Pole Figures and Their Expansion

The expansion coefficients of the spherical harmonics for a deliberate distribution g q , y/) are easily computed from 

The uniaxial orientation parameter is the most simple way to characterize preferred orientation. It is simple, because it is only a number - in fact, for = n non-trivial expansion coefficient in a multipole expansion of the normalized 

Interpretation of for- For materials that exhibit fiber symmetry (i.e., g (p,yr) = g y )) induced by stmctural entities with fiber symmetry 

As are the other multipole-expansion coefficients, the uniaxial orientation parameter is computed from Eq. (9.6). For materials with fiber symmetry the relation simplifies and 

In practice, either a pole figure has been measured in a texture-goniometer setup, or a 2D SAXS pattern with fiber symmetry has been recorded. In the first case we take the measured intensity g (p) I q ,Shki = const) for the unnormaUzed pole figure. In the second case we can choose a reflection that is smeared on spherical arcs and project in radial direction over the range of the reflection. From the measured or extracted intensities I q ,s = const) we then compute the orientation parameter by numerical integration and normalization 

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