Neutron Scattering

material . Texture is an important parameter in view ofthe properties of condensed crystallne
matter, besides ofother material parameters as structure, phase composition, grain boundaries,
or strain [3] . The formation and changes of texture are driven or controlled by outer
influences, either already during cystallization by e.g . the existence of non-hydrostatic
conditions during crystal growth or after crystallization by natural deformation due to tectonic
events wich regard to geological material or,
wich regard to manufactured materials, by
artificial deformation ofproducts by mechanical treatments like rolling or casting.
The mean value of a property E of a texturized polyciystal is expressed, according to
equation (2), by an integration of over all crystallite
orientation distribution function f(g) :
orientations wich the aid of a so-called
E = fE(g)f(g)dg
1
J U+1
eI'C ~, ' (3).
Thus, É is expressed mathematically by a folding of structural coefficients e and texture
coefficients C . The full mathematical decription of this so-called harmonic series expansion
method has been developed by H .J . Bunge [4] . The actual goal of a texture analysis is the
experimental determination of the orientation distribution fonction by diffraction measurements
.
3 . Orientation Distribution Function
The texture of a polyciystalline sample is expressed by its orientation distribution function
f(g), generally abbreviated as ODF, according to the decmition
f(g) - (4).
V dg
Thus, the ODF is defined by the volume fraction of crystallites that have the orientation g
within a certain infmitesimal orientation element dg . The orientation g can bc described by a
transformation matrix [gilk] representing the orientation of the individual crystallites (coordinate
system KK) with reference to a common sample coordinate system Kp (Fig . 18 .5) .
Fig . 18 .5 :
Schematic representation ofa texturizedsample in a coordinate system Kp ivith
individual orientation of crystallites and their coordinate system KK
18- 4