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.

scholarly journals Pole Figure Inversion Using Finite Elements Over Rodrigues Space

2002 ◽  
Vol 35 (2) ◽  
pp. 113-144 ◽  
Author(s):  
Nathan R. Barton ◽  
Donald E. Boyce ◽  
Paul R. Dawson
Keyword(s):  
Finite Elements ◽  
Pole Figure ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Pole Figures ◽  
Orientation Distribution Functions ◽  
Pole Figure Data ◽  
Straight Lines ◽  
And Inversion

Using finite elements over Rodrigues space, methods are developed for the formation and inversion of pole figures. The methods take advantage of the properties of Rodrigues space, particularly the fact that geodesics corresponding to pole figure projection paths are straight lines. Both discrete and continuous pole figure data may be inverted to obtain orientation distribution functions (ODFs) in Rodrigues space, and we include sample applications for both types of data.

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 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.

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 Texture Analysis of a Zinc Layer on a Steel Substrate Using Neutron Diffraction

1993 ◽  
Vol 21 (2-3) ◽  
pp. 71-78
Author(s):  
H.-G. Brokmeier
Keyword(s):  
Distribution Function ◽  
Neutron Diffraction ◽  
Texture Analysis ◽  
Orientation Distribution Function ◽  
Steel Substrate ◽  
Orientation Distribution ◽  
Pole Figures ◽  
Iron And Zinc

This paper describes the application of neutron diffraction to investigate the texture of a zinc layer 8 μm in thickness. In a nondestructive way both the texture of the zinc layer as well as the texture of the steel substrate were studied. Therefore, pole figures of iron ((110), (200) and (211)) and of zinc ((0002), (101¯0), (101¯1); and (101¯3)/(112¯0)) were measured; additionally the orientation distribution function of iron and zinc were calculated.

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.

A New Method for Orientation Distribution Function Analysis

1985 ◽  
Vol 29 ◽  
pp. 443-449
Author(s):  
Munetsugu Matsuo ◽  
Koichi Kawasaki ◽  
Tetsuya Sugai
Keyword(s):  
Distribution Function ◽  
Spherical Harmonics ◽  
Orientation Distribution Function ◽  
Function Analysis ◽  
Orientation Distribution ◽  
Symmetry Operation ◽  
Composite Function ◽  
Odd Order ◽  
Pole Figures ◽  
Generalized Spherical Harmonics

AbstractAs a means for quantitative texture analysis, the crystallite orientation distribution function analysis has an important drawback: to bring ghosts as a consequence of the presence of a non-trivial kernel which consists of the spherical harmonics of odd order terms. In the spherical hamonic analysis, ghosts occur in the particular orientations by symmetry operation from the real orientation in accordance with the symmetry of the harmonics of even orders. For recovery of the odd order harmonics, the 9th-order generalized spherical harmonics are linearly combined and added to the orientation distribution function reconstructed from pole figures to a composite function. The coefficients of the linear combination are optimized to minimize the sum of negative values in the composite function. Reproducibility was simulated by using artificial pole figures of single or multiple component textures. Elimination of the ghosts is accompanied by increase in the height of real peak in the composite function of a single preferred orientation. Relative fractions of both major and minor textural components are reproduced with satisfactory fidelity In the simulation for analysis of multi-component textures.

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