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 Xray diffraction, in particular
Today’s objective
• To know about 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
RD
2
4
8
TD
Stereogram
Pole figure
Pole figure
• Grains those
are oriented
along (001) in
the predefined
reference will
show intensity
around the
(100) poles
ND
RD
100
100
010
010
TD
001
RD
TD
ND
001
(100) Pole Figure
Schematic representation of the orientation
distribution in (100) pole figure
• Pole figures essentially represent the orientation
spread around the predefined pole or reference
Orientations representation in a pole figure: Cubic
Case
• (001) Standard stereographic
projection of a cubic crystal
• (001) Pole lies at the
center of stereogram
100
110
110
111
010
011
111
101
111
010
001 011
101
111
110
110
100
Orientations representation in a pole figure: A
Cubic Case
100
110
110
111
If only {111} orientations are
010
present in the sample
011
111
101
001
101
111
010
011
111
110
110
100
All the orientations appear around
{111} in the stereogram
Corresponding Orientations100representation in a pole figure
110
110
111
010
011
111
101
111
010
001 011
101
111
110
110
100
100
100
111
010
011
111
101
111
111
010
001 011
101
100
010
011
111
111
110
110
110
110
110
110
101
111
010
001 011
101
111
110
110
100
(100)[110] Orientation representation in sample frame of
reference
ND
[100]
ZZ
Rolling direction
ZY
XX
RD
TD
(100) Pole figure
RD
TD
(111) Pole figure
[110] RD
RD
TD
(110) Pole figure
Crystal orientation represented in the RD, TD and ND of rolling coordinate
Representation of orientation in polycrystalline material
Pole figures
corresponding to
above crystal
configurations
RD
RD
100
1000
4000
TD
TD
(111) Or any other Pole figure
(111) Pole figure
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
RD
100
Calculated PF 111
• 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)
010
111
• 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.
111
111
TD
010
001
• The texture component will be
(hkl)[uvw]. (e.g. the texture component is
(001)[100])
111
100
0.25
0.50
0.75
1.00
1.50
2.00
2.50
3.00
The pole density locations
coincides with (111) poles of
the (001) stereogram
3.50
4.00
4.50
5.00
8.00
• 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]
Representation of orientations using
Inverse pole figure (IPF)
•
•
•
•
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.
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
Questions
1.
2.
What is a pole figure?
Identify the following figures. What are they called? Describe the texture
represented by each of them:
RD
100
1000
4000
TD
001
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