Modified Scherrer Equation to Estimate More Accurately Nano-Crystallite Size Using XRD

Monshi, Ahmad; Foroughi, Mohammad Reza; Monshi, Mohammad Reza

doi:10.4236/wjnse.2012.23020

Cited by 1,627 publications

(617 citation statements)

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“…It is also interesting to emphasize that, according to the materials obtained and the methodology employed in this paper, an increase in crystallite size also resulted in an increase in specific surface area. In this case, it was confirmed that, in fact, "crystallite size" is not a synonymous for "particle size", as it is emphasized by other authors 45,48 , once that the individual particles may contain several crystallites 41 . In addition, it is well known that the specific surface area and particle size values have an inverse relation to each other, which can be represented by Eq.…”

Section: Resultssupporting

confidence: 66%

Effect of Urea Excess on the Properties of the MgAl2O4 Obtained by Microwave-Assisted Combustion

et al. 2017

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In this paper, magnesium aluminate spinels were prepared by microwave-assisted combustion, using urea as fuel. In order to evaluate the effect of the urea excess used in the synthesis, its mass was added in a range of 1.0 to 2.5 times the stoichiometric amount required. The materials produced were characterized by TGA, FTIR, XRF, XRD, BET, SEM and TEM. The results demonstrated that magnesium aluminate spinel was formed in all solids, but the crystallinity degree and the specific surface area increased according to the amount of urea that was used in the synthesis. The use of excess fuel in the preparation was therefore advantageous, since it eliminated the need of the calcination step, at high temperatures, in order to stabilize the spinel phase and improve the crystallinity of the solid. The heat generated in the combustion process was sufficient to develop the formation of a nanocrystalline structure and produce high purity materials, with a save of 99.4% in energy.

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Section: Resultssupporting

confidence: 66%

Effect of Urea Excess on the Properties of the MgAl2O4 Obtained by Microwave-Assisted Combustion

et al. 2017

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“…Then, the intercept of ln K/L as well as the crystallite size was obtained by plotting ln β against ln (1/cosθ). 15 Homogeneity of formed crystallite size was evaluated using a statistical method of Gaussian distribution as displayed in Eqn. 2 as:…”

Section: Preparation Of Chitosan-coated Magnetic Nanoparticlesmentioning

confidence: 99%

"CHARACTERISTICS AND MAGNETIC PROPERTIES OF CHITOSAN-COATED Fe3O4 NANOPARTICLES PREPARED BY EX-SITU CO-PRECIPITATION METHOD"

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Chitosan-coated iron oxide nanoparticles were synthesized by ex-situ co-precipitation method. Ammonia solution was dropped into the solution containing ferrous and ferric salts through a syringe pump to form Fe3O4 nanoparticles. Nanoparticles produced were then coated and crosslinked with chitosan and tripolyphosphate/sulfate, respectively. The physical and magnetic properties of chitosan-Fe3O4 nanoparticles were characterized using Scanning Electron Microscopy (SEM), X-Ray Diffraction (XRD), and Electron Spin Resonance (ESR) respectively. The results showed that the ratio enhancement between chitosan:Fe3O4 increased the particle size, while the crystallite size decreased. Morphology and particle size were also influenced by the ratio of crosslinkers. It was found that the higher tripolyphosphate content contributed to the smaller size and more spherical morphology. In addition, the influence of crosslinking time toward crystallite size was determined by tuning stirring time. The result showed that the longer duration of crosslinking time, the larger crystallite size of chitosan-coated Fe3O4 was obtained.

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“…But, K can has a deviation from the value of about unity, because it no only depends on the size and shape of the crystal [3,8,10]. Moreover, the Scherrer constant K is more often taken as about 0.9 [7,9,[11][12][13], as derived in Scherrer's original paper with K=2[2ln(2)/π]2 [10].…”

Section: Introductionmentioning

confidence: 99%

“…D values from XRD analysis [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and TEM [1,18,19] have been reported. However, some discrepancies were found between the D values from XRD analysis and other techniques, such as TEM.…”

Section: Introductionmentioning

confidence: 99%

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Nanostructured titanium dioxide average size from alternative analysis of Scherrer's Equation

et al. 2018

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RESUMOQuantificar o tamanho de materiais em escala nanométrica é um dos desafios a serem superados, uma vez que existem técnicas diferentes. A equação de Scherrer modificada foi usada para estimar o tamanho das partículas de dióxido de titânio em escala nanométrica. Dióxido de titânio com tamanho nominal de nanopartícu-la de 21 nm foi usado como padrão para determinar a precisão da equação modificada. A partir dos dados de raios-X, para a amostra sem tratamento térmico foi obtido um valor médio do tamanho das nanopartículas de 20,63 nm. Um tratamento estatístico foi usado para fazer uma correlação entre o valor estimando pela equação de Scherrer modificada e o valor nominal de 21nm. Um desvio de 0,70 foi encontrado entre o valor calculado e o valor nominal, indicando uma concordância entre os valores. Adicionalmente, a influência da temperatura sobre o tamanho médio das nanopartículas de dióxido de titânio foi pesquisada.Palavras-chave: Nanomateriais, Equação de Scherrer, Dióxido de Titânio. ABSTRACTThe materials sizing in nano-scale is a challenge to be overcome, because the size determined by various methods differ. In order to shed light about the nanomaterials sizing, a modified Scherrer's equation was applied to estimate more accurately the nanostructured titanium dioxide crystal size. The manufactured titanium dioxide-nanostructured powder with nominal average size about 21nm was used as the reference standard to determine the accurate of modified equation. From X-ray diffraction data, an average crystal size about 20.63 nm was achieved for unheated sample. To establish a relation between the result obtained with modified Scherrer's equation and the nominal average crystal size, a statistical treatment and a comparative assessment were performed. The average absolute divergence does not exceed 0.70 nm. The value of crystal size determined from X-ray data was in good agreement with that informed by the supplier. Additionally, the behavior of sample was studied as a function of temperature.

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Modified Scherrer Equation to Estimate More Accurately Nano-Crystallite Size Using XRD

Cited by 1,627 publications

References 6 publications

Effect of Urea Excess on the Properties of the MgAl2O4 Obtained by Microwave-Assisted Combustion

Effect of Urea Excess on the Properties of the MgAl2O4 Obtained by Microwave-Assisted Combustion

"CHARACTERISTICS AND MAGNETIC PROPERTIES OF CHITOSAN-COATED Fe3O4 NANOPARTICLES PREPARED BY EX-SITU CO-PRECIPITATION METHOD"

Nanostructured titanium dioxide average size from alternative analysis of Scherrer's Equation

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