Neutron Scattering

.
.
It is convenient to plot these Eulerian parameters as cal tesian coordinates in a these-dimensional
space which is called the Euler (orientation) space (Fig . 18 .8) . Each ciystal orientation is
represented by a point in the Euler space . The orientations of all crystallites of the ensemble
are then represented by a point distribution in Euler space . A texture obtained as a continuons
distribution fonction can bc represented by equilevel contour lines (Fig . 18 .8) which may bc
completed to equilevel surfaces as it is shown in the example in Fig . 18 .9 . and its planar
sections in Fig . 18 .10 . The Euler space is a distorted space with a metric quite différent from
the usual these-dimensional space . Textures of geological samples are usually visualized by
other, more descriptive representations which are closer to common sense (see chapter 5 .1 .) .
wz
f
~P r
Fig. 18 .8 : Crystallite orientations in Eulerian angles : one crystallie (left), all crystallites
(middle) tivith equilevel contour lines (right)
a
Î Q ,
n
Ao
~ ~ s
a
~~ ~
~ s s
~`
a U1
O
cb (~
Q7 " 6An :7a " a . q
v 5 ._ 0 3r x
'J)
~ _
j0 " Q 45 " s
0517
SO"
j
SS'
p 4
iL Fn~
~1 .
n
,
'
Y
~" K
Fig. 18 .9 : ODF ofa Cu rolling
texture represented by an equilevel
orientation surface in the 3-dim
f0 69 ~D" 95
XF
.
i é p~i w 1 .é . n'? jr i e »Zb rr i ci0e c
-Z
Fig . 18.10 (right) : ODF represent
ation ofFig. 18.9 by a sequence of
sections with constant rp2
iis p 's~ fI" csroa i~,an
C(ai)j o ~ 95°I
18-6