Neutron Scattering

measurements can be performed in transmission geometiy on spherical, cylindrical or even
inegular shaped specimens and complete pole figures are obtained without applying any
intensity corrections . Neutron diffraction measurements can be carried out at a rauch higher
degree ofaccuracy than other techniques to calculate the orientation distribution function.
5.0 Pole Figures and ODF
An experimental pole figure Pal yields the orientation distribution of the crystallites with
respect to one particular crystallographic direction [hkl] which represents the actual scattering
vector s ofthe diffraction experiment. There is no information, however, on the orientation of
Fig. 19 .18 : Scattering experimment with scattering vector c = [hkl] perpendicular to scattering
plane (hkl) (hatched) yields no information on the orientation ofany [uvw] inside theplane
the crystallites perpendicular to the scattering vector, i .e . inside the plane (hkl) (compare Fig .
18 .18) . As the pole figure represents a two-dimensional orientation distribution, it is thus an
integral of the three-dimensional orientation distribution function f(g) taken over a rotation
about scattering vector s = [hkl] :
Phki(y) = 1 f f(g)dy with y = ta, R} (5).
2;r
Equation (5) may bc called the fundamental relation of texture analysis. It is evident that the
ODF f(g) is generally not completely determined by one pole figure. One needs the additional
information of other crystallographic directions, i.e . other pole figures . The factor 1/2ir in
equation (5) results from a normalization wich respect to the definition of a statistical
orientation distribution :
f(g)eatistical = 1, ff(g)dy = 1, Phkl(a> R)statistical = 1 (6) .
Pole densities are expressed in multiples of the random density (m.r .d.) .