ON THE SOLVABILITY OF MAXIMUM ENTROPY MOMENT PROBLEMS IN TEXTURE ANALYSIS

2012 ◽  
Vol 22 (12) ◽  
pp. 1250043 ◽  
Author(s):  
MICHAEL JUNK ◽  
JOHANNES BUDDAY ◽  
THOMAS BÖHLKE
Keyword(s):  
Distribution Function ◽  
Maximum Entropy ◽  
Orientation Distribution ◽  
Moment Problems ◽  
Topological Groups ◽  
Crystallite Orientation ◽  
Locally Compact ◽  
Texture Coefficients ◽  
Moment Functions ◽  
The Moment

The estimation of the crystallite orientation distribution function based on the leading texture coefficients can be rephrased as a maximum entropy moment problem. In this paper, we prove the solvability of these moment problems under quite general assumptions on the moment functions which carries over to general locally compact and σ-compact Hausdorff topological groups.

A software for diffraction stress factor calculations for textured materials

2012 ◽  
Vol 27 (2) ◽  
pp. 114-116 ◽  
Author(s):  
Thomas Gnäupel-Herold
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Elastic Constants ◽  
Orientation Distribution Function ◽  
Lattice Strain ◽  
Orientation Distribution ◽  
Crystallite Orientation ◽  
Interaction Models ◽  
Grain Interaction ◽  
Textured Materials

A software for the calculation of diffraction elastic constants (DEC) for materials both with and without preferred orientation was developed. All grain-interaction models that can use the crystallite orientation distribution function (ODF) are incorporated, including Kröner, Hill, inverse Kröner, and Reuss. The functions of the software include: reading the ODF in common textual formats, pole figure calculation, calculation of DEC for different (hkl,φ,ψ), calculation of anisotropic bulk constants from the ODF, calculation of macro-stress from lattice strain and vice versa, as well as mixture ratios of (hkl) of overlapped reflections in textured materials.

scholarly journals A Test of the Refinement Procedure for Determining the Crystallite Orientation Distribution: Polyethylene Terephthalate

Texture ◽  
1972 ◽  
Vol 1 (1) ◽  
pp. 9-16 ◽  
Author(s):  
W. R. Krigbaum ◽  
Anna Marie Harkins Vasek
Keyword(s):  
Distribution Function ◽  
Polyethylene Terephthalate ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Fiber Texture ◽  
Fiber Axis ◽  
Crystallite Orientation ◽  
Plane Normal ◽  
Pole Figures ◽  
Refinement Procedure

A test of the refinement procedure for improving the crystallite orientation distribution function is presented for a fiber texture sample of polyethylene terephthalate. This is a particularly difficult example because the triclinic unit cell offers no simplification due to symmetry, and the pole figures are sharply peaked. The analysis employed 17 observed pole figures and an additional 29 unobserved pole figures reconstructed from the crystallite orientation distribution function. After three cycles of refinement, in which the maximum value of the coefficient was increased from 6 to 16, the standard deviations, σq and σw, of the plane-normal and crystallite orientation distributions were reduced by about a factor of 3. The refined crystallite orientation distribution function indicates that the c-axis tends to align along the fiber axis for this polyethylene terephthalate sample.

scholarly journals Coordinate Free Tensorial Representation of the Orientation Distribution Function With Harmonic Polynomials

1993 ◽  
Vol 21 (4) ◽  
pp. 233-250 ◽  
Author(s):  
David D. Sam ◽  
E. Turan Onat ◽  
Pavel I. Etingof ◽  
Brent L. Adams
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Measurement Data ◽  
Orientation Distribution ◽  
Harmonic Polynomials ◽  
Crystallite Orientation ◽  
Orientation Measurement ◽  
Three Dimensional Space

The crystallite orientation distribution function (CODF) is reviewed in terms of classical spherical function representation and more recent coordinate free tensorial representation (CFTR). A CFTR is a Fourier expansion wherein the coefficients are tensors in the three-dimensional space. The equivalence between homogeneous harmonic polynomials of degree k and symmetric and traceless tensors of rank k allows a realization of these tensors by the method of harmonic polynomials. Such a method provides for the rapid assembly of a tensorial representation from microstructural orientation measurement data. The coefficients are determined to twenty-first order and expanded in the form of a crystallite orientation distribution function, and compared with previous calculations.

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