Powder diffraction line profiles from the size and shape of nanocrystallites

2011 ◽  
Vol 44 (5) ◽  
pp. 945-953 ◽  
Author(s):  
K. R. Beyerlein ◽  
R. L. Snyder ◽  
P. Scardi
Keyword(s):  
Powder Diffraction ◽  
Numerical Procedure ◽  
Tangent Plane ◽  
Diffraction Peak ◽  
Line Profiles ◽  
Integration Technique ◽  
Debye Function ◽  
Size And Shape ◽  
Crystallite Sizes ◽  
Good Agreement

A numerical procedure to carry out the integral on the powder diffraction sphere in reciprocal space and obtain accurate powder diffraction peak profiles for small crystallites is presented. In doing so, the literature surrounding the effect of crystallite size and shape on the powder peak profile is briefly reviewed. Powder patterns simulated by this technique are compared with those calculated by the tangent plane approximation and Debye function for spherical, cubic and cylindrical crystallites having sizes of only a few nanometres. The tangent plane approximation is found to produce inaccurate peak profiles and peak positions in simulated patterns of the cubic and cylindrical nanocrystallites. This performance is in contrast to that of the proposed powder integration technique, which results in powder patterns that are in good agreement with those from the Debye function, for all crystallite sizes and shapes considered here.

scholarly journals A review of Debye Function Analysis

2013 ◽  
Vol 28 (S2) ◽  
pp. S2-S10 ◽  
Author(s):  
Kenneth R. Beyerlein
Keyword(s):  
Diffraction Pattern ◽  
Powder Diffraction ◽  
Function Analysis ◽  
Reciprocal Space ◽  
Spherical Particles ◽  
Complete Agreement ◽  
Line Profiles ◽  
Debye Function

The employment of the Debye function to model line profiles in the powder diffraction pattern from small crystallites is briefly reviewed. It is also demonstrated that for the case of very small spherical particles, it is necessary to average patterns from multiple constructions of the particle to have complete agreement with reciprocal space models. In doing so it is demonstrated that the technique of Debye function analysis is best suited for systems with only a few possible atomic arrangements.

Synthesis of cerium oxide (CeO2) by co-precipitation for application as a reference material for X-ray powder diffraction peak widths

2018 ◽  
Vol 33 (1) ◽  
pp. 21-25 ◽  
Author(s):  
Anderson Márcio de Lima Batista ◽  
Marcus Aurélio Ribeiro Miranda ◽  
Fátima Itana Chaves Custódio Martins ◽  
Cássio Morilla Santos ◽  
José Marcos Sasaki
Keyword(s):  
Powder Diffraction ◽  
Function Analysis ◽  
Diffraction Peak ◽  
Debye Function ◽  
Fourier Decomposition ◽  
Diffraction Peaks ◽  
Diffraction Patterns ◽  
Pattern Modeling ◽  
Co Precipitation ◽  
Peak Widths

Several methods can be used to obtain, from powder diffraction patterns, crystallite size and lattice strain of polycrystalline samples. Some examples are the Scherrer equation, Williamson–Hall plots, Warren/Averbach Fourier decomposition, Whole Powder Pattern Modeling, and Debye function analysis. To apply some of these methods, it is necessary to remove the contribution of the instrument to the widths of the diffraction peaks. Nowadays, one of the main samples used for this purpose is the LaB6 SRM660b commercialized by the National Institute of Standard Technology; the width of the diffraction peak of this sample is caused only by the instrumental apparatus. However, this sample can be expensive for researchers in developing countries. In this work, the authors present a simple route to obtain micron-sized polycrystalline CeO2 that have a full width at half maximum comparable with the SRM660b and therefore it can be used to remove instrumental broadening.

X-Ray Powder Diffraction Pattern for Reaction-HIPed A118Ti2Mg3

1992 ◽  
Vol 7 (4) ◽  
pp. 223-225 ◽  
Author(s):  
Frank W. Gayle ◽  
Francis S. Biancaniello ◽  
Robert J. Schaefer ◽  
Rodney D. Jiggets
Keyword(s):  
Experimental Data ◽  
Diffraction Pattern ◽  
Powder Diffraction ◽  
Hot Isostatic Pressing ◽  
Diffraction Peak ◽  
X Ray Diffraction ◽  
Atomic Site ◽  
X Ray ◽  
Ideal Stoichiometry ◽  
Good Agreement

AbstractThe cubic Al18Ti2Mg3 phase (184 atoms/unit cell, Z = 8, space group Fdm) has been fabricated by reaction hot isostatic pressing. Quantitative energy dispersive X-ray analysis showed the phase to have nearly ideal stoichiometry. Interplanar spacings and diffraction peak intensities have been determined by X-ray diffraction. The experimental data show good agreement with the pattern calculated using atomic site positional parameters for A118Cr2Mg3, confirming that A118Cr2Mg3 is the prototype for A118Ti2Mg3.

Local atomic structure in tetragonal pure ZrO2nanopowders

2010 ◽  
Vol 43 (2) ◽  
pp. 227-236 ◽  
Author(s):  
Leandro M. Acuña ◽  
Diego G. Lamas ◽  
Rodolfo O. Fuentes ◽  
Ismael O. Fábregas ◽  
Márcia C. A. Fantini ◽  
...  
Keyword(s):  
Tetragonal Phase ◽  
Local Structure ◽  
X Ray Diffraction ◽  
X Ray ◽  
Atomic Structures ◽  
Crystallite Sizes ◽  
Exafs Study ◽  
The Difference ◽  
X Ray Absorption ◽  
Good Agreement

The local atomic structures around the Zr atom of pure (undoped) ZrO2nanopowders with different average crystallite sizes, ranging from 7 to 40 nm, have been investigated. The nanopowders were synthesized by different wet-chemical routes, but all exhibit the high-temperature tetragonal phase stabilized at room temperature, as established by synchrotron radiation X-ray diffraction. The extended X-ray absorption fine structure (EXAFS) technique was applied to analyze the local structure around the Zr atoms. Several authors have studied this system using the EXAFS technique without obtaining a good agreement between crystallographic and EXAFS data. In this work, it is shown that the local structure of ZrO2nanopowders can be described by a model consisting of two oxygen subshells (4 + 4 atoms) with different Zr—O distances, in agreement with those independently determined by X-ray diffraction. However, the EXAFS study shows that the second oxygen subshell exhibits a Debye–Waller (DW) parameter much higher than that of the first oxygen subshell, a result that cannot be explained by the crystallographic model accepted for the tetragonal phase of zirconia-based materials. However, as proposed by other authors, the difference in the DW parameters between the two oxygen subshells around the Zr atoms can be explained by the existence of oxygen displacements perpendicular to thezdirection; these mainly affect the second oxygen subshell because of the directional character of the EXAFS DW parameter, in contradiction to the crystallographic value. It is also established that this model is similar to another model having three oxygen subshells, with a 4 + 2 + 2 distribution of atoms, with only one DW parameter for all oxygen subshells. Both models are in good agreement with the crystal structure determined by X-ray diffraction experiments.

Evaluation of Reference X-ray Diffraction Patterns in the ICDD Powder Diffraction File

1990 ◽  
Vol 34 ◽  
pp. 369-376
Author(s):  
G. J. McCarthy ◽  
J. M. Holzer ◽  
W. M. Syvinski ◽  
K. J. Martin ◽  
R. G. Garvey
Keyword(s):  
Powder Diffraction ◽  
X Ray Diffraction ◽  
Powder Diffraction File ◽  
Cd Rom ◽  
X Ray ◽  
Binary Oxides ◽  
Diffraction Patterns ◽  
Input Format ◽  
Good Agreement

AbstractProcedures and tools for evaluation of reference x-ray powder patterns in the JCPDSICDD Powder Diffraction File are illustrated by a review of air-stable binary oxides. The reference patterns are evaluated using an available microcomputer version of the NBS*A1DS83 editorial program and PDF patterns retrieved directly from the CD-ROM in the program's input format. The patterns are compared to calculated and experimental diffractograms. The majority of the oxide patterns have been found to be in good agreement with the calculated and observed diffractograms, but are often missing some weak reflections routinely observed with a modern diffractometer. These weak reflections are added to the PDF pattern. For the remainder of the phases, patterns are redetermined.

LDA Measurements and Numerical Prediction of Pulsatile Laminar Flow in a Plane 90-Degree Bifurcation

1988 ◽  
Vol 110 (2) ◽  
pp. 129-136 ◽  
Author(s):  
J. M. Khodadadi ◽  
N. S. Vlachos ◽  
D. Liepsch ◽  
S. Moravec
Keyword(s):  
Laminar Flow ◽  
Numerical Study ◽  
Numerical Procedure ◽  
Stokes Number ◽  
Flow Rate Ratio ◽  
Velocity Measurements ◽  
Numerical Predictions ◽  
Dependent Variables ◽  
Separation Zones ◽  
Good Agreement

An experimental and numerical study of pulsatile laminar flow in a plane 90-degree bifurcation is presented. Detailed LDA velocity measurements of the oscillatory flow field have been carried out. The numerical predictions, which are based on an iterative, finite-difference numerical procedure using primitive dependent variables, are in good agreement with the measurements. The results show that one separation zone is established near the bottom wall of the main duct and another near the upstream wall of the branch. The location and size of the separation zones vary within the cycle and are influenced by the Reynolds number, the flow rate ratio, and the Stokes number.

scholarly journals The Effective Temperature of Am Stars

1993 ◽  
Vol 138 ◽  
pp. 208-212
Author(s):  
C. Megessier ◽  
C. van’t Veer
Keyword(s):  
Effective Temperature ◽  
Balmer Line ◽  
Line Profiles ◽  
Flux Method ◽  
Infra Red ◽  
Good Agreement

AbstractThe values of the effective temperature derived for Am stars by the infra-red flux method and from the Balmer line profiles are in very good agreement. They are hotter by more than 300K than the Teff given by Lane and Lester (1984) and cooler by about 200K than those obtained by Dworetsky et al (1986).

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