scholarly journals X-ray diffraction study of crystallite size-distribution and strain in carbon blacks

2000 ◽  
Vol 661 ◽  
Author(s):  
T. Ungár ◽  
J. Gubicza ◽  
G. Ribárik ◽  
T. W. Zerda
Keyword(s):  
Crystallite Size ◽  
Size Distribution ◽  
Fourier Coefficients ◽  
Shape Anisotropy ◽  
X Ray Diffraction ◽  
Strain Anisotropy ◽  
X Ray ◽  
Carbon Blacks ◽  
Size Profile ◽  
Crystallite Shape

ABSTRACTThe crystallite size and size-distribution in carbon blacks in the presence of strain are determined by recently developed procedure of X-ray diffraction peak profile analysis. The Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well established ab initio functions of size and strain peak profiles. Strain anisotropy is accounted for by expressing the mean square strain in terms of average dislocation contrast factors. Crystallite shape anisotropy is modelled by ellipsoids incorporated into the size profile function. To make the fitting procedure faster, the Fourier transform of the size profile is given as an analitical function. The method is applied to carbon blacks treated at different preassures and temperatures. The microstructure is characterised in terms of crystallite size distribution, dislocation density, and crystallite shape anisotropy.

scholarly journals Crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals

2001 ◽  
Vol 34 (3) ◽  
pp. 298-310 ◽  
Author(s):  
T. Ungár ◽  
J. Gubicza ◽  
G. Ribárik ◽  
A. Borbély
Keyword(s):  
Crystallite Size ◽  
Size Distribution ◽  
Fourier Coefficients ◽  
Profile Analysis ◽  
Nanocrystalline Powder ◽  
Dislocation Model ◽  
Size Distributions ◽  
Strain Anisotropy ◽  
Diffraction Profile ◽  
X Ray

Two different methods of diffraction profile analysis are presented. In the first, the breadths and the first few Fourier coefficients of diffraction profiles are analysed by modified Williamson–Hall and Warren–Averbach procedures. A simple and pragmatic method is suggested to determine the crystallite size distribution in the presence of strain. In the second, the Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well establishedab initiofunctions of size and strain profiles. In both procedures, strain anisotropy is rationalized by the dislocation model of the mean square strain. The procedures are applied and tested on a nanocrystalline powder of silicon nitride and a severely plastically deformed bulk copper specimen. The X-ray crystallite size distributions are compared with size distributions obtained from transmission electron microscopy (TEM) micrographs. There is good agreement between X-ray and TEM data for nanocrystalline loose powders. In bulk materials, a deeper insight into the microstructure is needed to correlate the X-ray and TEM results.

The Determination of Crystallite Size and Size Distribution from Broadened X-Ray Diffraction Lines

1961 ◽  
Vol 5 ◽  
pp. 94-103 ◽  
Author(s):  
H. F. Quinn ◽  
P. Cherin
Keyword(s):  
Harmonic Analysis ◽  
Size Distribution ◽  
Fourier Coefficients ◽  
Distribution Functions ◽  
Composite Sample ◽  
X Ray Diffraction ◽  
X Ray ◽  
Mean Size ◽  
The Mean

AbstractMagnesium oxide crystallites having mean dimensions in the range of 25–1000 A can be prepared by controlled thermal decomposition of the carbonate.Following some earlier investigations of Birks and Friedman, we have determined the mean size and size distribution of several such MgO samples from the broadened X-ray diffraction lines which they exhibit. Contrary to the procedure of the above investigators, the harmonic analysis due to Stokes has been used to correct for instrumental broadening and values of mean-size and size-distribution functions obtained from the Fourier coefficients by the methods of Warren and Averbach.The results obtained are compared with average sizes and distributions obtained by direct examination of the samples in an electron microscope.A composite sample has been prepared by mixing known quantities of the sample previously studied. The distribution function obtained by harmonic analysis of one diffraction line of the composite sample is compared with the function calculated from the distributions of its components.Conclusions are drawn concerning the significance of the results obtained by the Warren technique: in particular, the average sizes obtained by this method are compared with those given by the approximate method used by Birks and Friedman.

Particle size and microstrain measurement in ADI alloys

2002 ◽  
Vol 17 (2) ◽  
pp. 119-124 ◽  
Author(s):  
Jorge L. Garin ◽  
Rodolfo L. Mannheim ◽  
Marco A. Soto
Keyword(s):  
Particle Size ◽  
Crystallite Size ◽  
Size Distribution ◽  
Cold Work ◽  
Cold Deformation ◽  
Diffraction Line ◽  
Column Length ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray

In this study we deal with the determination of crystallite-size distribution and microstrain measurement in austempered ductile irons (ADI) subjected to cold deformation, by means of x-ray diffraction line broadening. The deformation process imposed on the material yields the formation of microstrain and crystallite size domains within each grain, which are somehow related to the mechanical behavior of the alloy. Three series of samples were cold-worked from 2.5% to 20.0% of thickness reduction in order to determine the domain size and microstrain induced in the material, in terms of the original thickness of the castings and the percentage of cold work. The x-ray diffraction line-broadening effects were analyzed by means of the Warren–Averbach method, which allowed the separation of size and strain parameters. The particle size distribution resulted in an average column length in the range of 15.7–24.9 nm in the ferrite phase, while the austenite phase showed values varying between 13.4 and 36.3 nm. On the other side, the overall root mean square strain varied from 0.000 85 to 0.003 93 for ferrite and from 0.000 65 to 0.004 38 for austenite. In all of the studied cases the average column length decreased with increasing deformation, while the initial thickness of the cast samples did not show any clear correlation with increasing deformation.

Comparative X-ray diffraction study of the crystalline microstructure of tetragonal and monoclinic vanadium–zirconium dioxide solid solutions produced from gel precursors

2009 ◽  
Vol 42 (2) ◽  
pp. 198-210 ◽  
Author(s):  
Marek Andrzej Kojdecki ◽  
Esther Ruiz de Sola ◽  
Francisco Javier Serrano ◽  
José María Amigó ◽  
Javier Alarcón
Keyword(s):  
Thermal Treatment ◽  
Crystallite Size ◽  
Size Distribution ◽  
Solid Solutions ◽  
Normal Component ◽  
Growth Stages ◽  
X Ray Diffraction ◽  
Microstructural Characteristics ◽  
X Ray ◽  
Crystalline Microstructure

The microstructural characteristics of solid solutions, prepared by heating dried gel precursors with nominal compositions VxZr1−xO2(0 ≤x≤ 0.1) at 723 and 1573 K, were determined from X-ray diffraction patterns. The crystalline microstructure of the resulting specimens, characterized by a prevalent crystallite shape, a volume-weighted crystallite size distribution and a second-order lattice strain distribution, was found to depend on the vanadium content. A characteristic feature of all size distributions was their bimodality, explained as a result of transformations between tetragonal and monoclinic phases during thermal treatment. A comparative study of the microstructure of both zirconia phases has been carried out, enabling reconstruction of a probable course of crystallization of both pure and vanadium-doped zirconias: on heating a sample, nucleation and the early growth stages involve crystallites of both phases; then on annealing and cooling, the crystallites of one phase transform into the other, depending on the thermal treatment temperature. Each logarithmic normal component of the crystallite size distribution of the resulting phase can be attributed to one of these processes. The limit of solubility of vanadium in tetragonal and monoclinic zirconia is estimated from the microstructural characteristics.

Broadening Microstructure Analysis Program(BMAP): an isotropic and anisotropic crystallite size and strain calculator

2015 ◽  
Vol 48 (6) ◽  
pp. 1729-1733 ◽  
Author(s):  
E. Khalafalla Mahmoud ◽  
M. R. Ebeid ◽  
M. A. Kaid ◽  
M. G. S. Ali
Keyword(s):  
Crystallite Size ◽  
Line Profile ◽  
Sol Gel ◽  
Software Tool ◽  
Average Crystallite Size ◽  
X Ray Diffraction ◽  
Strain Anisotropy ◽  
X Ray ◽  
Least Squares Fit ◽  
Measured Line

BMAPcalculator is a simplified software tool to obtain microstructure characteristics and to investigate their isotropic and anisotropic nature using some common broadening methods. The Scherrer and Stokes–Wilson methods as well as the Williamson–Hall plot (microstructure isotropy) and modified Williamson–Hall models (strain anisotropy) are implemented in the calculations. TheBMAPinput data are the X-ray diffraction peak parameters (the full width at half-maximum or integral breadth and peak position) of a measured line profile and of a reference one. The components of the measured line profile or corrected broadening are based on several approximations (Cauchy, Gauss or Voigt). The linear least-squares fit is used to calculate the size–strain values, and the correlation coefficient for accepting the results. The calculator is applied to an X-ray diffraction experiment of NiO nanoparticles prepared by a sol–gel method for testing. The results ofBMAPcalculator and theMAUDprogram, combined with an anisotropic Popa rules approach, are compared. The uniform stress model based on the Cauchy approximation is the most suitable one in cubic nanostructure nickel oxide, with an average crystallite size of 24 nm and anisotropic strains of 1.54 × 10−3, 0.61 × 10−3, 1.77 × 10−3and 1.49 × 10−3using the {111}, {200}, {220} and {311} reflections, respectively. Generally, for non-Rietveld users, it is useful to collect different methods into one program to depict the anisotropic nature of materials.

scholarly journals Quartz Crystallite Size and Moganite Content as Indicators of the Mineralogical Maturity of the Carboniferous Chert: The Case of Cherts from Eastern Asturias (Spain)

Minerals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 611
Author(s):  
Celia Marcos ◽  
María de Uribe-Zorita ◽  
Pedro Álvarez-Lloret ◽  
Alaa Adawy ◽  
Patricia Fernández ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Crystallite Size ◽  
Archaeological Sites ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Infrared And Raman Spectroscopy ◽  
First Time ◽  
Geological Formations

Chert samples from different coastal and inland outcrops in the Eastern Asturias (Spain) were mineralogically investigated for the first time for archaeological purposes. X-ray diffraction, X-ray fluorescence, transmission electron microscopy, infrared and Raman spectroscopy and total organic carbon techniques were used. The low content of moganite, since its detection by X-ray diffraction is practically imperceptible, and the crystallite size (over 1000 Å) of the quartz in these cherts would be indicative of its maturity and could potentially be used for dating chert-tools recovered from archaeological sites. Also, this information can constitute essential data to differentiate the cherts and compare them with those used in archaeological tools. However, neither composition nor crystallite size would allow distinguishing between coastal and inland chert outcrops belonging to the same geological formations.

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