scholarly journals Normalizing Incomplete Experimental Pole Figures by Means of the Vector Method

1984 ◽  
Vol 6 (2) ◽  
pp. 97-103 ◽  
Author(s):  
H. Schaeben ◽  
A. Vadon
Keyword(s):  
Texture Analysis ◽  
Pole Figure ◽  
Axial Symmetry ◽  
Full Range ◽  
Inverse Pole Figure ◽  
Vector Method ◽  
Pole Figures ◽  
The Matrix

The vector method of quantitative texture analysis provides a new solution of the problem of normalizing incomplete experimental pole figures. It basically makes use of the fact that the matrix σ*(hkl) to which the corresponding matrix σ(hkl) reduces in case of: (1) axial symmetry in terms of pole figures; or (2) fiber textures in terms of orientations, is full range. In this case σ*(hkl) actually establishes the correspondence between the axial symmetrical direct pole figure and the corresponding inverse pole figure with respect to the normal ON of the sample.

Texture Analysis with Area Detectors

2005 ◽  
Vol 105 ◽  
pp. 71-76 ◽  
Author(s):  
Kurt Helming ◽  
Uwe Preckwinkel
Keyword(s):  
Texture Analysis ◽  
Pole Figure ◽  
Data Sets ◽  
Angle Of Incidence ◽  
Surface Layers ◽  
Area Detector ◽  
Texture Information ◽  
Pole Figures ◽  
Information Depth

Starting from simple geometric considerations concerning directions and orientations, intelligent strategies for pole figure measurements were developed for the area detector. The amount and quality of texture information contained in measured or available data sets can be directly controlled. The texture approximation is done by the component method. The method does not have any restrictions concerning the grids of sample directions in the pole figures. An almost constant information depth can be obtained at a low angle of incidence of the primary beam for the study of thin surface layers.

scholarly journals An Investigation Into the Accuracy of the Vector Method by Comparison With ECP Measurements

1989 ◽  
Vol 10 (2) ◽  
pp. 117-134 ◽  
Author(s):  
R. Shimizu ◽  
J. Harase ◽  
K. Ohta
Keyword(s):  
Pole Figure ◽  
Direct Measurement ◽  
Orientation Distribution ◽  
Vector Method ◽  
Inversion Result ◽  
X Ray ◽  
Pole Figures ◽  
The Mean ◽  
Actual Orientation ◽  
Good Agreement

In an attempt to investigate the accuracy of the vector method for crystal texture analysis, a comparison has been made between the inversion result of the pole figure made by X-ray studies using the VM and the inversion result of the pole figure made by ECP. A comparison has been made between the inversion by the pole figure generated by direct measurement of orientations by ECP and the actual orientation distribution (measured by ECP) displayed in the same mode. The materials studied were recrystallized Fe–3% Si and Fe–50% Ni. The main findings were:• In the mean intensities of each individual Box, the inversion results of pole figures made from orientations determined by ECP were in good agreement with the inversion from (100) pole figures made by X-ray or actual orientation distribution (made by ECP) displayed in the same mode as the vector method.• For Fe–3% Si, quite a good agreement was obtained between the results inverted from X-ray pole figure and the direct measurement by ECP for the intensity distribution of minor texture component along ζ angle. It was concluded from these investigations that the inversion of the pole figure by the vector method is accurate enough for most practical purposes.

scholarly journals Minimal Pole Figure Ranges for Quantitative Texture Analysis

1992 ◽  
Vol 19 (1-2) ◽  
pp. 45-54 ◽  
Author(s):  
K. Helming
Keyword(s):  
Texture Analysis ◽  
Pole Figure ◽  
Practical Interest ◽  
Texture Measurement ◽  
Pole Figures

The use of only a small number of incomplete pole figures for texture determinations is of practical interest for reducing the effort of texture measurement. The determination of minimal pole figure ranges (MPR) is explained and the use of MPR is demonstrated on an example.

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 Comments to a Publication of T.I. Savyolova Concerning Domains of Dependence in Pole Figures

1998 ◽  
Vol 30 (3-4) ◽  
pp. 207-227 ◽  
Author(s):  
S. Matthies ◽  
C. Esling
Keyword(s):  
Texture Analysis ◽  
Pole Figure ◽  
Common Knowledge ◽  
Practical Importance ◽  
Three Dimensional ◽  
Data Sets ◽  
Starting Solution ◽  
Pole Figures ◽  
General Difference ◽  
Dimensional Object

A questionable publication of T.I. Savyolova is analysed. The paper claims, that it is possible to determine Ph(y) pole figure values for y∈Y(h;h0,Y0) using only data from y∈Y0 of a single pole figure Ph0(y). The contradiction to the common knowledge can be resolved well understanding that there is a general difference between the term solutions (or continuation of solutions) of an ultrahyperbolic equation (satisfied by the axis distribution function A(h, y)) and the term pole figure. Pole figures considered in texture analysis are two-dimensional projections of a three-dimensional object (the ODF f(g)). For limited data sets the equation ΔhA(h,y)=ΔyA(h,y) bears only a necessary, but not sufficient character in order to get solutions of interest, i.e. it cannot be guaranteed that a h-specific continuation of a starting solution Ph0(y) will be a “h-projection” of the same ODF, which belongs to a concrete sample and possesses the “h0-projection” Ph0(y).Consequently, to name such a h-specific continuation “pole figure” is incorrect. The consideration of formal (unambiguous only by artificial conditions) continuations of solutions may be mathematically interesting, but is of no practical importance for texture analysis. Examples (already considered by the authors about twenty years ago) are given, how to construct in a much more simple way continuations of solutions of the same useless type like in the paper under discussion.

The Construction Of Quantitative Inverse Pole Figures Using the Available Odf Data

1993 ◽  
Vol 37 ◽  
pp. 465-471
Author(s):  
Charles Peng ◽  
Lu Ting
Keyword(s):  
Computer Program ◽  
Pole Figure ◽  
Plastic Flow ◽  
Flow Behavior ◽  
Inverse Pole Figure ◽  
Cold Forming ◽  
X Ray ◽  
Bcc Metals ◽  
Pole Figures ◽  
Polycrystalline Aggregates

AbstractThe ODF calculation is, to a large extent, responsible for the increased interest in texture analysis. Accurate pole figures and ODF plots can be routinely obtained in the laboratory from x-ray units equipped with precision controlling devices. For studies of the plastic flow behavior of polycrystalline aggregates, it is important to present the texture results in a manner readily usable for these analyses. For samples having a simple concentrated texture, the presentation of the data in terms of conventional pole figures and ODF plots is usually adequate. Additional work however is frequently needed when the analysis is involved with a more complex texture. A method is described for constructing the quantitative inverse pole figure using the available ODF data. Attention is focused on the construction of inverse pole figures for FCC and BCC metals. Examples are given of the plastic flow analyses for copper and tantalum which were produced by different cold-forming processes to yield a multitude of texture elements. The modification and rearrangement of the computer program necessary to accomplish this task will be discussed.

Study of the texture of polycrystalline FCC materials using one incomplete direct pole figure

2020 ◽  
Vol 86 (12) ◽  
pp. 32-39
Author(s):  
S. M. Mokrova ◽  
V. N. Milich
Keyword(s):  
Texture Analysis ◽  
Pole Figure ◽  
Texture Component ◽  
Optimal Number ◽  
Polycrystalline Materials ◽  
Reliability Parameters ◽  
Pole Figures ◽  
Polar Figure ◽  
Material Texture ◽  
Fcc Materials

The article deals with the algorithm for texture analysis of polycrystalline materials using one direct pole figure (DPF). It is shown that the incomplete direct polar figure {111} for fcc materials contains the necessary information about the material texture. The algorithm provides identification of the preferred texture components in a multicomponent texture material and determination of their properties. The proposed algorithm is as follows. The upper hemisphere of the digital representation of the DPF is scanned by a polar complex of vectors that are normal to the reflection planes. Then the reliability parameters for each orientation are calculated and a set of the most reliable orientations is formed. The chosen orientations are recalculated to the Rodrigues space wherein the preferred texture components are formed by clustering. At the same time, an iterative algorithm with symmetry operators is used to avoid the umklapp effect. Each texture component is represented by the following parameters: Rodrigues mean vector, Miller indices, and Euler angles. The share and scattering of the texture component are also calculated. A method for selecting the optimal number of clusters providing presentation of the texture with the desired degree of detail is proposed. This is achieved by comparing two incomplete direct pole figures taken for {111} and {200} to select the maximum cluster scattering value on which the number of formed predominant texture components depend. The developed algorithm seems promising for rapid texture analysis, in analysis of sharp and weak textures and when there are less than three DPFs.

scholarly journals An Improvement of Vector Method by Allocation of Intensities Based on the Crystallographic Symmetry

1989 ◽  
Vol 10 (2) ◽  
pp. 101-116 ◽  
Author(s):  
R. Shimizu ◽  
K. Ohta ◽  
J. Harase
Keyword(s):  
Texture Analysis ◽  
Crystal Symmetry ◽  
Residual Vector ◽  
Reflection And Transmission ◽  
Vector Method ◽  
X Ray ◽  
Textural Component ◽  
Pole Figures ◽  
Crystallographic Symmetry

An investigation has been carried out utilizing model and experimental pole figures made by X-ray technique in order to examine the use of the vector method as a means of the texture analysis. The main findings are as follows:• From crystal symmetry considerations positions and magnitudes of peaks along the ζ angle can be predicted. There are discrepancies in these intensity peaks and in some cases the peaks are missing altogether.• This problem was solved by the allocation of intensities such that equal intensities are obtained at the crystallographic symmetry positions.• Even a slightly mismatched combination of the reflection and transmission pole figures caused an increase in residual vector (R) resulting in the failure of the analysis for the minor textural component.

scholarly journals Neutron Texture Analysis of Melt-Textured YBCO Bulk Samples

1999 ◽  
Vol 33 (1-4) ◽  
pp. 75-92
Author(s):  
Lothar Schmidt ◽  
Martin Ullrich ◽  
Werner F. Kuhs
Keyword(s):  
Quantitative Analysis ◽  
Texture Analysis ◽  
Pole Figure ◽  
Error Estimation ◽  
Superconducting Phase ◽  
Ybco Bulk ◽  
Pole Figures ◽  
Counting Statistics

Neutron texture measurements on YBCO bulk samples show a very sharp texture of the superconducting phase YBa2Cu3O7-x with half-widths of less than 5°. Even with a rather coarse measurement grid of only 722 points per complete pole figure, satisfactory results for the recalculated (002) pole figures could be obtained. However, for a reliable calculation of a complete ODF, finer grids will have to be used. Due to the importance of a good alignment of the c-axes in the material, a quantitative analysis of the (002) pole figures, including an error estimation due to measurement grid and counting statistics, was made. An outline for the determination of a reliable background estimate is given.

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