Routine Crystallite-Size Determination by X-Ray Diffraction Line Broadening

1961 ◽  
Vol 5 ◽  
pp. 104-116 ◽  
Author(s):  
R. C. Rau
Keyword(s):  
Crystallite Size ◽  
Ceramic Materials ◽  
Diffraction Line ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Routine Basis ◽  
Crystallite Sizes ◽  
Standard Set ◽  
Sintering Characteristics

AbstractIncreasing interest in the sintering characteristics of various ceramic materials has resulted in the need for a knowledge of the crystallite sizes of many constituent ceramic powders. Standard X-ray diffraction line-broadening techniques have been utilized to determine these crystallite sizes. This paper presents a general review of the theory of line broadening as a means of measuring crystallite size and gives the methods and modifications used to perform this type of analysis rapidly and on a routine basis.Four modifications have been used in the determination of crystallite size routinely by X-ray line broadening. These methods are (1) a graded set of powder photographs, (2) a computer program to calculate sizes from diffractometer data, (3) a set of crystallite-size curves for a given material for use with diffractometer data, and (4) a standard set of curves to use with diffractometer data for any strain-free materials. The preparation, use, and limitations of each of these methods is presented.

Dislocations, crystallite size, and planar faults in nanocrystalline ceria

2009 ◽  
Vol 24 (3) ◽  
pp. 228-233 ◽  
Author(s):  
S. R. Aghdaee ◽  
V. Soleimanian
Keyword(s):  
Grain Size ◽  
Dislocation Density ◽  
Crystallite Size ◽  
Cerium Oxide ◽  
Diffraction Line ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Nanocrystalline Ceria ◽  
Hall Plot

The modified Williamson–Hall and Warren–Averbach methods were used successfully for analyzing experimentally observed anisotropic X-ray diffraction line broadening and for determining reliable values of crystallite size and dislocation density in cerium oxide. The modified Williamson–Hall plot gives 22.3(2) nm for volume-weighted crystallite size, while the modified Warren–Averbach produces 18.0(2) nm for area-weighted grain size. The dislocation density and effective outer cut-off radius of dislocations obtained from the modified Warren–Averbach method are 1.8(3)×1015 m−2 and 15.5(1) nm, respectively.

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.

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.

X-ray diffraction line broadening on vibrating dry-milled Two Crows sepiolite

2006 ◽  
Vol 54 (3) ◽  
pp. 390-401 ◽  
Author(s):  
Joaquin Bastida ◽  
Marek A. Kojdecki ◽  
Pablo Pardo ◽  
Pedro Amorós
Keyword(s):  
Diffraction Line ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray

X-Ray Diffraction Analysis on Crystallite Development of Nanostructured Aluminium

2006 ◽  
Vol 118 ◽  
pp. 53-58
Author(s):  
Elisabeth Meijer ◽  
Nicholas Armstrong ◽  
Wing Yiu Yeung
Keyword(s):  
Crystallite Size ◽  
Room Temperature ◽  
Annealing Temperature ◽  
Equal Channel Angular Extrusion ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
Integral Breadth ◽  
X Ray ◽  
Heat Treated ◽  
Diffraction Peaks

This study is to investigate the crystallite development in nanostructured aluminium using x-ray line broadening analysis. Nanostructured aluminium was produced by equal channel angular extrusion at room temperature to a total deformation strain of ~17. Samples of the extruded metal were then heat treated at temperatures up to 300oC. High order diffraction peaks were obtained using Mo radiation and the integral breadth was determined. It was found that as the annealing temperature increased, the integral breadth of the peak reflections decreased. By establishing the modified Williamson-Hall plots (integral breadth vs contract factor) after instrumental correction, it was determined that the crystallite size of the metal was maintained ~80 nm at 100oC. As the annealing temperature increased to 200oC, the crystallite size increased to ~118 nm. With increasing annealing temperature, the hardness of the metal decreased from ~60 HV to ~45 HV.

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