak analysis and Transmission Electron Microscopy (TEM) images are very much intercorrelated. From the UV–visible reflectance spectrum, the band gap of the CeO2 nanoparticles was estimated to be about 3.51 eV. The blue-green emissions were observed from the photoluminescence spectrum of CeO2 nanoparticles, due to the presence of oxygen vacancy and oxygen interstitial defects. The Commission Internationale de l'Eclairage (CIE) coordinates were estimated and the results indicate that the prepared sample may be quite useful in cool light sources. Furthermore, the present synthetic technique has recently been adopted as an expedient alternative to generate CeO2 nanoparticles, as this synthetic approach is economic, eco-friendly, and free from unwanted by-products.

X-ray peaks profile analysis, optical and cathodoluminescence investigations of cobalt-doped ZnO nanoparticles

Effects of Co doping on the structural and optical properties of ZnO oxide nanoparticles (NPs) prepared by a solvothermal method are reported. X-ray diffraction examinations using Rietveld refinement confirms the hexagonal wurtzite symmetry ZnO phase nanostructure belonging to P63mc space group. No segregated secondary phases or Co rich clusters were detected. The X-ray diffraction peaks shifts towards higher angle gradually as the concentration of nominal Co content increases in ZnO. This shifting in peak position reflect that Co is well replaced Zn in ZnO matrix. With increasing the Co content to 3%, both lattice parameters a and c of the hexagonal ZnO tended to gradually decrease, suggesting substitutional doping of Co at the tetrahedral Zn2+sites. For Co loading of5%, these trends reversed and the lattice showed a gradual expansion, which is explained by additional interstitial incorporation of Co. The Williamson-Hall (W–H) method with various models i.e. uniform deformation model (UDM), uniform stress deformation model (USDM) and uniform deformation energy density model (UDEDM), as well as size-strain plot (SSP) method, and the morphological observations using transmission electron microscopy (TEM) image were used to evaluate the crystallite size as well as the lattice strain. Optical studies carried out by diffuse reflectance spectroscopy (DRS) indicated a decrease in the value of the band gap from 3.238 eV to 2.993 eV with increasing Co doping concentration. The obtained results are confirmed by cathodoluminescence technique.

Evaluation of crystallite size and micro-strain during mechanical milling process of composite material AA6005A+ 10% nano-TiC

Powder metallurgy process (by high-energy mechanical milling) was used to obtain a nanostructured aluminum matrix composite. Powders of the AA6005A alloy (particle size <63 μm) was utilized as matrix, and 10% by weight of nano-sized TiC particles (20-30 nm) as reinforcement. Composite powder was characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM). Microstructural changes produced during the milling process, such as modification of crystallite size and micro-strain of matrix lattice were determined using the three Williamson-Hall (W-H) analysis models: UDM (Uniform Deformation Model), USDM (Uniform Stress Deformation Model) and UDEDM (Uniform Deformation Energy Density Model). The results show that crystallite size decreases and micro-strain increases sharply in the first few hours of milling and then both parameters remain stable until 10 hours. The three W-H models present a coefficient of determination R2 close to the unit indicating that are suitable to determine crystallite size and lattice micro-strain of nanostructured composite obtained.

Strain and Grain Size Determination of CeO2 and TiO2 Nanoparticles: Comparing Integral Breadth Methods versus Rietveld, μ-Raman, and TEM

Various crystallite size estimation methods were used to analyze X-ray diffractograms of spherical cerium dioxide and titanium dioxide anatase nanoparticles aiming to evaluate their reliability and limitations. The microstructural parameters were estimated from several integral breadth methods such as Scherrer, Monshi, Williamson–Hall, and their variants: (i) uniform deformation model, (ii) uniform strain deformation model, and (iii) uniform deformation energy density model. We also employed the size–strain plot and Halder–Wagner method. For this purpose, an instrumental resolution function of an Al2O3 standard was used to subtract the instrumental broadening to estimate the crystallite sizes and strain, and the linear regression analysis was used to compare all the models based on the coefficient of determination. The Rietveld whole powder pattern decomposition method was introduced for comparison purposes, being the best candidate to fit the X-ray diffraction data of metal-oxide nanoparticles. Refined microstructural parameters were obtained using the anisotropic spherical harmonic size approach and correlated with the above estimation methods and transmission electron microscopy images. In addition, μ-Raman spectra were recorded for each material, estimating the mean crystallite size for comparison by means of a phonon confinement model.