1. Today’s objective
We have learnt
• How do the crystallites arrange in a polycrystalline
material
• How to represent polycrystal information in
stereographic projection
• Macro- and micro- texture
• The principles of macro or bulk texture
measurements by X-ray diffraction
• To know the texture measurement procedure
by X-ray diffraction
2. Second step:Fix the Bragg angle for the peak for which
the pole figure is to be measured.
-Pole figure is measured with 5-axis
goniometer – Schulz Reflection Method
-X-ray beam must not be transmitted through
the specimen thickness>~0.2 mm
First step: Record the X-ray diffraction pattern (normal
Bragg scan) to identify the peak position
-Deviation of relative intensities in a θ/2θ scan
from powder file indicate the presence of
texture but it is not possible to identify the
texture component by normal Bragg scan
Measurement strategy:
3. • 2 axes used to set Bragg angle. One has to choose a
specific crystallographic plane with /2θ axes, the plane
for which the pole figure has be determined.
• Third axis tilts specimen plane w.r.t. the focusing plane.
This is actually the rotation about an axis perpendicular
to the sheet surface (angle )
• Fourth axis spins the specimen about its normal. This
rotation is about an orthogonal axis through angle .
• Fifth axis oscillates the Specimen under the beam. This
is a simple translation – to and fro – it improves the
statistical averaging of the texture measurement by
increasing the number of grains that are sampled
What are the 5 axes of the goniometer?
4. • Diffractometer is set in Bragg-Brentano geometry
This geometry also
implies that the
incident beam is
divergent and
diffracted beam is
convergent
• The combination of angles by which the sample rotates, leads to
irradiation of almost all the crystallites.
In Bragg-Brentano Geometry, Eulerian cradle is set in such a way
that the circle coincides with the bisector of the angle between
incident and diffracted beam, and any direction on the pole figure
can be brought parallel to this direction by the two rotations 90-
and corresponding to the pole figure coordinates and .
5. 1. Source;2. Divergence slit; 3. Narrow horizontal slit; 4. Specimen; 5. Major
circle of the goniometer; 6. Receiving slit; 7. Counter.
One of the oldest models of X-ray texture goniometer is shown here.
The figure clearly depicts all the components of the diffractometer
based on Schulz reflection geometry.
Figure adapted from:
“Introduction to
texture”
by M. Hatherly and
W.B. Hutchinson
6. A modern texture goniometer at Indian Institute of Science,
Bangalore
Mark the difference!!
7. • The already set Bragg peak (for example, 111 or 200 for face centred cubic
materials) is recorded for all the combinations of angles
• Next, the specimen is arranged with RD pointing vertically. This
leads to sheet normal bisect angle between incident and diffracted
beams, ND coincides with diffracting vector K.
In this case, measured intensity comes from the (hkl) planes ||
sheet plane
• The specimen is rotated by = 90o (along Euler Cradle). Tphis leads
to RD || K . In this situation, the measured intensity corresponds
to RD.
This type of rotation gives radial scan of the pole figure.
• Next, the specimen is rotated by = 90o (about axis perpendicular
to specimen surface). This situation corresponds to TD || K.
The diffracted intesity is sampled around the periphery of
the pole figure.
8. • A fast rotation through + a slow rotation through is equal to the
diffracted intensity along the spiral trace
Total intensity to the counter
• This way for each combination of and , the same Bragg peak (hkl) is
recorded. The intensity variation for different angles gives an account of
texture present in the material, as shown below.
• The intensity is
normalised by recording
a diffraction pattern
from a powder (random)
sample.
• The intensity ratio is
plotted on a polar graph
to result in a pole figure.
9. Practical Aspects
• Typical to measure three PFs for the 3 lowest values of
Miller indices.
• Why?
– A single PF does not uniquely determine orientation(s),
texture components because only the plane normal is
measured, but not directions in the plane (2 out of 3
parameters).
– Multiple PFs required for calculation of Orientation
Distribution.
10. Questions
1. If you are given two identical looking samples of a metallic material, how will
you decide whether this is a single crystal or a polycrystal? If you are given a
single crystal and unable to get a particular diffraction pattern, what will you do
to locate the same.
2. In the measurement complete (111) pole figure, if the data is recorded at 5
intervals in both and angles, how many times the (111) peaks are recorded?
3. Describe the role of all the axes in a five axis goniometer as used in Schulz
reflection geometry.
4. Can you measure the (111) pole figure for a steel samples? If yes, which peak will
be fixed for measurement of texture?
5. 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
