Universal Scherrer equation for graphene fragments

Carbon ◽  
2020 ◽  
Vol 162 ◽  
pp. 475-480 ◽  
Author(s):  
Daniel J. Lim ◽  
Nigel A. Marks ◽  
Matthew R. Rowles
Keyword(s):  
2007 ◽  
Vol 561-565 ◽  
pp. 495-498 ◽  
Author(s):  
Jin Liang Huang ◽  
Xiao Wang ◽  
Liu Shuan Yang ◽  
Chun Wei Cui ◽  
Xing Hua Yang

The cubic pyrochlore phase Bi1.5ZnNb1.5O7 nanopowder was successfully synthesized by the hydrothermal method (HTM) from the starting materials: Bi(NO3)3·5H2O, ZnO, Nb2O5 and the mineralizer: KOH. The XRD patterns prove that the cubic pyrochlore phase Bi1.5ZnNb1.5O7 nanopowder can be obtained by HTM, and TEM photographs show that the powders present the regularly granular shape, when the hydrothermal reactions were conducted at synthesis temperatures 140~220°C and reaction time for 6~48h. The crystalline sizes of the powders were calculated by the Scherrer equation to be about 43~49nm. The crystalline sizes decreased both with the increase in synthesis temperature and the prolonged reaction time until they reached to the minimum size about 43nm at 220°C for 24h.However, they tended to increase when the reaction time was above 24h.


2015 ◽  
Vol 1112 ◽  
pp. 57-61 ◽  
Author(s):  
Amalia Sholehah ◽  
Akhmad Herman Yuwono

In the present work, ZnO nanostructures were synthesized via wet chemistry method. The seeding solution was prepared from zinc nitrate tetrahydrate and hexamethylenetetramine. Prior to the heating process, the seeding solution was immersed in cold bath (0°C). XRD analysis had shown sharp peaks in diffractogram, indicating the high crystallinity of ZnO nanostructures. The crystallite size was determined using Scherrer equation and Williamson-Hall method. Other relevant parameters including stress, strain, and energy density were calculated using Williamson-Hall assuming UDM, UDSM, and UDEDM. The results had revealed that crystallite size calculated with Williamson-Hall method is more accurate than Scherrer equation.


2012 ◽  
Vol 496 ◽  
pp. 379-382
Author(s):  
Rui Song Yang ◽  
Ming Tian Li ◽  
Chun Hai Liu ◽  
Xue Jun Cui ◽  
Yong Zhong Jin

The Cu0.81Ni0.19 has been synthesized directly from elemental powder of nickel and copper by mechanical alloying. The alloyed Cu0.81Ni0.19 alloy powders are prepared by milling of 8h. The grain size calculated by Scherrer equation of the NiCu alloy decreased with the increasing of milling time. The end-product was analyzed by X-ray diffraction (XRD), scanning electron microscopy (SEM)


2016 ◽  
Vol 230 (9) ◽  
Author(s):  
Mauro Coduri ◽  
Michela Maisano ◽  
Maria Vittoria Dozzi ◽  
Elena Selli

AbstractPreferential growth of anatase crystallites along different directions is known to deeply affect their photocatalytic properties, especially with respect to the exposure of the reactive {001} facets. Its extent can be easily quantified through simple geometric calculations, on the basis of crystal sizes extracted for specific directions by means of X-Ray Diffraction data analysis. Nevertheless, the actual results depend on the method employed for such a quantification. Here we report on a comparative morphological investigation, performed by employing the Scherrer equation and the line profile from Rietveld refinements, on shape-controlled anatase photocatalysts produced by employing HF as capping agent. Compared to the Rietveld-based method, the use of the Scherrer equation produces a systematic underestimation of crystallite dimensions, especially concerning the [100] direction, which in turn causes the percentage of exposed {001} crystal facets to be underestimated. Neglecting instrumental-related effects may further reduce the estimate.


2020 ◽  
Vol 10 (18) ◽  
pp. 6279
Author(s):  
JinAh Hwang ◽  
Moonhee Choi ◽  
Hyo-Soon Shin ◽  
Byeong-Kwon Ju ◽  
MyoungPyo Chun

Ni1−xZnxFe2O4 (x = 0.5, 0.6, 0.7) nanoparticles were synthesized by a thermal decomposition method. The synthesized particles were identified as pure spinel ferrite structures by X-ray diffraction analysis, and they were calculated to be 46–51 nm in diameter by the Scherrer equation, depending on the composition. In the FE-SEM image, the ferrite nanoparticles have spherical shapes with slight agglomeration, and the particle size is about 50 nm, which was consistent with the value obtained by the Scherrer equation. The lattice parameter of the ferrite nanoparticles monotonically increased from 8.34 to 8.358 Å as the Zn concentration increased from 0.5 to 0.7. Initially, the saturation magnetization value slowly decreases from 81.44 to 83.97 emu/g, then quickly decreases to 71.84 emu/g as the zinc content increases from x = 0.5, through 0.6, to 0.7. Ni1−xZnxFe2O4 toroidal samples were prepared by sintering ferrite nanoparticles at 1250 °C and exhibited faceted grain morphologies in the FE-SEM images with their grain sizes being around 5 µm regardless of the Zinc content. The real magnetic permeability (μ′) of the toroidal samples measured at 5 MHz was monotonically increased from 106, through 150, to 217 with increasing the Zinc content from x = 0.5, through 0.6, to 0.7. The cutoff frequency of the ferrite toroidal samples was estimated to be about 20 MHz from the broad maximum point in the plot of imaginary magnetic permeability (μ″) vs. frequencies, which seemed to be associated with domain wall resonance.


Clay Minerals ◽  
1999 ◽  
Vol 34 (4) ◽  
pp. 601-617 ◽  
Author(s):  
M. Jaboyedoff ◽  
B. Kübler ◽  
Ph. Thélin

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.


2020 ◽  
Vol 13 (2) ◽  
Author(s):  
Pepi Helza Yanti ◽  
Yendro Gandi

Hidroksiapatit (HAp) merupakan salah satu senyawa biokeramik yang digunakan dalam berbagai aplikasi.  Pada penelitian ini telah dilakukan sintesis hidroksiapatit (HAp) dengan metode pengendapan menggunakan cangkang lokan (Geloina coaxans) dan H3PO4  sebagai prekursor. Analisis menggunakan X-Ray Flourocence (XRF) menunjukkan bahwa komposisi kimia utama pada cangkang lokan (Geloina coaxans) adalah CaO.  Produk terbaik diperoleh melalui waktu kalsinasi pada suhu 900 oC selama 180 menit yang ditunjukkan dengan puncak yang memiliki intensitas tertinggi pada 2θ = 31,7o dan puncak spesifik lainnya untuk hidroksiapatit pada 2θ = 32,89o, 32, 17o, 25,86o dan 49,46o. Difraktogram dibandingkan dengan JCPDS (No 09-0432). Berdasarkan perhitungan menggunakan persamaan Scherrer, didapatkan ukuran kristal dari hidroksiapatit (HAp) adalah 26,62 nm. Analisis menggunakan FTIR juga telah dilakukan untuk mengidentifikasi gugus fungsi pada hidroksiapatit yang diperoleh. Dari spektrum FTIR menunjukkan adanya pita serapan yang khas untuk gugus  OH‒, CO32- dan PO43-pada hidroksiapatit. Morfologi partikel berbentuk granular seperti bola dan gumpalan yang tidak seragam diperoleh melalui analisis menggunakan SEM.. ABSTRACT  Hydroxyapatite (HAp) is a bioceramic compound that is used in various applications. In this research, hydroxyapatite (HAp) synthesis has been carried out by precipitation method using Geloina coaxans shell and H3PO4 as precursors. Analysis using X-Ray Flourocence (XRF) showed that the main chemical composition of Geloina coaxans shell was CaO. The best product was obtained by calcination at 900 oC for 180 minutes indicated by a peak having the highest intensity at 2θ = 31.7o and other specific peaks for hydroxyapatite at 2θ = 32.89o, 32 ,17o, 25.86o and 49.46o. The difractogram was compared to JCPDS (No 09-0432). Based on calculations using the Scherrer equation, the crystallite size of hydroxyapatite was 26.62 nm. Analysis using FTIR has also been carried out to identify the functional groups of the hydroxyapatite obtained. The FTIR spectrum showed that there were unique absorption bands  for OH‒, CO32- and PO43- groups on hydroxyapatite. Analysis using SEM showed that the morphology was granular like balls and non-uniform aggregate


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