scholarly journals The Misorientation Distribution Function

1986 ◽  
Vol 6 (3) ◽  
pp. 201-215 ◽  
Author(s):  
J. Pospiech ◽  
K. Sztwiertnia ◽  
F. Haessner
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Two Dimensional ◽  
Misorientation Distribution ◽  
Rotation Axes

The analysis of misorientations has up to now usually be carried out by comparing the values obtained experimentally using two dimensional distributions of rotation axes or rotation angles with the distribution calculated by Mackenzie for the statistically random case. In this paper the presentation of the distribution of the misorientations is based on the three dimensional orientation distribution function (ODF) (as described by Bunge). The new function is termed the misorientation distribution function (MDF) to differentiate it from the ODF. The advantages in using this function are presented and illustrated by three MDF's derived from the work of Haessner, Pospiech and Sztwiertnia.

Orientation Distribution of Fiber Suspensions in Extensional Flow

2013 ◽  
Vol 785-786 ◽  
pp. 981-984 ◽  
Author(s):  
Zan Huang ◽  
Jin Ping Qu ◽  
Ji Wei Geng ◽  
Shu Feng Zhai ◽  
Shi Kui Jia
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Orientation Distribution Function ◽  
Fiber Orientation ◽  
Extensional Flow ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Fiber Suspensions ◽  
Short Fibers ◽  
Fiber Orientation Distribution

An orientation distribution function is adopted to describe three-dimensional orientation distribution of short fibers suspensions in extensional flow. A mathematical model of evolution process on fiber orientation distribution function is established by analytical method. Numerical simulation is also used to describe two and three dimensional orientation distribution of fibers. Therefore, analytical solution of differential equation on forecast fiber orientation distribution is deduced.

Improvements in the Quantitative Evaluation of Three-Dimensional Texture. II. The Pole-Figure-Multiplying Method

1995 ◽  
Vol 28 (5) ◽  
pp. 532-533 ◽  
Author(s):  
L.-G. Yu ◽  
H. Guo ◽  
B. C. Hendrix ◽  
K.-W. Xu ◽  
J.-W. He
Keyword(s):  
Distribution Function ◽  
Texture Analysis ◽  
Pole Figure ◽  
Quantitative Evaluation ◽  
Orientation Distribution Function ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Simple Method ◽  
Pole Figures

A new simple method is proposed for determining the orientation distribution function (ODF) for three-dimensional texture analysis in a polycrystal based on the reality that the accuracy of an ODF is dependent on both the accuracy of each measured pole figure and the number of pole figures.

scholarly journals Coordinate Free Tensorial Representation of the Orientation Distribution Function With Harmonic Polynomials

1993 ◽  
Vol 21 (4) ◽  
pp. 233-250 ◽  
Author(s):  
David D. Sam ◽  
E. Turan Onat ◽  
Pavel I. Etingof ◽  
Brent L. Adams
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Measurement Data ◽  
Orientation Distribution ◽  
Harmonic Polynomials ◽  
Crystallite Orientation ◽  
Orientation Measurement ◽  
Three Dimensional Space

The crystallite orientation distribution function (CODF) is reviewed in terms of classical spherical function representation and more recent coordinate free tensorial representation (CFTR). A CFTR is a Fourier expansion wherein the coefficients are tensors in the three-dimensional space. The equivalence between homogeneous harmonic polynomials of degree k and symmetric and traceless tensors of rank k allows a realization of these tensors by the method of harmonic polynomials. Such a method provides for the rapid assembly of a tensorial representation from microstructural orientation measurement data. The coefficients are determined to twenty-first order and expanded in the form of a crystallite orientation distribution function, and compared with previous calculations.

Improvements in the Quantitative Evaluation of Three-Dimensional Texture. I. The Nature of the Information Obtained from Pole Figures

1995 ◽  
Vol 28 (5) ◽  
pp. 527-531 ◽  
Author(s):  
L.-G. Yu ◽  
H. Guo ◽  
B. C. Hendrix ◽  
K.-W. Xu ◽  
J.-W. He
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Angular Resolution ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
High Angular Resolution ◽  
Area Theorem ◽  
Pole Figures ◽  
Experimental Resolution

The sources of indefiniteness in the orientation-distribution-function (ODF) description of crystalline texture are shown to result from the integral nature of the pole-figure measurement. An equipartition-area theorem is proved and it is shown that current methods use too few pole figures, which are measured to an unnecessarily high angular resolution. The experimental resolution is considered and the number of pole figures needed for ODF analysis is calculated as a function of the required ODF resolution.

On-Line Determination of Texture in Deep Drawing Steel Sheet by Two-Dimensional X-Ray Diffraction

2012 ◽  
Vol 572 ◽  
pp. 322-327 ◽  
Author(s):  
An Min Yin ◽  
Quan Yang ◽  
Xiao Chen Wang ◽  
Fei He ◽  
You Zhao Sun
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Deep Drawing ◽  
Orientation Distribution ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
On Line ◽  
The Impact

This paper described the application of a diffraction system based on X-ray area detector on pole figure measurement as well as corresponding computation of orientation distribution functions and the principle of rapid measurement texture. The impact of calculates the orientation distribution function on the conditions of the two-dimensional X-ray diffraction was analyzed; this was illustrated by an example of deep drawing steel sheets texture measurement. ̙̈́˰͇̱̓˰̶̴̿̾ͅ˰̸̱̈́̈́˰̷̱̹͂̿̈́̈́̾˰̸̵̈́˰͇̈́̿˽̴̵̹̹̱̼̽̾̓̿̾˰̴̵̵̳̈́̈́̿͂˰̈́̿˰̸̵̈́˰̵̱̹̱̀̀͂̿̀͂̈́˰̂θ position then fix it, reduce the sample rotation; the texture determination time can be significantly reduced. Reduce the Measuring range of angle χ˰̴̱̾ φ˰̴̵̿̓˰̾̿̈́˰̶̶̵̱̳̈́˰̸̵̈́ calculation of orientation distribution function, it also can significantly reduce the measurement of diffraction data. Several technical problems appeared on the on-line determination of texture based on an X-ray two-dimensional detector system and the possibility to improve the measurement speed and accuracy in the industrial production applications were then discussed.

scholarly journals Evaluation by Computer Simulation of Certain Errors in the Three Dimensional Texture Analysis

1978 ◽  
Vol 3 (1) ◽  
pp. 27-36
Author(s):  
M. Humbert ◽  
F. Wagner ◽  
R. Baro
Keyword(s):  
Computer Simulation ◽  
Distribution Function ◽  
Texture Analysis ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Experimental Errors

The influence of certain experimental errors in pole-figure determination on the accuracy of calculated coefficients of the orientation distribution function has been analyzed.

Influence of extinction phenomenon on determination of the orientation distribution function

2006 ◽  
Vol 2006 (suppl_23_2006) ◽  
pp. 175-180
Author(s):  
G. Gómez-Gasga ◽  
T. Kryshtab ◽  
J. Palacios-Gómez ◽  
A. de Ita de la Torre
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Orientation Distribution
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