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.

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.

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.

Textures Applied to Mechanical Processing Technology Assessment in Ancient Bronze

2005 ◽  
Vol 495-497 ◽  
pp. 719-724
Author(s):  
R.E. Bolmaro ◽  
B. Molinas ◽  
E. Sentimenti ◽  
A.L. Fourty
Keyword(s):  
Orientation Distribution ◽  
Distribution Functions ◽  
Archaeological Sites ◽  
Mechanical Processing ◽  
Post Processing ◽  
X Ray Diffraction ◽  
Mechanical Process ◽  
X Ray ◽  
Pole Figures ◽  
Microscopic Inspection

Some ancient metallic art craft, utensils, silverware and weapons are externally undistinguishable from modern ones. Not only the general aspect and shape but also some uses have not changed through the ages. Moreover, when just some small pieces can be recovered from archaeological sites, the samples can not easily be ascribed to any known use and consequently identified. It is clear that mechanical processing has changed along history but frequently only a "microscopic" inspection can distinguish among different techniques. Some bronze samples have been collected from the Quarto d’Altino (Veneto) archaeological area in Italy (paleovenetian culture) and some model samples have been prepared by a modern artisan. The sample textures have been measured by X-ray Diffraction techniques. (111), (200) and (220) pole figures were used to calculate Orientation Distribution Functions and further recalculate pole figures and inverse pole figures. The results were compared with modern forging technology results. Textures are able to discern between hammering ancient techniques for sheet production and modern industrial rolling procedures. However, as it is demonstrated in the present work, forgery becomes difficult to detect if the goldsmith, properly warned, proceeds to erase the texture history with some hammering post-processing. The results of this contribution can offer to the archaeologists the opportunity to take into consideration the texture techniques in order to discuss the origin (culture) of the pieces and the characteristic mechanical process developed by the ancient artisan. Texture can also help the experts when discussing the originality of a certain piece keeping however in mind the cautions indicated in this publication.

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 {111} Orientation Induced Anisotropy of Shape Memory Effect in NiTiNb Pipe Joints

Metals ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 776
Author(s):  
Mingyan Sun ◽  
Qichao Fan ◽  
Yingying Wang ◽  
Qin Yang ◽  
Jie Chen ◽  
...  
Keyword(s):  
Shape Memory ◽  
Shape Memory Effect ◽  
Memory Effect ◽  
Electron Backscatter Diffraction ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Induced Anisotropy ◽  
Texture Intensity ◽  
Pole Figures ◽  
Pipe Joints

This work aims to clarify the influence of texture type and intensity on the shape memory effect (SME) in NiTiNb shape memory alloy (SMA) pipe joints, especially revealing the causes for the anisotropy of SME via texture changes. Three NiTiNb rods with different intensities of the {111}<110> texture were fabricated, and their microstructures, crystalline orientation distribution functions and inverse pole figures were obtained by X-ray diffraction and electron backscatter diffraction measurements. Simultaneously, the SME was characterized by inner-diameter recoverability of the corresponding pipe joints. For a given intensity of the {111}<110> texture, the SME of the NiTiNb pipe joints strongly depended on the expansion direction due to {111}<110> orientation-induced anisotropy of SME. In addition, both the SME and anisotropy of NiTiNb pipe joints increased with the increased intensity of the {111}<110> texture. Therefore, a suitable expansion direction and strong texture intensity should be considered for high SME in NiTiNb pipe joints.

Texture Evolution in Rolled Mg-13wt%Li-X Alloy

2007 ◽  
Vol 546-549 ◽  
pp. 347-350 ◽  
Author(s):  
Li Li ◽  
Tie Tao Zhou ◽  
Huan Xi Li ◽  
Chang Qi Chen ◽  
Qiu Lin Wu ◽  
...  
Keyword(s):  
Texture Evolution ◽  
Orientation Distribution ◽  
Fiber Texture ◽  
Distribution Functions ◽  
Thickness Reduction ◽  
Rolled Sheet ◽  
Pole Figures ◽  
Cold Rolled ◽  
Orientation Distribution Functions

Texture evolution in Mg-13wt%Li-X alloy cold-rolled from 1.35 mm to 0.34 mm thickness was investigated, by obtaining pole figures and orientation distribution functions (ODFs). Punching tests were conducted to reveal the effect of texture nature on formability. It was found that: (1) the textures of the as-received sheet are characterized by α fiber texture, a γ fiber texture and a cubic texture in both cold-rolled and annealed conditions; (2) with thickness reduction though rolling, the intensity of the γ fiber texture continuously increases and finally the γ fiber texture connects into {111} tube texture, the texture of <11 0> orientation flows towards {223}<11 0> along α fiber, the cubic texture of {001}<100> turns into {035}<100>, while some grains concentrate at {011}<41 1> orientation; (3) good punching behavior of the cold-rolled sheet corresponds to the appearance of a well-developed γ fiber texture.

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 Cyclic Textures in Aluminium Wires

Texture ◽  
1972 ◽  
Vol 1 (1) ◽  
pp. 31-49 ◽  
Author(s):  
U. Schläfer ◽  
H. J. Bunge
Keyword(s):  
Neutron Diffraction ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Axially Symmetric ◽  
Fibre Texture ◽  
Pole Figures ◽  
Processing Variables ◽  
Orientation Distribution Functions ◽  
The Wire

Three-dimensional orientation distribution functions were calculated from neutron diffraction pole figures of unwound cylinders taken at different distances from the centre of cold drawn Al-wires. Their features change from the axially symmetric type at the very centre of the wire towards a texture near to the rolling type at the surface. Relations between the three-dimensional function and ordinary fibre texture pole figures were used to study the dependence of the textures on certain processing variables for cold drawn as well as recrystallized wires.

Evaluation of Developed Texture during Cold-Rolling Deformation of Ti-Nb-Ta-Zr Biocompatible Alloy

2013 ◽  
Vol 592-593 ◽  
pp. 366-369
Author(s):  
Vasile Danut Cojocaru ◽  
Isabelle Thibon ◽  
Doina Raducanu ◽  
Ion Cinca ◽  
Thierry Gloriant ◽  
...  
Keyword(s):  
Corrosion Resistance ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Mechanical Processing ◽  
Specific Strength ◽  
High Specific Strength ◽  
Ti Alloys ◽  
Pole Figures ◽  
Cold Rolled ◽  
Rolling Deformation

During the last decade the titanium alloys were extensively used in a variety of applications due to their good mechanical properties, high biocompatibility and corrosion resistance. β-type Ti alloys composed of Nb, Ta and Zr elements have received much attention, because they feature high specific strength, bio-corrosion resistance, no allergic problems and biocompatibility. A Ti-29Nb-9Ta-10Zr (wt.%) alloy was subjected to thermo-mechanical processing and testing. Two states were investigated: recrystallized and 80% cold-rolled. Data concerning phase structure and developed texture, expressed by Inverse Pole Figures (IPFs) and Orientation Distribution Functions (ODFs), was obtained and analyzed.

scholarly journals Pole Figure Inversion Using Finite Elements Over Rodrigues Space

2002 ◽  
Vol 35 (2) ◽  
pp. 113-144 ◽  
Author(s):  
Nathan R. Barton ◽  
Donald E. Boyce ◽  
Paul R. Dawson
Keyword(s):  
Finite Elements ◽  
Pole Figure ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Pole Figures ◽  
Orientation Distribution Functions ◽  
Pole Figure Data ◽  
Straight Lines ◽  
And Inversion

Using finite elements over Rodrigues space, methods are developed for the formation and inversion of pole figures. The methods take advantage of the properties of Rodrigues space, particularly the fact that geodesics corresponding to pole figure projection paths are straight lines. Both discrete and continuous pole figure data may be inverted to obtain orientation distribution functions (ODFs) in Rodrigues space, and we include sample applications for both types of data.

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