Neutron Scattering

Further important structure related anisotropic properties of speeial technological relevance
are e .g. meehanical hardness, elasticity, thermal expansion, electrical conductivity,
magnetic induction or corrosive resistance . The single- ciystalline anisotropy may be
described by a direction dependent three-dimensional property-specific surface as shown in
Fig . 18 .3 for the linear (elastic) Young modulus of iron with its cubic crystal structure. The
directional dependence of a property E is a function of well-defined crystallographic
directions h :
E (g) = f(h) = f(hkl) (1)
With repeet to any direction g in the three-dimensional spaee, the directional dependence of E
can be expressed mathematically as a series of spherical harmonics T with parameters ~,, ~I
and v and its coefficients e aecording to
E(g) _ eâ vTz v (g) (2)
ti u v
The vast majority of solid crystalline matter, however, does not exist in form of single
ciystals but is of polycrystalline nature. The material is buht up macroscopically by a multitude
of crystallites or grains which can bc arranged in many different orientations (compare
Fig . 18 .4) . In case of a statistical orientation distribution of the crystallites the structurespecific
orientation dependences ofthe properties disappear macroscopically and the material
becomes quasi-isotropie .
Fig . 18.4 :
Schematic representation ofrandom (left) andpreferred orientations (right) of
graphit-type crystallites (compare Fig. 18 .2)
This loss of anisotropy can bc compensated for by the existence or the generation of texture .
Texture is defmed by the patial orientation distribution of crystallites in pol clystalline
matter . In case of a statistical orientation distribution one speaks of a random texture . The
above defmition of texture which is widely accepted and used today disregards any effects
due to différent shapes or sizes ofthé ciystallites . A (non-random) texture performs a transfer
of structure relevant microscopie single- crystalline anisotropies to thé polycrystalline bulk
18- 3