Page 59 - Handbook of Properties of Textile and Technical Fibres

40 Handbook of Properties of Textile and Technical Fibres

The profile fitting provides information at different scales: from the identification of
phases, to the index of crystallinity, the ratio of oriented amorphous regions, the degree
of orientation as well as crystallite sizes.

2.3.5.1 Indentification of amorphous regions and index of
crystallinity

The evolution of amorphous peak parameters such as intensity (peak area), peak width,
and position reveals that part of the amorphous domain depends on orientation.
Changes in the position of the amorphous halo, e.g., with a maximum value for equa-
torial scans show that this amorphous phase consists of denser oriented and less dense
isotropic regions.
Xoa, index of oriented amorphous domain and Xia, index of isotropic amorphous
domain can be defined from peak intensity variations I (4) assuming that the isotropic
amorphous component remained independent of the 4 angle. Quantification of the
isotropic amorphous and oriented amorphous regions remain the prime interest of
the WAXD measurements coupled with profile fitting. Finally, the crystallinity index,
Xc, can be defined as the ratio between the intensity diffracted by crystalline regions
and the total intensity diffracted integrated over the 4 directions. The relevance of Xc
can be easily verified by more conventional techniques such as differential scanning
calorimetry (DSC).

2.3.5.2 Orientation degree
To quantify the orientation of the crystalline and/or amorphous regions, an analysis of
the intensity as a function of azimuthal angle has been developed by Hermans et al. for
cellulose fibers (Hermans, 1948). The degree of orientation can be calculated as the
Hermans orientation factor (Alexander, 1969):

1
2
f f ¼ 3 cos f 1 (2.15)
2
with f, the angle between the normals of crystalline planes diffracting and the refer-

p
ence fiber axis f ¼ 4 .
2

2
The mean cos f was determined from the following expression, assuming rota-
tional symmetry about the fiber axis:
R p=2 2
2 0

IðfÞsin f cos f df
cos f ¼ (2.16)
p=2
R
0 IðfÞsin f df
with IðfÞ the diffracted intensity at 4.
Hermans orientation factor being equal to 0 for a random distribution, 1 for a total
alignment of the identities, and 1/2 if all are perpendicular to the fiber axis.