Relevant bibliographies by topics / Scherrer formula

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Academic literature on the topic 'Scherrer formula'

Author: Grafiati
Published: 4 June 2025
Last updated: 6 July 2025

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Journal articles on the topic "Scherrer formula"

1

Sumadiyasa, Made, and I. B. S. Manuaba. "Determining Crystallite Size Using Scherrer Formula, Williamson-Hull Plot, and Particle Size with SEM." BULETIN FISIKA 19, no. 1 (2018): 28. http://dx.doi.org/10.24843/bf.2018.v19.i01.p06.

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It has been determined the crystallite size by XRD technique using Scherrer equation and Williamson-Hull Plot method. While the particle size is determined by SEM using Image-J software. For this purpose, synthesized samples of compound Gd0,95La0.05Ba2Cu3O7-d phase. From the calculation results, obtained the crystallite size in nanometers order, however the crystallite size resulting from the Scherrer equations and Scherrer Modified is different, i.e. 63.1675 nm and 67.0005 nm. The results of the crystallite size calculation by the scherrer equation directly and modified differed from that of the Williamson-Hull Plot method (97,3040 nm). Meanwhile, the results of the Williamson-Hull Plot methods and SEM show almost the same value (98.7297nm).
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Rahavi, Soheila, Ahmad Monshi, Rahmatollah Emadi, Ali Doostmohammadi, and Hamed Akbarian. "Determination of Crystallite Size in Synthetic and Natural Hydroxyapatite: A Comparison between XRD and TEM Results." Advanced Materials Research 620 (December 2012): 28–34. http://dx.doi.org/10.4028/www.scientific.net/amr.620.28.

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The study reported here focuses on the crystallite size of synthetic hydroxyapatite (HAp) obtained using sol-gel method and natural HAp obtained by processing the natural bone. Human and camel bones were used for obtaining natural HAp. HAp particles were produced, characterized and compared for their crystallite size. The average crystallite size of the samples was derived from the X-ray Diffraction (XRD) data using the Scherrer formula and a new method called modified scherrer equation that was came by developing the Scherrer formula. The results showed the crystallite size of HAp gained from different sources were different. The crystallite size of synthetic, human and camel bone-derived HAp, were approximately 18, 23 and 29 nanometer, respectively. These values were less than those obtained from TEM images. It seems that calculated crystallite size using XRD data and Scherrer equations is less than the real size. This important finding must be taken into consideration in applying Scherrer equations.
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Jaboyedoff, M., B. Kübler, and Ph Thélin. "An empirical Scherrer equation for weakly swelling mixed-layer minerals, especially illite-smectite." Clay Minerals 34, no. 4 (1999): 601–17. http://dx.doi.org/10.1180/000985599546479.

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AbstractThe Scherrer equation links the measured width of an X-ray diffraction peak (Scherrer width, SW) to the number of stacked cells (N) in the direction normal to the diffracting planes. The formula is only valid for one d-value occurring in the coherently diffracting domain. This equation can be modified for weakly swelling mixed-layer minerals. This assumes that the peak broadening caused by the mixed-layering is proportional to the amount of swelling component (S) and that the effects of size and mixed-layering are additive.If two SW can be measured on XRD patterns from samples treated in two different ways (such as air dried or glycolated), N and S can be determined. This equation is applicable to illite-smectite mixed-layer minerals with high illitic content. The results are most accurate for N>30. The use of Scherrer's equation is discussed.
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Smilgies, Detlef-M. "Scherrer grain-size analysis adapted to grazing-incidence scattering with area detectors." Journal of Applied Crystallography 42, no. 6 (2009): 1030–34. http://dx.doi.org/10.1107/s0021889809040126.

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Ever since its formulation, the Scherrer formula has been the workhorse for quantifying finite size effects in X-ray scattering. Various aspects of Scherrer-type grain-size analysis are discussed with regard to the characterization of thin films with grazing-incidence scattering methods utilizing area detectors. After a brief review of the basic features of Scherrer analysis, a description of resolution-limiting factors in grazing-incidence scattering geometry is provided. As an application, the CHESS D1 beamline is characterized for typical scattering modes covering length scales from the molecular scale to the nanoscale.
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Hall, B. D., D. Zanchet, and D. Ugarte. "Estimating nanoparticle size from diffraction measurements." Journal of Applied Crystallography 33, no. 6 (2000): 1335–41. http://dx.doi.org/10.1107/s0021889800010888.

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Nanometre-sized particles are of considerable current interest because of their special size-dependent physical properties. Debye–Scherrer diffraction patterns are often used to characterize samples, as well as to probe the structure of nanoparticles. Unfortunately, the well known `Scherrer formula' is unreliable at estimating particle size, because the assumption of an underlying crystal structure (translational symmetry) is often invalid. A simple approach is presented here which takes the Fourier transform of a Debye–Scherrer diffraction pattern. The method works well on noisy data and when only a narrow range of scattering angles is available.
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Zhu, Yan, Xiao Zhang, and Shuai Yuan. "The Preparation of ZrO2 and the Influence of the Calcination Temperature." Advanced Materials Research 1095 (March 2015): 67–71. http://dx.doi.org/10.4028/www.scientific.net/amr.1095.67.

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nanoZrO2ceramic powders have excellent properties in many field. In order to obtain nanoZrO2powder with excellent properties, the study of preparation methods become a hotspot. The nanoZrO2powders new preparation technology from cheap raw materials is target of this paper. nanoZrO2powers were preparated from ZrOCl2and NaCO3as raw material. The optimum technology parameters were determined as follow, namely at 40°C, C (ZrOCl2) =0.4mol/L, C (NaCO3) =1.0mol/L, 2% the surface activity agent. nanoZrO2powders preparated were characterized by XRD, TEM and Electron Diffraction . The results show that the ZrO2powders prepared are crystal and the sizes are nanometer. The ZrO2average sizes were calculated with the scherrer formula. The nanoZrO2sizes change with temperature was discussed. The result is ageerment with that calculated with the scherrer formula.
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Bolotnikova, Anastasiia. "DETERMINATION OF THE SIZES OF PARTICLES OF SUPERCONDUCTING CUPRATE Y3Ba5Cu8OX BY MEANS OF DIFFERENT METHODS." Technology transfer: fundamental principles and innovative technical solutions 4 (November 30, 2020): 10–13. http://dx.doi.org/10.21303/2585-6847.2020.001504.

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The superconducting cuprate Y3Ba5Cu8Ox was obtained with the help of sol-gel technology (sample C), co-precipitation of hydroxocarbonates (sample B) and solid-phase synthesis methods (A). Based on the results of scanning electron microscopy and methods based on the analysis of X-ray diffraction data: the Williamson-Hall construction and the Scherrer formula, features of the microstructure of the synthesized samples are established. The smallest particle size has a sample that has been synthesized by the sol-gel method. The tendency to aggregation and sedimentation for this sample is the smallest. The sample obtained by the co-precipitation method has larger grains and a higher tendency to aggregate. The size of the microparticles and the tendency to aggregate for the sample synthesized by the solid-phase method are greatest. The morphology of particles was studied using three methods: SEM, Scherrer and Williamson-Hall formulas and the following results were found: particle size depends on the synthesis method, but a relatively narrow size distribution within one synthesis method remains, the value of crystal lattice microdeformation for samples increases in a line: C sample– A sample– B sample. Thus, the work was carried out for determining the size, structure and morphology of superconducting phases. It expands knowledge in the field of research of superconducting compounds
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Wang, Bing, Li Dan Tang, and Jian Zhong Wang. "Synthesis and Characterization of Nanocrystalline ZnO Powders by a Novel Combustion Synthesis Method." Advanced Materials Research 152-153 (October 2010): 674–78. http://dx.doi.org/10.4028/www.scientific.net/amr.152-153.674.

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Nanocrystalline ZnO powders have been synthesized by a novel combustion synthesis method using glycine and urea as mixed fuels and zinc nitrates as oxidant. The as-synthesized ZnO powders are characterized by DSC, XRD and SEM. Results show that the as-synthesized ZnO powders show well crystalline with hexagonal crystal structure and purity without any other impurities and the particle sizes are about 50~70nm calculated by the Scherrer formula.
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Choudhary, Pankaj, P. Saxena, A. Yadav, V. N. Rai, and A. Mishra. "Dielectric and ferroelectric properties of CoCr2O4 nanoceramics." Journal of Advanced Dielectrics 09, no. 03 (2019): 1950015. http://dx.doi.org/10.1142/s2010135x19500152.

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CoCr2O4 nanoceramics are prepared by sol–gel auto combustion method. Synchrotron X-ray diffraction analysis affirms the single-phase pristine cubic structure with space group [Formula: see text]. Debye–Scherrer method estimates the crystallite size of main intense peak to be [Formula: see text][Formula: see text]nm. Prominent bands obtained in infrared spectra at 448 and 599[Formula: see text]cm[Formula: see text] are due to metal–oxygen stretching bond present at tetrahedral and octahedral sites. Dielectric parameters decrease as frequency increases from [Formula: see text] to [Formula: see text][Formula: see text]Hz that can be interpreted by Maxwell–Wagner-type interfacial polarization. Complex impedance spectra (Nyquist plot) reveal arc like behavior, which is mainly due to intergrain (grain boundary) resistance that also exhibits conducting nature of the nanoceramics. Weak ferroelectricity is mainly associated with the partial reversal of the polarization. Leakage current behavior follows the Ohmic and Child square law. Electron conduction process was interpreted by space-charge limited current (SCLC) mechanism. Leakage current behavior observed in cobalt chromite nanoceramics is mainly attributed to the oxygen vacancies.
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Cheng, Xian Zhong, Kuang Cheng, Jin Liu, and Xue Fang Sun. "Synthesis and Characterizations of Nanoparticle Sulfur Using Eggshell Membrane as Template." Materials Science Forum 675-677 (February 2011): 279–82. http://dx.doi.org/10.4028/www.scientific.net/msf.675-677.279.

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Nanoparticles of sulfur with an average diameter of 5-35 nm were successfully prepared using eggshell membrane (ESM) as template in the the presence of surfactant Tween-80. The products were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and fourier transform infrared spectroscopy (FTIR). The sizes of the nanoparticles sulfur were estimated by Debye-Scherrer formula according to XRD spectrum. Based on the detailed investigation, a possible synthesis mechanism is discussed here.
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Book chapters on the topic "Scherrer formula"

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Padinjare Kunnath, Manikandan, and Malaidurai Maduraipandian. "Optical X-Ray Diffraction Data Analysis Using the Williamson–Hall Plot Method in Estimation of Lattice Strain-Stress." In Research Anthology on Synthesis, Characterization, and Applications of Nanomaterials. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-8591-7.ch025.

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Lattice stress and strain was analysed with estimated crystalline size of the synthesised ZnFe2O4 nanoparticles from x-ray diffraction data using Williamson-Hall (W-H) method. This very peculiar method was used to analyse the other physical parameters such as strain, stress, and energy density. Values calculated from the W-H method include uniform deformation model, uniform deformation stress model, and uniform deformation energy density model. These are very useful methods to label each data point on the Williamson-Hall plot according to the index of its reflection. Particularly, the root mean square value of strain was calculated from the interplanar distance using these three models. The three models have given different strain values by reason of the anisotropic nature of the nanopartcles. The average grain size of ZnFe2O4 nanoparticles estimated from FESEM image, Scherrer's formula, and W-H analysis is relatively correlated.
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Padinjare Kunnath, Manikandan, and Malaidurai Maduraipandian. "Optical X-Ray Diffraction Data Analysis Using the Williamson–Hall Plot Method in Estimation of Lattice Strain-Stress." In Applications and Techniques for Experimental Stress Analysis. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-1690-4.ch008.

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Lattice stress and strain was analysed with estimated crystalline size of the synthesised ZnFe2O4 nanoparticles from x-ray diffraction data using Williamson-Hall (W-H) method. This very peculiar method was used to analyse the other physical parameters such as strain, stress, and energy density. Values calculated from the W-H method include uniform deformation model, uniform deformation stress model, and uniform deformation energy density model. These are very useful methods to label each data point on the Williamson-Hall plot according to the index of its reflection. Particularly, the root mean square value of strain was calculated from the interplanar distance using these three models. The three models have given different strain values by reason of the anisotropic nature of the nanopartcles. The average grain size of ZnFe2O4 nanoparticles estimated from FESEM image, Scherrer's formula, and W-H analysis is relatively correlated.
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Choudhary, Sumitra, Vikas Sharma, Abhishek Sharma, Ajay Kumar, and Parveen Kumar. "Analyzing the Properties of Zinc Oxide (ZnO) Thin Film Grown on Silicon (Si) Substrate, ZnO/Si Using RF Magnetron Sputtering Approach." In Modeling, Characterization, and Processing of Smart Materials. IGI Global, 2023. http://dx.doi.org/10.4018/978-1-6684-9224-6.ch014.

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In this work, ZnO single layer thin film of 100 nm is deposited on a Si substrate using RF magnetron sputtering. Base pressure of 1.0×10−5 mbar, RF power of 100W at Ar flow 15 sccm and room temperature were process parameters. The average crystallite size of ZnO layer, deposited on Si substrate, using Scherrer's formula was 108.16 nm. XRD verifies the crystalline nature of ZnO with various peaks at (002), (101) and (103) planes. Using AFM technique, ZnO had an Average Surface Roughness (Ra) of 2.75 nm and RMS roughness (Rq) of 3.70 nm. From Hall measurements at room temperature, the authors determined that ZnO is a n-type semiconductor having a resistivity of 1 to 100 Ωcm. The layer's sheet resistance was 7.05×103 Ω/sq, and its resistivity was 7.05×10−2 Ωcm. The Raman spectra analysis confirmed the presence of Raman active modes in the sample, confirming the existence of certain vibrational modes. In PL spectra, an emission peak was observed at 380.30 nm, which closely resembled pure ZnO. These results collectively shows that the ZnO/Si thin films grown on Si demonstrated excellent quality.
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Dadamiah PMD Shaik, Dr, Dr Md Sameer Ahmed, and Mrs Anjum Begum. "OPTICAL, MAGNETIC AND ELECTROCHEMICAL PROPERTIES OF SPINEL MN3O4, CO3O4 NANOSTRUCTURES." In Futuristic Trends in Chemical Material Sciences & Nano Technology Volume 3 Book 9. Iterative International Publishers, Selfypage Developers Pvt Ltd, 2024. http://dx.doi.org/10.58532/v3becs9p4ch4.

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Manganese oxide (Mn3O4) and Cobalt oxide (Co3O4) nanocrystals were synthesized using a straightforward and cost-effective combustion method. Structural analysis through X-Ray Diffraction, FTIR Spectroscopy, and Raman Spectroscopy confirmed structure to be tetragonal for Mn3O4 with space group of I41/amd (141) and the cubical for Co3O4 with space group Fd3m (227). The usual microscopic crystal sizes were determined using the Debye Scherer formula, resulting in approximately 14 nm & 22 nm for manganese oxide and cobalt oxide respectively. Scanning electron microscopic pictures displayed irregular and uniform spherical grains for Co3O4 and Mn3O4 respectively, with typical grain sizes of 120 nm & 100 nm. EDS and XPS spectra showed clear binding energy peaks for Mn, Co, and O2, confirming the chemical purity of the samples. The optical band gap of the nanocrystal Mn3O4 and Co3O4 were 2.93 eV, 2.50 eV respectively. Magnetic analysis revealed a sturdy ferromagnetic nature at 5 Kelvin temperature for both Mn3O4 and Co3O4 nanocrystals. Electrochemical investigations demonstrated that Mn3O4 nanocrystals exhibited excellent performance as electrodes for electrochemical capacitors. At a current density of 0.5 Ampere/g, they achieved higher specific capacitance of 417 Farad/g, maintaining nearly 100% coloumbic efficiency after 600 cycles and displaying decent cyclical stability for upto ten thousand cycles. Alternatively, Co3O4 showed inferior electrochemical behavior, indicating that Mn3O4 nanocrystals possess superior mass transport of electrolyte ions into the electrode, making them more suitable for electrochemical capacitors.
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Conference papers on the topic "Scherrer formula"

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Raza, Rizwan, Ghazanfar Abbas, and Bin Zhu. "GDC-Y2O3 Oxide Based Two Phase Nanocomposite Electrolytes." In ASME 2010 8th International Conference on Fuel Cell Science, Engineering and Technology. ASMEDC, 2010. http://dx.doi.org/10.1115/fuelcell2010-33322.

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An oxide based two phase nanocomposite electrolyte (Ce0.9Gd0.1O2) was synthesized by a co-precipitation method and coated with Yttrium oxide (Y2O3). The nanocomposite electrolyte showed the significant performance of power density 750mW/cm2 and higher conductivities at relatively low temperature 550°C. Ionic conductivities were measured with electrochemical impedance spectroscopy (EIS) and DC (4 probe method). The structural and morphological properties of the prepared electrolyte were investigated by means of High Resolution Scanning Electron Microscopy (HRSEM). The thermal stability was determined with Differential Scanning Calorimetry (DSC). The particle size was calculated with Scherrer formula and compare with SEM results, 15–20 nm is in a good agreement with the SEM and X-ray diffraction (XRD) results. The purpose of the study to introduce the functional nanocomposite materials, for advanced fuel cell technology (NANOCOFC) to meet the challenges of solid oxide fuel cell (SOFC).
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Abbas, Ghazanfar, Rizwan Raza, Muhammad Ashraf Chaudhry, and Bin Zhu. "Preparation and Characterization of Nanocomposite Calcium Doped Ceria Electrolyte With Alkali Carbonates (NK-CDC) for SOFC." In ASME 2010 8th International Conference on Fuel Cell Science, Engineering and Technology. ASMEDC, 2010. http://dx.doi.org/10.1115/fuelcell2010-33325.

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The entire world’s challenge is to find out the renewable energy sources due to rapid depletion of fossil fuels because of their high consumption. Solid Oxide Fuel Cells (SOFCs) are believed to be the best alternative source which converts chemical energy into electricity without combustion. Nanostructured study is required to develop highly ionic conductive electrolyte for SOFCs. In this work, the calcium doped ceria (Ce0.8Ca0.2O1.9) coated with 20% molar ratio of two alkali carbonates (CDC-M: MCO3, where M = Na and K) electrolyte was prepared by co-precipitation method in this study. Ni based electrode was used to fabricate the cell by dry pressing technique. The crystal structure and surface morphology was characterized by X-Ray Diffractometer (XRD), Scanning Electron Microscopy (SEM) and High Resolution Transmission Electron Microscopy (HRTEM). The particle size was calculated in the range of 10–20nm by Scherrer’s formula and compared with SEM and TEM results. The ionic conductivity was measured by using AC Electrochemical Impedance Spectroscopy (EIS) method. The activation energy was also evaluated. The performance of the cell was measured 0.567W/cm2 at temperature 550°C with hydrogen as a fuel.
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Grimm, Sandra Biewers, Daniel Weis, and Anita Latz. "SUBJECTIVITY AND SOCIAL RECOGNITION: THEORETICAL AND EMPIRICAL PERSPECTIVES ON THE VALUE OF NON-FORMAL EDUCATION FROM THE PERSPECTIVE OF YOUNG PEOPLE." In International Conference on Education and New Developments. inScience Press, 2022. http://dx.doi.org/10.36315/2022v1end008.

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"Due to its principles of voluntariness and openness, and because of its diverse offer of experiential and subject?related educational opportunities, open youth work is increasingly seen as having a special potential in supporting the acquisition of key competences and life skills. But which educational opportunities are meant here and what form of education are we talking about here at all? These are the questions addressed by the qualitative?reconstructive study ""Educational Experiences in Non?formal Settings"", which is being conducted at the Centre for Childhood and Youth Research (CCY) at the University of Luxembourg. The study examines the subjective educational experiences of young people in open youth work on the basis of ethnographic observations in youth centers, in problem-centered interviews and group discussions with young people as well as a supplementary quantitative survey. The study is based on an understanding of education that follows the tradition of subject?scientific theory (v. Humboldt, Koller) as well as the recognition theory (Honneth) and discusses education with concepts of self?determination and maturity in dealing with social norms and routines. The starting point of this consideration is that education can be determined as the transformation of the relationship to the self and the world. It is also linked to the theoretical work of Albert Scherr (1996), who defines the development of self?awareness, self?esteem, self?determination and thus ultimately subjectivity as the central educational goals of youth work. Empirically, it is thus not primarily a matter of investigating processes of knowledge acquisition, but rather of describing ""innovative moments in the development of individual ways of thinking and acting (Koller, 2018, p.112). The results of the data analysis show a differentiated description of youth?related educational occasions and marks small?scale experiences of the appropriation of personal, social and everyday life references. They also highlight moments of expanding young people's ways of thinking, possibilities of action and dispositions in the context of open youth work. The high importance of social recognition as a basic prerequisite for educational processes (among the young people involved) becomes visible."
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