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.

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.

X-ray diffraction characterization of microstrain in some uranium alloys

1998 ◽  
Vol 13 (2) ◽  
pp. 89-95
Author(s):  
G. Kimmel ◽  
D. Dayan
Keyword(s):  
Thermal Stresses ◽  
Cold Work ◽  
Solubility Limit ◽  
Diffraction Line ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Semiquantitative Method

Taking advantage of the feasibility to obtain well-prepared surfaces, an extensive work has been done in studying X-ray diffraction line broadening effects from flat polycrystalline samples of uranium and uranium alloys. The broadening analysis has been used as a semiquantitative method for measuring inhomogeneity of alloying, hardness, and residual thermal stresses. Good correlation between the microstrain and the hardness was found after heat treatments and cold work. A comparable correlation was found between the microstrain in the supersaturated α-uranium phase quenched from the γ region, and the concentration of the alloying elements. The measured microstrain in the supersaturated α-uranium phase was used as a quantitative value for determination of the solubility limit of Ta and W in γ-uranium. As a result of this study it was found that the limit of solubility is approximately 2.6 and 2.0 at. % for Ta and W, respectively.

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.

Determination of particle size distribution in an Fe2O3-based catalyst using magnetometry and x-ray diffraction

1992 ◽  
Vol 7 (7) ◽  
pp. 1856-1860 ◽  
Author(s):  
Manjula M. Ibrahim ◽  
Jianmin Zhao ◽  
Mohindar S. Seehra
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Mössbauer Measurements ◽  
Log Normal ◽  
Log Normal Distribution

In this paper, the techniques of SQUID magnetometry and line broadening in x-ray diffraction are employed for determining an important parameter for catalysts, viz. the particle size distribution. Magnetization versus temperature (5 K–400 K) and magnetization versus field (up to 55 kOe) data are reported for an α–Fe2O3 based catalyst. After determining the region of superparamagnetism, the distribution function f(r) is determined assuming a log normal distribution and Langevin paramagnetism of superparamagnetic particles. The distribution is found to be fairly symmetric with center near 65 Å and range of 35 to 115 Å. From line-broadening of Bragg peaks in x-ray diffraction, particle radii varying between 75 Å and 110 Å are obtained. These results are compared with the reported Mössbauer measurements of Huffman et al. on the same sample.

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.

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