1. Today’s objective
We have learnt
•How do crystallites arrange in a polycrystalline
material
•How to represent polycrystal information in
stereographic projection
•The diffraction phenomenon, in general, and X-
ray diffraction, in particular
• To know about pole figure
2. 2
4
8
RD
TD
Stereogram Pole figure
Pole figure
• Orientation of crystallites can be represented through
pole figures, which are modified form of stereographic
projection.
Stereogram: A representation of 3D unit cell in 2D plane
Pole figure: Stereogram of polycrystal with sample
frame of reference embedded
3. RD
ND TD
001
100
010
RD
ND
TD
001
100
010
Pole figure
(100) Pole Figure
Schematic representation of the orientation
distribution in (100) pole figure
• Grains those
are oriented
along (001) in
the predefined
reference will
show intensity
around the
(100) poles
• Pole figures essentially represent the orientation
spread around the predefined pole or reference
7. ZZ
XX
ZY
Rolling direction
(100)[110] Orientation representation in sample frame of
reference
(100) Pole figure (111) Pole figure (110) Pole figure
RD
TD
RD
TD
RD
TD
Crystal orientation represented in the RD, TD and ND of rolling co-
ordinate
[100]
[110] RD
ND
8. Representation of orientation in polycrystalline material
100
1000
4000
RD
TD
RD
TD
(111) Pole figure
(111) Or any other Pole figure
Pole figures
corresponding to
above crystal
configurations
9. 100
001 010
100
010
111 111
111
111
8.00
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.75
0.50
0.25
Calculated PF 111
How to read the orientation from the pole figures?
• If the (hkl) pole figure has region of high
intensity at the centre, choose the (hkl)
standard projection
• Coincide the centre of (any) stereogram
with ND position of the (hkl) pole figure (e.g.
the (001) position of the stereogram is
coincided with ND of the (111) pole figure in
the figure)
• Note the pole (uvw) coinciding with RD of
the pole figure. (e.g. (100) pole is coincident
with RD in the pole figure given here.
• The texture component will be
(hkl)[uvw]. (e.g. the texture component is
(001)[100]) The pole density locations
coincides with (111) poles of
the (001) stereogram
RD
TD
10. • If the measured (hkl) pole figure does not have a region
of high intensity at the centre then exclude the (hkl)
projection and take any other projection to index the
pole figure
• Rotate the projection in such a manner that the regions
of high intensity in the measured pole figure coincide
with the (hkl) poles of the projection
• Note the pole (hkl) on the projection coinciding the ND
position of the measured pole figure and the pole (uvw)
coinciding the RD position of the pole figure
• The texture component will be (hkl)[uvw]
11. • When it is necessary to compare the texture of uniaxially
deformed materials, it can be done conveniently by plotting the
crystal axes in a single stereographic triangle.
• In this case, the sample direction is projected in a unit
stereographic triangle – this means the specimen direction is
projected in a crystal frame of reference – contrary to the pol
figure where crystal directions are projected in specimen frame
of reference. Therefore such a construction is known as Inverse
pole figure (IPF).
• Texture of extruded, compressed or wire drawn materials are
represented by IPFs. To present the texture of rolled materials,
one needs to present 3 IPFs, the ones diplaying ND, RD and TD
individually.
• The texture of thin films, where only sample plane normal
direction need to be presented, can also be represented by IPFs.
Representation of orientations using
Inverse pole figure (IPF)
12. Example of inverse pole figure for a drawn wire
Wire drawing axis
• The wire axes coincide with the
[110] direction of the crystals
• The crystal orientations can be
shown in crystal frame of
reference (IPF)
The crystals orientated
along (110), the wire axes,
orientation contours will
form near (110) in the IPF
13. Questions
1. What is a pole figure?
2. Identify the following figures. What are they called? Describe the texture
represented by each of them:
001
100
1000
4000
RD
TD
3. Pole figures represent orientation of
(a) Sample w.r.t crystal
(b)Crystal w.r.t sample
(c) Both (a) & (b)
(d)None of (a) & (b)
4. In a 111 pole figure measurement, only 111 planes of crystals parallel to
sample surface diffract. True/False
