Truncation correction in the Fourier (Warren–Averbach) analysis of diffraction line profiles for the determination of accurate crystallite size and microstrains

1984 ◽  
Vol 40 (a1) ◽  
pp. C412-C412
Author(s):  
J. I. Langford ◽  
R. Delhez ◽  
Th. H. de Keijser ◽  
E. J. Mittemeijer ◽  
D. Louër
Keyword(s):  
Crystallite Size ◽  
Diffraction Line ◽  
Line Profiles

Application of the method of moments to X-ray diffraction line profiles from paracrystals: Native cellulose fibres

1981 ◽  
Vol 14 (6) ◽  
pp. 421-431 ◽  
Author(s):  
G. B. Mitra ◽  
P. S. Mukherjee
Keyword(s):  
Method Of Moments ◽  
Diffraction Line ◽  
Line Profiles ◽  
X Ray Diffraction ◽  
Cellulose Fibres ◽  
Distortion Parameter ◽  
X Ray ◽  
Central Moments ◽  
Two Parameters

The `microparacrystallite size' and `distortion parameter' of delignified ramie, hemp and jute have been determined – with the assumption that these materials are paracrystalline in nature – with the second and fourth central moments of X-ray diffraction line profiles. A new method of curvature correction has been developed. Background as well as non-additivity corrections have also been accounted for. Theories of determining the `microparacrystallite size' and the `distortion parameter' from single reflections independently from each of these two central moments have been developed, and described. Determination of these two parameters for several directions in the samples studied have been based on the above work. It has been shown that, in conformity with the recent findings of Hosemann & Balta Calleja [Ber. Bunsenges. Phys. Chem. (1980), 84, 91], the larger the paracrystalline distortion the smaller is the `microparacrystallite size'.

Determination of the Bone Mineral Crystallite Size and Lattice Strain from Diffraction Line Broadening

2002 ◽  
Vol 37 (11) ◽  
pp. 1234-1240 ◽  
Author(s):  
S. N. Danilchenko ◽  
O. G. Kukharenko ◽  
C. Moseke ◽  
I. Yu. Protsenko ◽  
L. F. Sukhodub ◽  
...  
Keyword(s):  
Crystallite Size ◽  
Bone Mineral ◽  
Lattice Strain ◽  
Diffraction Line ◽  
Line Broadening

Effect of a crystallite size distribution on X-ray diffraction line profiles and whole-powder-pattern fitting

2000 ◽  
Vol 33 (3) ◽  
pp. 964-974 ◽  
Author(s):  
J. I. Langford ◽  
D. Louër ◽  
P. Scardi
Keyword(s):  
Crystallite Size ◽  
Line Profile ◽  
Profile Analysis ◽  
Diffraction Line ◽  
Powder Pattern ◽  
Line Profile Analysis ◽  
Line Profiles ◽  
Diffraction Line Profile ◽  
Transmission Electron ◽  
Using Data

A distribution of crystallite size reduces the width of a powder diffraction line profile, relative to that for a single crystallite, and lengthens its tails. It is shown that estimates of size from the integral breadth or Fourier methods differ from the arithmetic mean of the distribution by an amount which depends on its dispersion. It is also shown that the form of `size' line profiles for a unimodal distribution is generally not Lorentzian. A powder pattern can be simulated for a given distribution of sizes, if it is assumed that on average the crystallites have a regular shape, and this can then be compared with experimental data to give refined parameters defining the distribution. Unlike `traditional' methods of line-profile analysis, this entirely physical approach can be applied to powder patterns with severe overlap of reflections, as is demonstrated by using data for nanocrystalline ceria. The procedure is compared with alternative powder-pattern fitting methods, by using pseudo-Voigt and Pearson VII functions to model individual line profiles, and with transmission electron microscopy (TEM) data.

Crystallite Size Broadening of Diffraction Line Profiles

2014 ◽  
pp. 15-48
Keyword(s):  
Crystallite Size ◽  
Size Distribution ◽  
Length Distribution ◽  
Finite Size ◽  
Distribution Functions ◽  
Diffraction Line ◽  
Line Profiles ◽  
Column Length ◽  
Line Shapes ◽  
Peak Broadening

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.

Quantum Resonances: Line Profiles and Dynamics

2003 ◽  
Vol 68 (3) ◽  
pp. 529-553 ◽  
Author(s):  
Ivana Paidarová ◽  
Philippe Durand
Keyword(s):  
Hydrogen Atom ◽  
Operator Theory ◽  
Quantum Dynamics ◽  
Line Profiles ◽  
Static Electric Field ◽  
Reversal Effect ◽  
Quantum Resonances ◽  
Energy Dependent ◽  
Effective Hamiltonians

The wave operator theory of quantum dynamics is reviewed and applied to the study of line profiles and to the determination of the dynamics of interacting resonances. Energy-dependent and energy-independent effective Hamiltonians are investigated. The q-reversal effect in spectroscopy is interpreted in terms of interfering Fano profiles. The dynamics of an hydrogen atom subjected to a strong static electric field is revisited.

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