TEXTURE ANALYSIS - Two-Dimensional X-Ray Diffraction - page 225

or

ð 2p ð 2

0 G hkl ða

; bÞcos a da db ¼ 2p ð8 : 11Þ

0

The pole density distribution function is a constant for a sample with a random
orientation distribution. Assuming the sample and instrument conditions are the same
except for the pole density distribution, the scaling factor can then be determined
experimentally from the integrated intensity collected with an ideal sample:

P
I Random
hkl

K hkl ða ; bÞ¼ ð8 : 12Þ

ða ; bÞ

where P is the constant pole density for the ideal sample. In practice, it can be given as
an arbitrary scaling factor. The pole density function is then given by

PI hkl ða ; bÞ

P hkl ða ; bÞ¼ ð8 : 13Þ

I Random
hkl

ða ; bÞ

Assuming the experimental conditions for the textured sample and the ideal
sample are exactly the same, taking P¼1, we can obtain the normalized pole density
function by

I hkl ða ; bÞ

G hkl ða ; bÞ¼ ð8 : 14Þ

I Random
hkl

ða ; bÞ

The integrated intensity from the textured sample without any correction can be
plotted according to the stereographic projection as an ''uncorrected'' pole figure. The
same can be done for the sample with a random orientation distribution to form a
''correction'' pole figure that contains only the factors to be corrected. The normalized
pole figure is then obtained by dividing the ''uncorrected'' pole figure by the
''correction'' pole figure. This experimental approach is feasible only if a similar
sample with random orientation is available.

8.4 DATA COLLECTION STRATEGY

8.4.1 Single Scan

Since a one-dimensional pole density mapping is created from each exposure with
two-dimensional X-ray diffraction (XRD 2 ), it is important to lay out a data collection
strategy so as to have the optimum pole figure coverage and less redundancy in data
collection. The pole figure coverage can be simulated from the diffraction 2u angle,
detector swing angle, detector distance, goniometer angles, and scanning steps.
Figure 8.5 shows the scheme generated by GADDS (Bruker AXS) software.
Figure 8.5(a) shows an example of a scheme generated at 2u ¼40 , v¼ 20 ,
c¼35.26 (xg ¼54.74 for a fixed-chi stage), and D¼7 cm with a f scan of 5
steps. Real data collection can use smaller scanning steps, such as 1-2 . The data