 ODF: Orientation Distribution Function 
Definition:  A three dimensional
representation of
the crystallite
orientation density
in a polycrystalline
material. 
Explanation:  In order to describe
the texture
of a
polycrystalline
specimen, the
orientations of the
grains relative to
the sample
coordinate system
need to be
determined. In this
respect,
a distribution
function is
introduced with
three
variables (e.g.
Euler angles), since
at least three
parameters are
necessary to give a
distinct
description. Such
function can either
be determined from
single orientation
measurements or from
pole figure data.
Finally, an ODF
describes the volume
fraction of a
specimen with a
certain orientation
compared to a sample
with randomly
distributed
orientations.
The most common way
to represent an ODF
is the Euler space
defined by three
orthogonal vectors
that correspond to
the Euler angles
φ1,
Φ, φ_{2}
needed to
describe uniquely an
orientation. It is
common practice to
represent ODFs in
form of equal
distance sections
along one of the
axes (usually
φ_{2}).
To display the
intensity
distribution in
these sections,
lines
of equal intensity
are used. 
Picture / Figure / Diagram: 

(a) Three dimensional illustration of the ODF (Euler space). (b) ODF displayed in equal distance (5°) sections along φ_{2}


SFBLink:  The crystallographic texture determines the anisotropy of materials’ properties. ODFs are used to display and analyze the texture evolution of high manganese steels during deformation and heat treatment. Additionally, the measured texture data is used as both input data for and validation of process simulations. 
References:  V. Randle und O. Engler, Introduction to Texture Analysis, CRC Press, 2000 G. Gottstein, Physikalische Grundlagen der Materialkunde, Berlin: Springer, 2007 

