Mathematical Modeling of the Orientation Distribution Function by the Vector Method of Quantitative Texture Analysis

1984 ◽  
Vol 123 (2) ◽  
pp. 425-434 ◽  
Author(s):  
H. Schaeben
Keyword(s):  
Mathematical Modeling ◽  
Distribution Function ◽  
Texture Analysis ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Vector Method

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 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.

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 Influence of Grain Number on Graphite Quantitative Texture Study

2003 ◽  
Vol 35 (3-4) ◽  
pp. 197-206
Author(s):  
T. A. Lychagina ◽  
D. I. Nikolayev
Keyword(s):  
Distribution Function ◽  
Texture Analysis ◽  
Elastic Properties ◽  
Orientation Distribution Function ◽  
Material Science ◽  
Orientation Distribution ◽  
Hexagonal Symmetry ◽  
Grain Number ◽  
Suggested Procedure ◽  
Definition Of

The present work is devoted to the study of the grain number influence on the quantitative texture analysis and on the values of averaged elastic properties. Number of grains does not influence mathematical definition of orientation distribution function (ODF) (Bunge, H.J. (1982). Texture Analysis in Material Science. Butterworths, London; Matthies, S., Vinel, G.W. and Helming, K. (1987). Standard Distributions in Texture Analysis. Akademie-Verlag, Berlin.); nevertheless, intuitively clear that, averaging procedure implies a ‘‘large’’ number of grains to make sense. In the present work we applied the already suggested procedure (Lychagina, T.A. and Nikolayev, D.I. (2003). Phys. Stat. Sol. (a), 195(N2), 322–334.) for the case of hexagonal symmetry to evaluate the influence of the grain number in the sample on the calculated elastic properties. This procedure was carried out for graphite that is one of the widespread, applicable and highly anisotropic materials.

scholarly journals Texture Analysis by Means of Model Functions

1993 ◽  
Vol 21 (2-3) ◽  
pp. 139-146 ◽  
Author(s):  
Th. Eschner
Keyword(s):  
Distribution Function ◽  
Texture Analysis ◽  
Orientation Distribution Function ◽  
Texture Component ◽  
Computational Efficiency ◽  
Special Functions ◽  
Orientation Distribution ◽  
Model Function

The conception of texture components is widely used in texture analysis. Mostly it is used to describe the orientation distribution function (ODF) qualitatively, and there are only a few special functions used to provide texture component calculations.This paper attempts to introduce another model function describing common texture components and giving a compromise between universality and computational efficiency.

Quantitative Texture Analysis from X-ray Diffraction Spectra

1997 ◽  
Vol 30 (4) ◽  
pp. 443-448 ◽  
Author(s):  
Y. D. Wang ◽  
L. Zuo ◽  
Z. D. Liang ◽  
C. Laruelle ◽  
A. Vadon ◽  
...  
Keyword(s):  
Distribution Function ◽  
Texture Analysis ◽  
Orientation Distribution Function ◽  
Diffraction Data ◽  
Polycrystalline Material ◽  
Orientation Distribution ◽  
New Method ◽  
X Ray Diffraction ◽  
X Ray

A method to obtain the orientation distribution function (ODF) of a polycrystalline material directly from X-ray diffraction spectra is presented. It uses the maximum-texture-entropy assumption to reduce the diffraction data needed for the ODF analysis. The validity of this new method is illustrated through two model examples.

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 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.

Sign in / Sign up

Export Citation Format

Share Document