Determination of the orientation distribution function from arbitrary pole figure regions

1990 ◽  
Vol 25 (6) ◽  
pp. 2846-2850 ◽  
Author(s):  
J. A. Szpunar ◽  
D. C. Hinz
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Orientation Distribution

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 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.

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

A software for diffraction stress factor calculations for textured materials

2012 ◽  
Vol 27 (2) ◽  
pp. 114-116 ◽  
Author(s):  
Thomas Gnäupel-Herold
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Elastic Constants ◽  
Orientation Distribution Function ◽  
Lattice Strain ◽  
Orientation Distribution ◽  
Crystallite Orientation ◽  
Interaction Models ◽  
Grain Interaction ◽  
Textured Materials

A software for the calculation of diffraction elastic constants (DEC) for materials both with and without preferred orientation was developed. All grain-interaction models that can use the crystallite orientation distribution function (ODF) are incorporated, including Kröner, Hill, inverse Kröner, and Reuss. The functions of the software include: reading the ODF in common textual formats, pole figure calculation, calculation of DEC for different (hkl,φ,ψ), calculation of anisotropic bulk constants from the ODF, calculation of macro-stress from lattice strain and vice versa, as well as mixture ratios of (hkl) of overlapped reflections in textured materials.

scholarly journals Properties of Projection Lines in the Space of the Orientation Distribution Function

1989 ◽  
Vol 10 (3) ◽  
pp. 243-264 ◽  
Author(s):  
A. Morawiec ◽  
J. Pospiech
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Analytical Description ◽  
Orientation Distribution ◽  
Orientation Space ◽  
The Relationship ◽  
Symmetry Operations

The relationship between the orientation distribution function (ODF) and the pole figure is based on the geometry of projection lines in the orientation space.The paper presents an analytical description of the projection lines and their transformations by symmetry operations. Using simple algebraical rules some properties of the projection lines as well as some properties of the associated projection lines (coupled due to the centrosymmetry of the pole figure) have been derived.

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