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.

scholarly journals The Resolution of Orientation Space With Reference to Pole-Figure Resolution

1982 ◽  
Vol 4 (4) ◽  
pp. 189-200 ◽  
Author(s):  
János Imhof
Keyword(s):  
Distribution Function ◽  
Data Structure ◽  
Texture Analysis ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Fundamental Equation ◽  
Orientation Distribution ◽  
Probabilistic Interpretation ◽  
Orientation Space ◽  
Pole Figure Data

The orientation distribution function depends on the measured pole-figure data structure. With reference to the divisions of the pole-figure the orientation space is divided into classes, such that contain orientations indistinguishable on the basis of pole-figure data. These classes should refer to distinguishable values of the orientation distribution function. Divisions of orientation space are considered in formulating the fundamental equation of texture analysis. Probabilistic interpretation of the fundamental equation is formulated.

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 Reproducible Textures

1982 ◽  
Vol 5 (2) ◽  
pp. 87-94 ◽  
Author(s):  
H. J. Bunge ◽  
C. Esling
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Simple Form ◽  
Polycrystalline Material ◽  
Orientation Distribution ◽  
Crystal Form ◽  
Axially Symmetric ◽  
Black And White

The orientation distribution function of a textured polycrystalline material may be split into an even and odd part; the latter is not reproducible from pole figure measurements as has been recently shown. The class of textures containing only a reproducible part is considered. In the case of axially symmetric textures (fibre textures), these take on a very simple form. They are, however, not the only type of reproducible textures as has been assumed. A sample having a reproducible texture is centrosymmetric, even in the most general case of non-centrosymmetric, enantiomorphic crystals of one crystal form only. Symmetry elements of this kind have been called non-conventional ones. They may be described by black-and-white or Shubnikov groups. Reproducible textures correspond to a non-conventional centre of inversion as an element of sample symmetry and vice versa.

Polycrystal elastic constants for triclinic crystal and physical symmetry

2006 ◽  
Vol 39 (4) ◽  
pp. 502-508 ◽  
Author(s):  
Peter R. Morris
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Weight Functions ◽  
Higher Symmetry ◽  
X Ray ◽  
Pole Figures ◽  
Generalized Spherical Harmonics ◽  
Physical Symmetry ◽  
Symmetry Operations

The problem of obtaining the Voigt average for the elastic stiffnesses with texture-describing weight functions has been solved for triclinic crystal and physical symmetries. The average is obtained by expanding theTijklmnpq, which relate the elastic stiffnesses in the rotated reference frame, c^{\,\prime}_{ijkl}, to those of the principal elastic stiffnesses,cmnpq, in generalized spherical harmonics, multiplying by the orientation distribution function and integrating over all orientations. The condition imposed to assure a unique expansion results in the absence of terms with oddL, so that the results are completely determinable from conventional X-ray pole figures. This is the most general case, from which all higher-symmetry solutions may be obtained by application of symmetry operations. The Reuss average for elastic compliances may be obtained in a similar fashion.

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.

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