scholarly journals Optimization of Texture Measurements—Part II: Further Applications: Optimal Smoothing

1999 ◽  
Vol 33 (1-4) ◽  
pp. 357-363
Author(s):  
V. Luzin
Keyword(s):  
Texture Analysis ◽  
Singular Integrals ◽  
Integral Kernel ◽  
Orientation Distribution ◽  
Quantitative Approach ◽  
Pole Density ◽  
Basic Principles ◽  
Density Data ◽  
Pole Figures ◽  
Optimal Smoothing

In our previous paper (Luzin, 1997. Proc. of Workshop “Neutron Textures and Stress Analysis”) the basic principles of the quantitative approach to optimize the texture measurements were outlined. This paper is the report of advances in this direction.The quantitative approach is used to solve the smoothing problem. Smoothing by singular integrals with an integral kernel used by Nikolayev and Ullemeyer (1996). Proc. of Workshop “Math. Methods of Texture Analysis”, Textures and Microstructures25, 149– 158 is used in this paper. It is shown how the optimal smoothing parameter depends on the grain statistics, i.e. the number of grains in the sample. The algorithm for optimal smoothing of real pole density data (pole figures) is proposed.Also, the application of optimal smoothing for solving the central problem of quantitative texture analysis (QTA), i.e. orientation distribution function (ODF) reproduction, is discussed.

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 Calculation of the Normalization Factor of Incomplete Pole Figures by Cubic Extrapolation

1986 ◽  
Vol 6 (3) ◽  
pp. 167-179 ◽  
Author(s):  
M. Dahms ◽  
H.-J. Bunge
Keyword(s):  
Spline Interpolation ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Pole Density ◽  
Normalization Factor ◽  
Texture Coefficients ◽  
Cubic Materials ◽  
Pole Figures ◽  
Experimental Errors ◽  
Normalization Factors

The calculation of orientation distribution functions from incomplete pole figures can be carried out by a least squares approximation of the texture coefficients Clμν and the normalization factors Nhkl to the available experimental data. This procedure is less susceptable to instabilities due to experimental errors if the normalization factors can be calculated independently of the coefficients Clμν. In the case of cubic materials, the relationship F20 = 0 to be fulfilled by pole figure values provides an independent condition for the calculation of the normalization factor. This condition can still be improved by taking the slopes of the pole density curves at α = αmax⁡ and α = 90° into account. An economic way to consider the slope in the pole figures is to use a cubic spline interpolation.

Application of ODF to the Rietveld Profile Refinement of Polycrystalline Solid

1993 ◽  
Vol 37 ◽  
pp. 49-57
Author(s):  
C. S. Choi ◽  
E. F. Baker ◽  
J. Orosz
Keyword(s):  
Three Dimensional ◽  
Inverse Pole Figure ◽  
Orientation Distribution ◽  
Pole Density ◽  
Diffraction Profile ◽  
Refinement Method ◽  
Pole Figures ◽  
Diffraction Patterns ◽  
Characterization Of Materials ◽  
Profile Refinement

The Rietveld profile refinement method is probably the most popular technique used for the crystallographic characterization of materials including crystal structures and phase analysis, but it has been used mostly with ideal powder sample, not with textured polycrystals, because effects of strong and complex textures. Most technological materials are fabricated by using thermo-mechanical forming processes, which inevitably produce strong and complex preferential orientations of the crystallites. Consequently, the diffraction patterns of a given technological material are not unique but vary considerably with the measuring direction, with intensity variations as large as factors of hundreds, depending on the degree of texture. The texture effect on the diffraction pattern of a certain sample direction is directly proportional to the pole density of the corresponding inverse pole figure, which can be obtained from the three-dimensional orientation distribution function (ODF) of the material. The ODFs of materials with high crystal symmetry, such as cubic, hexagonal, tetragonal, and orthorhombic, can be determined quite precisely, using modern texture analysis techniques (for example, Bungel, Wenk, and Kallend et al.). The pole density distributions of the inverse pole figures can be used in the diffraction profile calculation of a highly textured sample.

scholarly journals Resolution of Superimposed Diffraction Peaks in Texture Analysis of a YBa2Cu3O7 Polycrystal

1991 ◽  
Vol 13 (2-3) ◽  
pp. 189-197 ◽  
Author(s):  
John S. Kallend ◽  
R. B. Schwarz ◽  
A. D. Rollett
Keyword(s):  
Crystal Structure ◽  
Texture Analysis ◽  
Crystal Orientation ◽  
Orientation Distribution ◽  
Powder Sample ◽  
Oxide Superconductors ◽  
Pole Figures ◽  
Diffraction Peaks ◽  
Near Degeneracy ◽  
Magnetically Aligned

Texture measurements in polycrystalline 123 oxide superconductors are complicated by the superposition of Bragg reflections in the pole figures due to the near degeneracy of the crystal structure. A method is described, based on an extension of the WIMV algorithm, for resolving these superpositions and determining the crystal orientation distribution (OD). The method is exemplified by OD analysis of a magnetically aligned, strongly textured powder sample of YBa2Cu3O7.

Texture of extruded uranium alloy by neutron diffraction

1985 ◽  
Vol 18 (6) ◽  
pp. 413-418 ◽  
Author(s):  
C. S. Choi ◽  
H. J. Prask
Keyword(s):  
Neutron Diffraction ◽  
Orientation Distribution ◽  
Fiber Texture ◽  
Pole Density ◽  
Ti Alloy ◽  
Composite Alloy ◽  
Density Distributions ◽  
Uranium Alloy ◽  
Pole Figures ◽  
Combination Function

The pole-density distributions of two hydrostatically extruded samples, a U–0.75 wt.% Ti alloy and a U–0.75 wt % Ti/W composite alloy, were studied by neutron diffraction methods. Analysis of U 112, U 131 and U 111 pole figures revealed that the α-U phases of both samples possess a [010]/[340] duplex fiber texture with a probability ratio of approximately 2.8:1 in favor of the [010] direction. The W phase of the composite sample had a [110] fiber texture. The orientation distribution profiles of the fiber axes obtained from the rocking curves (as a function of the tilt angle) were represented best by a Gaussian–Lorentzian combination function. The full widths at half maximum of the distributions were approximately 21, 11, and 5° for the U [010], U [340] and W [110] fiber axes, respectively.

scholarly journals A New Approach to Describing Three-Dimensional Orientation Distribution Functions in Textured Materials–Part I: Formation of Pole Density Distribution on Model Pole Figures

1993 ◽  
Vol 22 (2) ◽  
pp. 73-85 ◽  
Author(s):  
V. N. Dnieprenko ◽  
S. V. Divinskii
Keyword(s):  
Coordinate System ◽  
Texture Component ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Pole Density ◽  
Texture Axis ◽  
Pole Figures ◽  
Orientation Distribution Functions ◽  
Textured Materials

New method for simulation of orientation distribution functions of textured materials has been proposed. The approach is based on the concept to describe any texture class by a superposition of anisotropic partial fibre components. The texture maximum spread is described in a “local” coordinate system connected with the texture component axis. A set of Eulerian angles γ1,γ2,γ3 are introduced with this aim. To specify crystallite orientations with respect to the sample coordinate system two additional sets of Eulerian angles are introduced besides γ1,γ2,γ3. One of them, (Ψ0,θ0,ϕ0), defines the direction of the texture axis of a component with respect to the directions of the cub. The other set, (Ψ1,θ1,ϕ1), is determined by the orientation of the texture component and its texture axis in the sample coordinate system. Analytical expressions approximating real spreads of crystallites in three-dimensional orientation space have been found and their corresponding model pole figures have been derived. The proposed approach to the texture spread description permits to simulate a broad spectrum of real textures from single crystals to isotropic polycrystals with a high enough degree of correspondence.

The iterative series-expansion method for quantitative texture analysis. II. Applications

1992 ◽  
Vol 25 (2) ◽  
pp. 259-267 ◽  
Author(s):  
M. Dahms
Keyword(s):  
Distribution Function ◽  
Series Expansion ◽  
Expansion Method ◽  
Orientation Distribution ◽  
Polycrystalline Materials ◽  
Pole Density ◽  
General Outline ◽  
Positivity Condition ◽  
Pole Figures ◽  
Series Expansion Method

The orientation distribution function (ODF) of the crystallites of polycrystalline materials can be calculated from experimentally measured pole density functions (pole figures). This procedure, called pole-figure inversion, can be achieved by the series-expansion method (harmonic method). As a consequence of the (hkl)-({\bar h}{\bar k}{\bar l}) superposition, the solution is mathematically not unique. There is a range of possible solutions (the kernel) that is only limited by the positivity condition of the distribution function. The complete distribution function f(g) can be split into two parts, \tilde {f}(g) and \tildes {f}(q), expressed by even- and odd-order terms of the series expansions. For the calculation of the even part \tilde {f}(g), the positivity condition for all pole figures contributes essentially to an `economic' calculation of this part, whereas, for the odd part, the positivity condition of the ODF is the essential basis. Both of these positivity conditions can be easily incorporated in the series-expansion method by using several iterative cycles. This method proves to be particularly versatile since it makes use of the orthogonality and positivity at the same time. In the previous paper in this series [Dahms & Bunge (1989) J. Appl. Cryst. 22, 439–447] a general outline of the method was given. This, the second part, gives details of the system of programs used as well as typical examples showing the versatility of the method.

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.

Quantitative texture analysis of a hydroxyapatite coatings plasma-sprayed on titanium substrates at different temperatures

2020 ◽  
Vol 86 (12) ◽  
pp. 23-31
Author(s):  
V. F. Shamray ◽  
V. N. Serebryany ◽  
A. S. Kolyanova ◽  
V. I. Kalita ◽  
V. S. Komlev ◽  
...  
Keyword(s):  
Texture Analysis ◽  
Room Temperature ◽  
Volume Fraction ◽  
Rietveld Method ◽  
Orientation Distribution ◽  
Hydroxyapatite Coatings ◽  
Spraying Parameters ◽  
Pole Figures ◽  
Different Temperatures ◽  
Plasma Sprayed

Artificial hydroxyapatite exhibits an excellent biocompatibility with tissues of human body. However, poor mechanical properties of hydroxyapatites and low reliability in wet environments restrict their use. These limitations can be overcome by applying the hydroxyapatite as a coating onto metallic implants. X-ray diffraction analysis (restoration of orientation distribution function from pole figures and the Rietveld method) and scanning electron microscopy have been used to study thick (~330 μm) plasma-sprayed hydroxyapatite coatings. The coatings were deposited onto Ti – 2Al – 1Mn alloy substrates, one of which was held at room temperature (20°C) whereas the other substrate was preheated to 550°C. The texture of the coating deposited on substrate held at room temperature is characterized by the (001)[510] orientation, the volume fraction of which is 0.08, while the coating deposited on preheated substrate has the (001)[410] orientation, the volume fraction of which is 0.10. Results of texture analysis are qualitatively supported by the Rietveld refinement data. The problem of the formation of basal texture in plasma-sprayed hydroxyapatite coatings is discussed in terms of quantitative texture analysis in relation to the differences in the substrate temperature and spraying parameters. It was concluded that the quantitative texture analysis is of importance for deeper understanding the effect of spraying parameters on the formation of hydroxyapatite coatings.

Quantitative neutron diffraction texture measurement applied to α-phase alumina and Ti3AlC2

2011 ◽  
Vol 44 (5) ◽  
pp. 1062-1070 ◽  
Author(s):  
JianFeng Zhang ◽  
Erich H. Kisi ◽  
Oliver Kirstein
Keyword(s):  
Single Crystal ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Pole Density ◽  
Texture Measurement ◽  
Area Detector ◽  
Neutron Diffractometer ◽  
Α Phase ◽  
Pole Figures ◽  
Crystal Properties

Orientation distribution functions, essential for making a quantitative connection between single-crystal and polycrystal properties, have been determined for extruded α-phase alumina, hot-pressed Ti3AlC2and cold isostatically pressed Ti3AlC2using experimental pole figures recorded on the fixed-wavelength neutron diffractometer KOWARI. Some practical improvements to the calculation of the pole-figure density from the raw area-detector data, and for constructing pole figures on ann×n° hemispherical grid, are presented. The textures give some insight into particle flow during manufacture. Directly measured material textures were compared with one-dimensional pole density functions, such as the March and Rietveld functions commonly used for the correction of preferred orientation in Rietveld refinements, as a means of assessing the utility of the latter for the computation of diffraction elastic constants and other polycrystal properties from a given set of single-crystal properties.

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