A crystallographic approach to the calculation of orientation diagrams

1983 ◽  
Vol 20 (6) ◽  
pp. 932-952 ◽  
Author(s):  
John Starkey
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Crystallographic Orientation ◽  
Crystal Orientation ◽  
Orientation Distribution ◽  
Polycrystalline Aggregate ◽  
Crystal Forms ◽  
Pole Figures ◽  
Orientation Matrix ◽  
Multiplicity Factor

Methods are described that use measured pole figures directly to calculate pole figures, inverse pole figures, and the crystal orientation matrix; this latter is a frequency distribution of the Euler rotations, which relate the crystal orientations in a polycrystalline aggregate to a standard crystallographic orientation. It is demonstrated that if data from crystal forms with different crystallographic multiplicities are to be compared the appropriate multiplicity factor must be applied to the data in the measured pole figures.These techniques are applied to computer-simulated fabrics and the data obtained are compared with data derived via the orientation distribution function. It is concluded that the data derived directly from the measured pole figures more closely represent the actual data. In the case of inverse pole figures the procedures based on the orientation distribution function yield results that are of doubtful geological significance.

Calculation of the crystal orientation distribution function from synchrotron radiation experimental data

1989 ◽  
Vol 22 (6) ◽  
pp. 559-561 ◽  
Author(s):  
J. A. Szpunar ◽  
P. Blandford ◽  
D. C. Hinz
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Synchrotron Radiation ◽  
Orientation Distribution Function ◽  
Crystal Orientation ◽  
Orientation Distribution ◽  
Pole Figures ◽  
Cold Rolled ◽  
Expansion Coefficients ◽  
Crystal Orientation Distribution Function

Series-expansion coefficients for an orientation distribution function (ODF) of cold-rolled aluminium sheet were calculated from the intensity of Debye–Scherrer rings obtained in an experiment using synchrotron radiation. Calculated and observed pole figures demonstrate that a sufficiently good approximation to the ODF is obtained from coefficients calculated to l = 8.

scholarly journals Study and classification of the Crystallographic Orientation Distribution Function of a non-grain oriented electrical steel using computer vision system

2019 ◽  
Vol 8 (1) ◽  
pp. 1070-1083
Author(s):  
Roberto Fernandes Ivo ◽  
Douglas de Araújo Rodrigues ◽  
José Ciro dos Santos ◽  
Francisco Nélio Costa Freitas ◽  
Luis Flaávio Gaspar Herculano ◽  
...  
Keyword(s):  
Computer Vision ◽  
Distribution Function ◽  
Orientation Distribution Function ◽  
Crystallographic Orientation ◽  
Electrical Steel ◽  
Vision System ◽  
Orientation Distribution ◽  
Computer Vision System

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.

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.

Quantitative X-Ray Analysis of Deformation Microtexture within Individual Grains

2005 ◽  
Vol 495-497 ◽  
pp. 983-988
Author(s):  
N.Yu. Ermakova ◽  
Nikolay Y. Zolotorevsky ◽  
Yuri Titovets
Keyword(s):  
Distribution Function ◽  
Uniaxial Compression ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
X Ray ◽  
Pole Figures ◽  
Single Grain ◽  
Individual Grains

The method is described which enables to determine the microtexture that is the orientation distribution within individual grains of a polycrystal. The microtexture is evaluated on the base of X-ray pole distributions measured for separate reflections, referred to as microscopic pole figures (MPF). The procedure for treatment of experimental MPF and the following computation of orientation distribution function is described in detail. Precision of the microtexture evaluation and possible ways of its improvement are discussed. As an example of the method application, orientation distribution within a single grain of aluminum polycrystal deformed by uniaxial compression up to 50% has been examined.

scholarly journals A Test of the Refinement Procedure for Determining the Crystallite Orientation Distribution: Polyethylene Terephthalate

Texture ◽  
1972 ◽  
Vol 1 (1) ◽  
pp. 9-16 ◽  
Author(s):  
W. R. Krigbaum ◽  
Anna Marie Harkins Vasek
Keyword(s):  
Distribution Function ◽  
Polyethylene Terephthalate ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Fiber Texture ◽  
Fiber Axis ◽  
Crystallite Orientation ◽  
Plane Normal ◽  
Pole Figures ◽  
Refinement Procedure

A test of the refinement procedure for improving the crystallite orientation distribution function is presented for a fiber texture sample of polyethylene terephthalate. This is a particularly difficult example because the triclinic unit cell offers no simplification due to symmetry, and the pole figures are sharply peaked. The analysis employed 17 observed pole figures and an additional 29 unobserved pole figures reconstructed from the crystallite orientation distribution function. After three cycles of refinement, in which the maximum value of the coefficient was increased from 6 to 16, the standard deviations, σq and σw, of the plane-normal and crystallite orientation distributions were reduced by about a factor of 3. The refined crystallite orientation distribution function indicates that the c-axis tends to align along the fiber axis for this polyethylene terephthalate sample.

Acoustoelastic Response of a Polycrystalline Aggregate With Orthotropic Texture

1985 ◽  
Vol 52 (3) ◽  
pp. 659-663 ◽  
Author(s):  
G. C. Johnson
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Effective Properties ◽  
Orientation Distribution ◽  
Polycrystalline Aggregate ◽  
Third Order ◽  
Effective Response ◽  
Third Order Elastic Constants ◽  
Generalized Spherical Harmonics ◽  
Crystalline Symmetry

Estimates of the effective second-order and third-order elastic constants of a polycrystalline aggregate exhibiting texture are presented for the case of orthotropic sample symmetry and cubic crystalline symmetry. The nature of the texture is brought into the analysis through the crystallites’ orientation distribution function which is written in a series of generalized spherical harmonics. The effective response is evaluated using a Voigt-type procedure in which the crystal stiffnesses are averaged over the orientation distribution function. In evaluating the results, it is found that only seven terms in the expansion for the orientation distribution function are required for the exact representation of the effective properties.

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