Strain and Grain Size of CeO2 and TiO2 Nanoparticles: Comparing Structural and Morphological Methods

Various crystallite size estimation methods were used to analyze X-ray diffractograms of spherical cerium dioxide and donut-like titanium dioxide anatase nanoparticles aiming to evaluate their reliability and limitations. The microstructural parameters were estimated from Scherrer, Monshi, Williamson-Hall, and their variants: i) uniform deformation model, ii) uniform strain deformation model, and iii) uniform deformation energy density model, and also size-strain plot, and Halder-Wagner method. For that, and improved systematic Matlab code was developed 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, where the Halder Wagner method gave the highest value (close to 1). Therefore, being the best candidate to fit the X-ray Diffraction data of metal-oxide nanoparticles. Advanced Rietveld was introduced for comparison purposes. Refined microstructural parameters were obtained from a nanostructured 40.5 nm Lanthanum hexaboride nanoparticles and correlated with the above estimation methods and transmission electron microscopy images. In addition, electron density modelling was also studied for final refined nanostructures, and μ-Raman spectra were recorded for each material estimating the mean crystallite size and comparing by means of a phonon confinement model.

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

Nanomaterials ◽

10.3390/nano11092311 ◽

2021 ◽

Vol 11 (9) ◽

pp. 2311

Author(s):

Yamerson Canchanya-Huaman ◽

Angie F. Mayta-Armas ◽

Jemina Pomalaya-Velasco ◽

Yéssica Bendezú-Roca ◽

Jorge Andres Guerra ◽

...

Keyword(s):

Crystallite Size ◽

Metal Oxide Nanoparticles ◽

Linear Regression Analysis ◽

Estimation Methods ◽

Deformation Model ◽

Size Estimation ◽

Uniform Deformation ◽

Integral Breadth ◽

X Ray ◽

Microstructural Parameters

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.

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X-ray Diffraction Analysis and Williamson-Hall Method in USDM Model for Estimating More Accurate Values of Stress-Strain of Unit Cell and Super Cells (2 × 2 × 2) of Hydroxyapatite, Confirmed by Ultrasonic Pulse-Echo Test

Materials ◽

10.3390/ma14112949 ◽

2021 ◽

Vol 14 (11) ◽

pp. 2949

Author(s):

Marzieh Rabiei ◽

Arvydas Palevicius ◽

Amir Dashti ◽

Sohrab Nasiri ◽

Ahmad Monshi ◽

...

Keyword(s):

Young’S Modulus ◽

Young's Modulus ◽

Ultrasonic Pulse ◽

High Accuracy ◽

Unit Cell ◽

Deformation Model ◽

X Ray Diffraction ◽

Uniform Deformation ◽

X Ray ◽

Pulse Echo

Taking into account X-ray diffraction, one of the well-known methods for calculating the stress-strain of crystals is Williamson-Hall (W–H). The W-H method has three models, namely (1) Uniform deformation model (UDM); (2) Uniform stress deformation model (USDM); and (3) Uniform deformation energy density model (UDEDM). The USDM and UDEDM models are directly related to the modulus of elasticity (E). Young’s modulus is a key parameter in engineering design and materials development. Young’s modulus is considered in USDM and UDEDM models, but in all previous studies, researchers used the average values of Young’s modulus or they calculated Young’s modulus only for a sharp peak of an XRD pattern or they extracted Young’s modulus from the literature. Therefore, these values are not representative of all peaks derived from X-ray diffraction; as a result, these values are not estimated with high accuracy. Nevertheless, in the current study, the W-H method is used considering the all diffracted planes of the unit cell and super cells (2 × 2 × 2) of Hydroxyapatite (HA), and a new method with the high accuracy of the W-H method in the USDM model is presented to calculate stress (σ) and strain (ε). The accounting for the planar density of atoms is the novelty of this work. Furthermore, the ultrasonic pulse-echo test is performed for the validation of the novelty assumptions.

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Investigations on Microstructural and Layer Disorder Parameters of Na-Montmorillonite-Glycine Intercalation Compounds

Dhaka University Journal of Science ◽

10.3329/dujs.v60i1.10331 ◽

2012 ◽

Vol 60 (1) ◽

pp. 25-29 ◽

Cited By ~ 2

Author(s):

Adnan Hossain Khan ◽

Parimal Bala ◽

AFM Mustafizur Rahman ◽

Mohammad Nurnabi

Keyword(s):

Crystallite Size ◽

Chain Length ◽

Line Profile ◽

Profile Analysis ◽

Interlayer Spacing ◽

Line Profile Analysis ◽

X Ray ◽

Microstructural Parameters ◽

Silicate Layers ◽

Layer Disorder

Glycine-Montmorillonite (Gly-MMT) composite has been synthesized through intercalation process using Na-Montmorillonite (Na- MMT) and glycine ethylester hydrochloride. Gly-MMT was employed for the synthesis of dipeptide (Gly-Gly-MMT). Microstructural parameters such as crystallite size, r.m.s. strain (<e2>1/2) and layer disorder parameters such as variation of interlayer spacing (g) and proportion of planes affected by such defects (?) of the samples have been calculated by X-ray line profile analysis. In comparison to Na-MMT the basal spacings (d001) of Gly-MMT and Gly-Gly-MMT were reduced by 2.4Å and 1.8Å respectively. The value of d001 of Gly-Gly-MMT (13.3 Å) suggests the monolayer orientation of dipeptide into interlayer spaces. It is also suggested that more homogeneity in the stacking of silicate layers is attained in Gly-Gly-MMT due to the increased chain length of the dipeptide and orientation in monolayer style.DOI: http://dx.doi.org/10.3329/dujs.v60i1.10331Dhaka Univ. J. Sci. 60(1): 25-29, 2012 (January)

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Crystallization of Cu60Zr20Ti20 bulk metallic glass by high pressure torsion

REVIEWS ON ADVANCED MATERIALS SCIENCE ◽

10.1515/rams-2019-0037 ◽

2019 ◽

Vol 58 (1) ◽

pp. 304-312

Author(s):

Ádám Révész ◽

András Horváth ◽

Gábor Ribárik ◽

Erhard Schafler ◽

David J. Browne ◽

...

Keyword(s):

High Pressure ◽

Metallic Glass ◽

Crystallite Size ◽

Bulk Metallic Glass ◽

High Pressure Torsion ◽

Average Crystallite Size ◽

Scanning Calorimetry ◽

X Ray ◽

Microstructural Parameters ◽

Profile Fitting

Abstract Bulk metallic glass of Cu60Zr20Ti20 composition has been synthesized by copper mold casting. Slices of the as-cast glass has been subjected to severe plastic deformation by high-pressure torsion for different whole turns. The microstructure and the thermal behavior of the deformed disks have been investigated by X-ray diffraction and differential scanning calorimetry. It was confirmed that the initial compression preceding the high pressure torsion induces crystallized structure, which shows only minor further changes upon the severe plastic shear deformation achieved by twisting the sample. The X-ray line profiles have been evaluated by the Convolutional Whole Profile Fitting algorithm in order to determine the evolution of the microstructural parameters, such as the median and variance of the crystallite size distribution, average crystallite size and dislocation density as a function of the number of revolutions. Hardness measurements by nanoindentation have also been carried out on the as-cast alloys and the deformed disks.

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Microstructural parameters and layer disorder accompanying dehydration transformation in Na-montmorillonite

Zeitschrift für Kristallographie - Crystalline Materials ◽

10.1524/zkri.2000.215.4.235 ◽

2000 ◽

Vol 215 (4) ◽

Cited By ~ 1

Author(s):

S.K. Srivastava ◽

P. Bala ◽

B.K. Samantaray ◽

Hartmut Haeuseler

Keyword(s):

Crystallite Size ◽

Structural Changes ◽

Profile Analysis ◽

Thermal Transformation ◽

Initial Slope ◽

Line Profile Analysis ◽

Line Profiles ◽

X Ray ◽

Microstructural Parameters ◽

Layer Disorder

Structural changes accompanying thermal transformation in Na-montmorillonite samples up to a temperature of 500°C have been investigated by X-ray line profile analysis. The method of Fourier initial slope and variance analysis of X-ray line profiles have been used to calculate the different microstructural parameters like crystallite size, r.m.s. strain (<e

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X-ray peak profile analysis of CoAl2O4 nanoparticles by Williamson-Hall and size-strain plot methods

Modern Electronic Materials ◽

10.3897/j.moem.4.1.33272 ◽

2018 ◽

Vol 4 (1) ◽

pp. 31-40 ◽

Cited By ~ 2

Author(s):

H. Irfan ◽

K Mohamed Racik ◽

S. Anand

Keyword(s):

Profile Analysis ◽

Spinel Phase ◽

Sol Gel ◽

Chelating Agent ◽

Cubic Phase ◽

Physical Parameters ◽

Deformation Model ◽

Uniform Deformation ◽

X Ray ◽

Peak Broadening

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.

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X-ray diffraction broadening analysis

Macedonian Journal of Chemistry and Chemical Engineering ◽

10.20450/mjcce.2015.642 ◽

2015 ◽

Vol 34 (1) ◽

pp. 39

Author(s):

Stanko Popović ◽

Željko Skoko

Keyword(s):

Crystallite Size ◽

Line Profile ◽

Chemical Properties ◽

Background Level ◽

X Ray Diffraction ◽

Transform Method ◽

Diffraction Profile ◽

X Ray ◽

Microstructural Parameters ◽

Integral Width

The microstructure is very important in research aimed to the development of new materials. The microstructural parameters, crystallite size, crystallite size distribution, crystallite strain, dislocation density and stacking fault probability, play a major role in physical and chemical properties of the material. These parameters can be determined by a proper analysis of X-ray diffraction line profile broadening. The observed XRD line profile of the studied sample, h(ε), is the convolution of the instrumental profile, g(ε), inherent in diffraction, and pure diffraction profile, f(ε), caused by small crystallite (coherent domain) sizes, by faultings in the sequence of the crystal lattice planes, and by the strains in the crystallites. That is, f(ε) is the convolution of the crystallite size/faulting profile, p(ε), and the strain profile, s(ε). The derivation of f(ε) can be performed from the measured h(ε) and g(ε) by the Fourier transform method, usually referred to as the Stokes method. That method does not require assumptions in the mathematical description of h(ε) and g(ε). The analysis of f(ε) can be done by the Warren-Averbach method, which is applied to the Fourier coefficients obtained by the deconvolution. On the other hand, simplified methods (which may bypass the deconvolution) based on integral widths may be used, especially in studies where a good relative accuracy suffices. In order to obtain the relation among integral widths of f(ε), p(ε) and s(ε), one assumes bell-shaped functions for p(ε) and s(ε). These functions are routinely used in the profile fitting of the XRD pattern and in the Rietveld refinement of the crystal structure. The derived crystallite size and strain parameters depend on the assumptions for the profiles p(ε) and s(ε). Integral width methods overestimate both strain and crystallite size parameters in comparison to the Warren-Averbach-Stokes method. Also, the crystallite size parameter is more dependent on the accuracy, with which the profile tails are measured and how they are truncated, than it is the strain parameter. The integral width also depends on the background level error of the pure diffraction profile. The steps and precautions, which are necessary in order to minimize the errors, are suggested through simple examples. The values of the crystallite size and strain parameters, obtained from integral widths derived by the Stokes deconvolution, are compared with those which followed from the Warren-Averbach treatment of broadening. Recent approaches in derivation of microstructure are also mentioned in short.

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Relationships between body size - otolith size for seven demersal fish species from the Marmara Sea, Turkey

Ege Journal of Fisheries and Aquatic Sciences ◽

10.12714/egejfas.37.3.09 ◽

2020 ◽

Vol 37 (3) ◽

pp. 267-274

Author(s):

İsmail Burak Daban ◽

Mukadder Arslan İhsanoglu ◽

Ali İsmen

Keyword(s):

Linear Regression Analysis ◽

Stomach Contents ◽

Demersal Fish ◽

Total Weight ◽

Coefficient Of Determination ◽

Morphometric Character ◽

Marmara Sea ◽

Size Estimation ◽

Total Length ◽

Length Width

The total length-otolith length (TL-OL), total length-otolith width (TL-OWi), total length-otolith weight (TL-OW) and total weight-otolith weight (TW-OW) relationships of seven fishes in the Marmara Sea, Turkey were calculated. Measurements of sagittal otoliths (length, width and weight) and individuals (total length and total weight) from these species (Gaidropsarus biscayensis, Mediterranean bigeye rockling; Arnoglossus kessleri, Scaldback; Solea solea, Common sole; Uranoscopus scaber, Stargazer; Lophius budegassa, Blackbellied angler, Lepidorhombus boscii, The four-spot megrim and Lesueurigobius friesii, Fries's goby) were given. Linear regression analysis (y = bx + a) was used to determine the relationship between each morphometric character and the coefficient of determination (r2) were calculated. Highest determination coefficient were determined for L. budegassa and A. kessleri to TW-OW, for S. solea, and U. scaber to TL-OL, for G. biscayensis and L. boscii to TL-OWi, for L. friesii to TL-OW. The relatively lower determination coefficients were found for G. biscayensis, compared with others. These relationships provide vital information on species identification and size estimation of fish in predator-prey studies, we believe these results will be useful in future studies of stomach contents.

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Estimation of accurate size, lattice strain using Williamson-Hall models, SSP and TEM of Al doped ZnO nanocrystals

Matériaux & Techniques ◽

10.1051/mattech/2018055 ◽

2018 ◽

Vol 106 (6) ◽

pp. 602 ◽

Cited By ~ 4

Author(s):

Milind Bodke ◽

Umesh Gawai ◽

Ashok Patil ◽

Babasaheb Dole

Keyword(s):

Energy Density ◽

Crystallite Size ◽

Lattice Strain ◽

Average Crystallite Size ◽

Physical Parameters ◽

Deformation Model ◽

Uniform Deformation ◽

Zno Nanocrystals ◽

Peak Broadening ◽

Doped Zno

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.

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Direct Observation of Crystalline Ordering In Naturally Graphitized Carbon Produced by Low Grade Metamorphism

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100078377 ◽

1977 ◽

Vol 35 ◽

pp. 162-163

Author(s):

Thomas R. McKee ◽

Peter R. Buseck

Keyword(s):

Crystallite Size ◽

Sedimentary Rocks ◽

Carbonaceous Material ◽

Low Grade ◽

X Ray ◽

Graphitized Carbon ◽

Transmission Electron ◽

Heat Treated ◽

Commercial Carbon ◽

Metamorphic Zone

Sediments commonly contain organic material which appears as refractory carbonaceous material in metamorphosed sedimentary rocks. Grew and others have shown that relative carbon content, crystallite size, X-ray crystallinity and development of well-ordered graphite crystal structure of the carbonaceous material increases with increasing metamorphic grade. The graphitization process is irreversible and appears to be continous from the amorphous to the completely graphitized stage. The most dramatic chemical and crystallographic changes take place within the chlorite metamorphic zone.The detailed X-ray investigation of crystallite size and crystalline ordering is complex and can best be investigated by other means such as high resolution transmission electron microscopy (HRTEM). The natural graphitization series is similar to that for heat-treated commercial carbon blacks, which have been successfully studied by HRTEM (Ban and others).

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