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

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

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

100

010 001

100

010

110 110

110 110

011

101

101

011

111

111 111

111

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

010 001

100

010

110 110

110 110

011

101

101

011

111

111 111

111

If only {111} orientations are present in the sample

All the orientations appear around {111} in the stereogram

Orientations representation in a pole figure: A Cubic Case

100

010 001

100

010

110 110

110 110

011

101

101

011

111

111 111

111

100

010 001

100

010

110 110

110 110

011

101

101

011

111

111 111

111

100

010 001

100

010

110 110

110 110

011

101

101

011

111

111 111

111

Corresponding Orientations representation in a pole figure

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

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

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

• 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]

• 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)

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. 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