Crystallite size distribution and lattice distortions in polyethylene from analyses of Debye‐Scherrer line profiles

In this chapter, the X-ray peak profile broadening caused by the finite size of scattering crystallites is studied in detail. According to Bertaut’s theorem, the line profile with the indices hkl is determined by the length distribution of columns building up the scattering crystallites normal to the hkl reflecting planes. The column length distribution determined from line profiles can be converted into crystallite size distribution. The effect of median and variance of crystallite size distribution on the shape of line profiles is also discussed. The line shapes for different crystallite size distribution functions (e.g. lognormal and York distributions) are given. It is shown that for spherical crystallites the peak broadening does not depend on the indices of reflections. The dependence of line profiles on the indices hkl is presented for various anisotropic shapes of crystallites.

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Structural changes on hot-rolling of polyethylene. II. Crystallite size distribution and lattice distortions

Journal of Polymer Science Polymer Physics Edition ◽

10.1002/pol.1977.180150503 ◽

1977 ◽

Vol 15 (5) ◽

pp. 787-793 ◽

Cited By ~ 2

Author(s):

Osamu Yoda ◽

Isamu Kuriyama

Keyword(s):

Crystallite Size ◽

Size Distribution ◽

Hot Rolling ◽

Structural Changes ◽

Lattice Distortions

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

MRS Proceedings ◽

10.1557/proc-661-kk9.2 ◽

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.

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Influence of Fuel in the Synthesis of ZnAl2O4 Catalytic Supports by Combustion Reaction

Materials Science Forum ◽

10.4028/www.scientific.net/msf.660-661.52 ◽

2010 ◽

Vol 660-661 ◽

pp. 52-57 ◽

Cited By ~ 8

Author(s):

Kaline Melo de Souto Viana ◽

Bruno Brito Dantas ◽

N.A.S. Nogueira ◽

J.M. Sasaki ◽

Normanda Lino de Freitas ◽

...

Keyword(s):

Particle Size ◽

Particle Size Distribution ◽

Crystallite Size ◽

Size Distribution ◽

Spinel Structure ◽

Morphological Characteristics ◽

Combustion Reaction ◽

Nanosized Particles ◽

Catalytic Supports ◽

Stoichiometric Proportion

The aim of this work is to evaluate the influence of fuel in the synthesis of ZnAl2O4 catalytic supports by combustion reaction. For this, it was used the fuels: urea, carbohidrazide, glycine and aniline. The total amount of reagents was calculated according to the theory of propellants and explosive using urea in the stoichiometric proportion (Φe = 1). The structural and morphological characteristics of the powders were evaluated by XRD, FTIR, TEM, SEM and particle size distribution. The results from XRD showed the formation of the normal cubic spinel structure. The powders presented nanosized particles with narrow agglomerates size distribution. The powders prepared with urea showed better value of surface area and smaller crystallite size.

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