Orientation density function-controlled pole probability density function measurements: automated adaptive control of texture goniometers

A novel control of a texture goniometer, which depends on the texture being measured itself, is suggested. In particular, it is suggested that the obsolete control with constant step sizes in both angles is replaced by an adaptive successive refinement of an initial coarse uniform grid to a locally refined grid, where the progressive refinement corresponds to the pattern of preferred crystallographic orientation. The prerequisites of this automated adaptive control is the fast inversion of pole intensities to orientation probabilities in the course of the measurements, and a mathematical method of inversion that does not require a raster of constant step sizes and applies to sharp textures.

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On the entropy to texture index relationship in quantitative texture analysis

Journal of Applied Crystallography ◽

10.1107/s0021889806055476 ◽

2007 ◽

Vol 40 (2) ◽

pp. 371-375 ◽

Cited By ~ 12

Author(s):

R. Hielscher ◽

H. Schaeben ◽

D. Chateigner

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Density Function ◽

Texture Analysis ◽

Sharp Inequality ◽

Probability Density Functions ◽

Density Functions ◽

Orientation Space ◽

Reconstruction Software ◽

Orientation Density

This communication demonstrates a sharp inequality between the L^{2}-norm and the entropy of probability density functions. This inequality is applied to texture analysis, and the relationship between the entropy and the texture index of an orientation density function is characterized. More precisely, the orientation space is shown to allow for texture index and entropy variations of orientation probability density functions between an upper and a lower bound for the entropy. In this way, it is proved that there is no functional relationship between entropy and texture index of an orientation probability density function as conjectured previously on the basis of practical numerical texture analyses using the widely used pole-to-orientation probability density function reconstruction softwareWIMV, known by the initials of its authors and their ancestors (Williams–Imhof–Matthies–Vinel). Synthetic orientation probability density functions were then synthesized, covering a large domain of variation for texture index and entropy, and used to check the numerical results of the same software package.

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Non-Parametric Comparison of Crystallographic Orientation Distributions

Materials Science Forum ◽

10.4028/www.scientific.net/msf.1016.1258 ◽

2021 ◽

Vol 1016 ◽

pp. 1258-1263

Author(s):

Helmut Schaeben

Keyword(s):

Density Function ◽

Crystallographic Orientation ◽

Orientation Distribution ◽

Sequential Design ◽

One Dimensional ◽

X Ray ◽

Design For X ◽

Orientation Density ◽

Orientation Distributions ◽

Definition Of

Revisiting a spiral design for X-ray pole figure measurementsand a symbolic definition of a cumulative crystallographic orientation distributiona one-dimensional deterministic approximately uniform sequential design is appliedto evaluate and cumulate a given orientation density function resulting in a properly definedcumulative crystallographic orientation distribution.It provides a complementary means to compare distributionsin terms of graphs and the Kolomogorov-Smirnov distance.

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