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1. Today’s objective
• To know the limitations of the texture
measurement procedure and ways to
overcome them

2. Defocussing error:
• X-ray beam becomes defocused at large tilt angles
(>~60°).
• The combination of the θ-2θ setting and the tilt of
the specimen face out of the focusing plane
spreads out the beam on the specimen surface.
• Above a certain spread, not all the diffracted
beam enters the detector.
• Therefore, at large tilt angles, the intensity
decreases for purely geometrical reasons.
• This loss of intensity must be compensated for,
using the defocussing correction.
Limitation of Schultz method

4. •Narrow divergence slit– affects total count rate and
statistical significance of
the measurement
•Wide receiving slit- reduces peak to background
ratio
•Larger Bragg angle by changing to a lower wavelength-
severe reduction in
count rate
•How to correct the Defocussing error?

5. • Background count must be subtracted.
Icorr = Imeas (,) – BG ()
• Defocusing correction required to increase the
intensity towards the edge of the PF.
Icorr = Imeas (,) – BG ()
U()
• Random texture (=uniform dispersion of orientations)
means same intensity in all directions.
• measured intensity from random sample decreases
towards edge of PF.
Some other corrections are also desired:
• Absorption
I(t)/I = 1- exp(-2t / Sin  Cos )
• Couting Statistics

6. Pole figure normalization
• In X-ray diffraction experiments, as done during the
determination of pole figures, the intensities are obtained in the
form of counts (or counts per second; cps). The pole density is
measured in terms of multiples of random intensity
• Normalization is the operation that ensures that “random” is
equivalent to an intensity of one.
• This is achieved by integrating the un-normalized intensity,
f(θ,ψ), over the full area of the pole figure, and dividing each
value by the result, taking account of the solid area.
• Thus, the normalized intensity, f( θ,ψ), must satisfy the following
equation, where the 2π accounts for the area of a hemisphere:
Inorm(, ) = (1/N). Icorr (, )

7. (1) What can be directly measured by experiment:
(a) inverse pole figure
(b) orientation distribution function
(c) pole figure
(d) all the above
(2) In the Schulz reflection method, which of the following is correct:
(a) the tilt angle  enables most of the grains to come under diffraction condition
(b) the rotation angle  enables most of the grains to come under diffraction condition
(c) the tilt angle  brings the diffraction vector coincident with the specimen axes
alternately
(d) the rotation angle  brings the diffraction vector coincident with the specimen axes
alternately
(3) Which of these are the limitations of pole figures:
(a) specific (hkl) planes can not be plotted
(b) poles in the final plot for a polycrystalline material are not identified with particular
crystals
(c) information about the crystallite location in a sample is absent
(d) the orientation of a crystal must be described relative to another
Questions