scholarly journals Determination of the Complete Orientation Distribution Function by the Zero-Range Method

1986 ◽  
Vol 6 (4) ◽  
pp. 289-313 ◽  
Author(s):  
H. P. Lee ◽  
H. J. Bunge ◽  
C. Esling
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Statistical Error ◽  
Orientation Distribution ◽  
Positivity Condition ◽  
Additional Information ◽  
Pole Figures ◽  
Zero Range

Because of the superposition of pole figures corresponding to symmetrically equivalent crystal directions, only the reduced orientation distribution function f∼(g) can be obtained directly by pole figure inversion. The additional information contained in the positivity condition of the ODF allows, however, the determination of an approximation to the “indeterminable” part and hence of the complete ODF f(g), if the texture has sufficiently large zero-ranges. The application of the method and the accuracy of the results was tested using two theoretical and one experimental textures. The accuracy of the complete ODF depends on the size of the zero-range, the errors in its determination, and on the errors, experimental and truncational, of the reduced ODF. The “physical zero” used in order to determine the zero-range is defined according to the statistical error of the pole figure measurement.

scholarly journals The Determination of Orientation Distribution Function From Incomplete Pole Figures - an Example of a Computer Program

1978 ◽  
Vol 3 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Jerzy Jura ◽  
Jan Pospiech
Keyword(s):  
Distribution Function ◽  
Computer Program ◽  
Orientation Distribution Function ◽  
Practical Importance ◽  
Orientation Distribution ◽  
Rhombic Symmetry ◽  
Pole Figures ◽  
Cubic System ◽  
Pole Figure Data

The use of incomplete pole figure data for defining the orientation distribution function (ODF) in a polycrystalline material is of great practical importance, because it enables the use of experimental data from a simplified measurement. The present paper provides the source text of a computer program for calculating the coefficients of ODF series expansion, Cℓμυ. The data for computations are in the incomplete pole figures of rhombic symmetry as determined by the back reflection or transmission technique for crystalline solids of the cubic system. Also described is the numerical method of determining the coefficients Cℓμυ, and the results so obtained are discussed.

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.

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.

scholarly journals Determination of the Orientation Distribution Function From One Pole-figure

1982 ◽  
Vol 5 (2) ◽  
pp. 73-86 ◽  
Author(s):  
János Imhof
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Conditional Probabilities ◽  
By Products

The values of the orientation distribution function and the data of the pole-figure are correlated by products of particular conditional probabilities. One of the possible approximations of these products are obtained and demonstrated with the help of an example showing how the orientation distribution function can thus be obtained.

Determination of pole figure coverage for texture measurements with neutron time-of-flight diffractometers

2018 ◽  
Vol 51 (3) ◽  
pp. 895-900 ◽  
Author(s):  
Shigehiro Takajo ◽  
Sven C. Vogel
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Time Of Flight ◽  
Orientation Distribution ◽  
Neutron Time ◽  
Crucial Parameter

The coverage of a given diffraction instrument as a percentage of the area 2π of a pole figure hemisphere is a crucial parameter of each diffraction instrument used for texture or strain pole figure determination. On the basis of this knowledge, the number of rotations and rotation angles for a full determination of the orientation distribution function can be optimized. However, the determination of this quantity is non-trivial. This paper presents a method that projects a given detector coverage into pole figure space, i.e. outlines the detector areas in a pole figure, and then determines the fraction of the entire 2π pole figure hemisphere around the sample that is covered. The freely available Generic Mapping Tools (GMT) and ImageJ are utilized for this quantification. With this method, it is shown that the empirically determined rotation angles for the HIPPO neutron time-of-flight diffractometer are close to optimal for a set of three rotations.

scholarly journals Non-Random Orientation Distribution Functions With Random Pole Figures

1979 ◽  
Vol 3 (3) ◽  
pp. 169-190 ◽  
Author(s):  
H. J. Bunge ◽  
C. Esling
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Random Orientation ◽  
Numerical Examples ◽  
Pole Figures ◽  
Orientation Distribution Functions

It is shown, theoretically and with numerical examples, that the orientation distribution function may vary between zero and two or even more times random while a corresponding pole figure is completely random.

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