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.

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.

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 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.

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 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.

scholarly journals Texture, Piezoelectricity and Ferroelectricity

1995 ◽  
Vol 23 (4) ◽  
pp. 221-236 ◽  
Author(s):  
L. Fuentes ◽  
O. Raymond
Keyword(s):  
Distribution Function ◽  
Barium Titanate ◽  
Texture Analysis ◽  
Technological Process ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Odd Order ◽  
Order Expansion ◽  
Orientation Distributions ◽  
Expansion Coefficients

A Quantitative Texture Analysis approach to polycrystal piezoelectric and ferroelectric phenomena is given. Monocrystal longitudinal piezoelectric moduli are expanded in Bunge's symmetry- adapted functional bases. Suitable expansion coefficients are given. Orientation Distribution Function based algorithms for polycrystal piezo-moduli prediction are presented. Significant odd-order expansion terms are calculated and their relation to ghost phenomena is commented. Polycrystal ferroelectricity is characterized. Quantitative describers associated to crystallographic and electric orientation distributions are presented and related. Their evolution during heat and poling processes is discussed. Two computer-simulated examples are analyzed: (a) Texture-modulated longitudinal piezo-modulus is calculated for an ideal quartz single-component texture. (b) Barium titanate fibre texture transformation during a hypothetical technological process is investigated.

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.

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