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.

Mechanical Spectroscopy Investigation of Liquid Pb-Bi Alloys

2012 ◽  
Vol 184 ◽  
pp. 434-439 ◽  
Author(s):  
Roberto Montanari ◽  
Alessandra Varone
Keyword(s):  
Distribution Functions ◽  
X Ray Diffraction ◽  
Mechanical Spectroscopy ◽  
X Ray ◽  
Neutron Spallation Source ◽  
Driven System ◽  
Spallation Source ◽  
Accelerator Driven System ◽  
The Mean ◽  
Diffraction Patterns

Liquid Pb–Bi eutectic alloy has been selected as coolant and neutron spallation source for the development of MYRRHA, an accelerator driven system. The alloy has been characterized in liquid state from melting (125 °C) to 650 °C by mechanical spectroscopy. Experiments have been carried out using hollow reeds of austenitic stainless steel filled with the Pb-Bi alloy and sealed at the extremities. From 350 °C to 520 °C modulus shows a remarkable drop accompanied by a broad internal friction maximum. In the same temperature range radial distribution functions, determined from X-ray diffraction patterns, evidenced variations of the mean distance between the 1st nearest neighbour atoms. The anelastic phenomena have been attributed to a structural re-arrangement of liquid metal. For comparison, other alloys of the Pb-Bi system with hypo-eutectic composition have been investigated.

The Use of the Pseudo-Voigt Function in the Variance Method of X-ray Line-Broadening Analysis

1997 ◽  
Vol 30 (4) ◽  
pp. 427-430 ◽  
Author(s):  
F. Sánchez-Bajo ◽  
F. L. Cumbrera
Keyword(s):  
Crystallite Size ◽  
Original Form ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
Stabilized Zirconia ◽  
X Ray ◽  
Variance Method ◽  
The Mean ◽  
Voigt Function

A modified application of the variance method, using the pseudo-Voigt function as a good approximation to the X-ray diffraction profiles, is proposed in order to obtain microstructural quantities such as the mean crystallite size and root-mean-square (r.m.s.) strain. Whereas the variance method in its original form is applicable only to well separated reflections, this technique can be employed in the cases where there is line-profile overlap. Determination of the mean crystallite size and r.m.s. strain for several crystallographic directions in a nanocrystalline cubic sample of 9-YSZ (yttria-stabilized zirconia) has been performed by means of this procedure.

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.

The determination of crystal size and disorder from X-ray diffraction photographs of polymer fibres. 1. The accuracy of determination of Fourier coefficients of the intensity profile of a reflection

1989 ◽  
Vol 22 (4) ◽  
pp. 363-371 ◽  
Author(s):  
R. Somashekar ◽  
I. H. Hall ◽  
P. D. Carr
Keyword(s):  
Crystal Size ◽  
Fourier Coefficients ◽  
Intensity Profile ◽  
X Ray Diffraction ◽  
Scattering Angle ◽  
X Ray ◽  
Fourier Cosine ◽  
High Harmonics ◽  
Lattice Planes

Methods which determine the number and disorder of lattice planes in a crystal from the Fourier cosine coefficients of the intensity profile of an X-ray reflection use only the low harmonics and require that the coefficients be normalized so that the zero harmonic is unity. Experimentally, the profiles can only be recorded over a smaller range of scattering angle than required by the theory, and it is necessary to subtract background, which is likely to be estimated with considerable error, before determining the coefficients. It is shown that with polymer fibres this causes serious errors in the normalization, and in the values of those low harmonics used in the size and disorder determination, and prevents reliable values being obtained. Methods which avoid normalization and use only high harmonics are needed. It is shown that disorder may be obtained in such a way, but not size, for which low-order normalized coefficients are essential. A method of extrapolation is described and tested which enables the accurate high harmonics to be used to improve the estimates of the low ones. Whilst this will yield more reliable values of crystal size than are obtainable from existing methods, the accuracy depends entirely on the validity of the extrapolation, which cannot be tested in many cases of interest.

Synthesis and Characterization of Surface Protected Nanocrystalline Particles of Titania

1998 ◽  
Vol 519 ◽  
Author(s):  
E. Scolan ◽  
C. Sanchez
Keyword(s):  
X Ray Diffraction ◽  
Elastic Light Scattering ◽  
Titanium Butoxide ◽  
X Ray ◽  
Toluene Sulfonic Acid ◽  
Nanocrystalline Particles ◽  
Mean Size ◽  
The Mean ◽  
Cp Mas Nmr

AbstractMonodisperse non-aggregated nanoparticles of titania are obtained through hydrolysis at 60°C of titanium butoxide in the presence of acetylacetone and para-toluene sulfonic acid. After drying the resulting xerosols can be dispersed without aggregation in water-alcoholic or alcoholic solutions. The characterizations of the nanoparticles have been carried out by using quasi-elastic light scattering (QELS), 13C 1H in solution and X-ray diffraction, TEM, TG-DTA, 13C CP-MAS NMR in the solid state. The mean size of the anatase oxide core can be adjusted in the I to 5 nanometer range by a careful tuning of the synthetic conditions. The anatase particles are surrounded by acetylacetonato ligands, para-toluene sulfonate based species and water.

Characterization of Ultra Fine Palladium Particles with the Mean Size of 20 A by X-Ray Diffraction

1981 ◽  
Vol 50 (9) ◽  
pp. 3071-3074 ◽  
Author(s):  
Ken-ichi Ohshima ◽  
Shigeki Yatsuya ◽  
Jimpei Harada
Keyword(s):  
X Ray Diffraction ◽  
X Ray ◽  
Mean Size ◽  
The Mean ◽  
Palladium Particles
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