scholarly journals ODF Calculation by Series Expansion from Incompletely Measured Pole Figures Using the Positivity Condition Part I—Cubic Crystal Symmetry

1987 ◽  
Vol 7 (3) ◽  
pp. 171-185 ◽  
Author(s):  
M. Dahms ◽  
H. J. Bunge
Keyword(s):  
Series Expansion ◽  
Iterative Procedure ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Crystal Symmetry ◽  
Cubic Crystal ◽  
Positivity Condition ◽  
Pole Figures ◽  
Orientation Distribution Functions

The calculation of orientation distribution functions (ODF) from incomplete pole figures can be carried out by an iterative procedure taking into account the positivity condition for all pole figures. This method strongly reduces instabilities which may occasionally occur in other methods.

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.

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.

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.

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.

scholarly journals An Evaluation of the Single Orientation Method for Texture Determination in Materials of Moderate Texture Strength

1990 ◽  
Vol 12 (1-3) ◽  
pp. 65-76 ◽  
Author(s):  
Stuart I. Wright ◽  
Brent L. Adams
Keyword(s):  
Pole Figure ◽  
Series Expansion ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Correlation Data ◽  
Pole Figures ◽  
Rolled Aluminum ◽  
Orientation Method ◽  
Pole Figure Data ◽  
Single Orientation

New microscopy technology has made it feasible to consider using single orientation measurements to obtain Orientation Distribution Functions (ODF). Single orientations are preferred over pole figure data in ODF calculations because the odd terms of the series expansion are not directly accessible when pole figures are used. However, the number of single orientation measurements required to calculate a statistically reliable ODF has generally been considered too large to practically obtain. This study found that the location of the major features of the ODF in rolled aluminum sheet were identifiable after only 100 measurements. However, the heights of the peaks and the secondary features required many more measurements to stabilize. Unless the orientation measurements can be automated or orientation correlation data is needed the pole figure method remains a more efficient means of obtaining the data necessary to measure texture.

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.

scholarly journals Anomalous Scattering and Null-Domain Ghost Corrections for Fibre Textures

1989 ◽  
Vol 10 (4) ◽  
pp. 347-360 ◽  
Author(s):  
L. Fuentes
Keyword(s):  
Orientation Distribution ◽  
Distribution Functions ◽  
Anomalous Scattering ◽  
Practical Procedure ◽  
Upper Limit ◽  
Domain Method ◽  
Pole Figures ◽  
Orientation Distribution Functions

The practical applicability of anomalous scattering and null-domain ghost corrections for fibre textures is theoretically evaluated. For a hypothetical asymmetric orientation distribution of quartz-like BPO4 highly absorpting crystals, slightly asymmetric anomalous scattering pole figures are predicted. On the basis of projection relations among orientation distribution functions and inverse pole figures, the special characteristics of the null-domain method for fibre textures are discussed, with the suggestion of a practical procedure to estimate (in favourable cases) an upper limit for ghosts effects.

scholarly journals Non-Random Orientation Distribution Functions With Random Pole Figures

1979 ◽  
Vol 3 (3) ◽  
pp. 169-190 ◽  
Author(s):  
H. J. Bunge ◽  
C. Esling
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Random Orientation ◽  
Numerical Examples ◽  
Pole Figures ◽  
Orientation Distribution Functions

It is shown, theoretically and with numerical examples, that the orientation distribution function may vary between zero and two or even more times random while a corresponding pole figure is completely random.

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