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

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:

• 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?

• 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 .

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

A modern texture goniometer at Indian Institute of Science,

Bangalore

Mark the difference!!

• 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.

• 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.

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.

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