According to SEM analysis, preferential growth along particular crystallographic axis
improved as shown in figure 3.2.
This setup was mounted on a piezo rotator which allows fine tuning of the relative angle between magnetic field and sample crystallographic axis
. This is required due to the strong angular dependence of magnetic properties .
Therefore, when a single crystal of anatase Ti[O.sub.2] is placed in a magnetic field, the crystal is rotated, and the crystallographic axis
of high [chi] is aligned in the direction of the magnetic field.
where ([cos.sup.2] [PHI]) is the average value of the cosine squared of the angle ([PHI]) between the film machine direction and a crystallographic axis
. The orientation factor f is zero for a random orientation, and 1.0 and 0.5 for a perfectly oriented sample parallel and perpendicular to the machine direction, respectively.
Quite accurately this observer noted that the composite stacks of crystals had grown up from matrix along the perpendicular crystallographic axis
a and collectively appeared rotated, or twisted, about that axis, the crystals' long axes c all being tilted regularly either to the right or the left.
If two components are equal to zero, the elongation leads in the direction of only one crystallographic axis
. If one component equals zero, the translation of a particular plane occurs, which results in parallel growth.
For the case of complete parallel alignment of crystallographic axis
with the fiber, [[phi].sub.j] is zero and [f.sub.j] becomes unity.
where j is a crystallographic axis
(j = a, b or c).
where [cos.sup.2][[phi].sub.i,j] was the mean square cosine of j pseudo-orthorhombic crystallographic axis
with respect to i principal stretch direction.
The degree of biaxial orientation of a specified crystallographic axis
was quantified with pole figure data by calculating White and Spruiell (26) biaxial orientation factors:
were used, here [[phi].sub.1j] and [[phi].sub.2j] are the angles between the machine and transverse directions and the j crystallographic axis
. The White-Spruiell biaxial orientation factor data is presented in Table 3 and is plotted in Fig.
where j represents the a, b, c crystallographic axes of the unit cell, [[phi].sub.j] the angle between the j crystallographic axis
and the fiber axis.