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.

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.

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 3D immersive visualization of micro-computed tomography and XRD texture datasets

2019 ◽  
Vol 34 (2) ◽  
pp. 97-102
Author(s):  
M. A. Rodriguez ◽  
T. T. Amon ◽  
J. J. M. Griego ◽  
H. Brown-Shaklee ◽  
N. Green
Keyword(s):  
Computed Tomography ◽  
Texture Analysis ◽  
Mechanical Strain ◽  
Three Dimensional ◽  
Multidimensional Analysis ◽  
Micro Computed Tomography ◽  
X Ray ◽  
3D Data ◽  
Pole Figures ◽  
Ct Data

Advancements in computer technology have enabled three-dimensional (3D) reconstruction, data-stitching, and manipulation of 3D data obtained on X-ray imaging systems such as micro-computed tomography (μ-CT). Likewise, intuitive evaluation of these 3D datasets can be enhanced by recent advances in virtual reality (VR) hardware and software. Additionally, the generation, viewing, and manipulation of 3D X-ray diffraction datasets, such as pole figures employed for texture analysis, can also benefit from these advanced visualization techniques. We present newly-developed protocols for porting 3D data (as TIFF-stacks) into a Unity gaming software platform so that data may be toured, manipulated, and evaluated within a more-intuitive VR environment through the use of game-like controls and 3D headsets. We demonstrate this capability by rendering μ-CT data of a polymer dogbone test bar at various stages of in situ mechanical strain. An additional experiment is presented showing 3D XRD data collected on an aluminum test block with vias. These 3D XRD data for texture analysis (χ, ϕ, 2θ dimensions) enables the viewer to visually inspect 3D pole figures and detect the presence or absence of in-plane residual macrostrain. These two examples serve to illustrate the benefits of this new methodology for multidimensional analysis.

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.

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. 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.

Three-dimensional Interactive Data Language pole figure visualization

2006 ◽  
Vol 21 (2) ◽  
pp. 102-104 ◽  
Author(s):  
Colleen S. Frazer ◽  
Mark A. Rodriguez ◽  
Ralph G. Tissot
Keyword(s):  
Pole Figure ◽  
Three Dimensional ◽  
Large Data ◽  
Peak Height ◽  
Large Data Sets ◽  
Data Sets ◽  
Interactive Data Language ◽  
Area Detector ◽  
Position Sensitive ◽  
Interactive Data

The Interactive Data Language has been used to produce a software program capable of advanced three-dimensional visualizations of pole figure and θ-2θ data. The data can also be used to calculate quantitative properties such as strain level and to minimize the peak-height texture effects in individual θ-2θ scans. The collection of the large data sets necessary for the analyses is facilitated by use of a position sensitive detector or area detector.

Three-dimensional orientation of poly(l-lactide) crystals under uniaxial drawing

RSC Advances ◽  
2016 ◽  
Vol 6 (15) ◽  
pp. 11943-11951 ◽  
Author(s):  
E. Lizundia ◽  
A. Larrañaga ◽  
J. L. Vilas ◽  
L. M. León
Keyword(s):  
Texture Analysis ◽  
Pole Figure ◽  
Three Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Strain Induced Crystallization ◽  
Induced Crystallization

Three-dimensional strain-induced crystallization upon poly (l-lactide) stretching revealed by X-ray diffraction texture analysis via pole figure measurements.

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 A New Library Program for Texture Calculations

1977 ◽  
Vol 2 (4) ◽  
pp. 225-241 ◽  
Author(s):  
F. Wagner ◽  
C. Esling ◽  
R. Baro
Keyword(s):  
Texture Analysis ◽  
Computing Time ◽  
Three Dimensional ◽  
Great Precision ◽  
Memory Space ◽  
Pole Figures ◽  
Library Program ◽  
Short Time ◽  
And Storage ◽  
Good Agreement

A new library program which allows the calculation and storage of the numerical tables necessary for a three-dimensional texture analysis is proposed. Its main characteristics are:–possibility of selecting the values to be stored according to the desired microscopic and macroscopic symmetries as well as to the step of exploration of the pole figures;–possibility of choosing the quantity of information to be stored for obtaining, in the further three-dimensional analysis, a good agreement between the computing time and the memory space; and–great precision of the stored values and short time of calculation due to the use of new and optimized aigorithms.

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