1. Measuring Strain Using X-Ray Diffraction
By: James Belasco

2. What is Strain? When a force is applied materials deform in two ways
It will deform and then revert to its original shape (reversible)
Change its shape permanently (irreversible)

3. The Structure of Materials
At the local level, solids are composed o crystalline lattices
Atoms in these crystal structures are arranged in different crystal shapes depending on the material

4. Lattice Under Stress In reversible strain the bonds act like springs
Strain “stretches” the bonds in the lattice without breaking them

5. Who’s More Flexible?

6. How does a polycrystalline material distribute strain?1 2 1 2 + = ? or

7. Polycrystalline Materials
Nanocrystalline structures are made of a large number of randomly oriented crystals
How does the bulk property of the material relate to the individual crystallites?

8. Figure Compliments of Matt Bibee, SULI 2006
The Value of X-Ray Diffraction
Normal Space
Diffraction Space d0 d0 d0
d2*
d1*
Strained
Sample
Strain
d2*
d1*
Figure Compliments of Matt Bibee, SULI 2006

9. Strain Equations x y z x
a = y z

10. The Apparatus
Detector
Sample
Beam

11. Straining Iron
[110]
[200]
Sets of crystals oriented in a particular direction from their own ring
Iron produces three rings
[211]

12. To Have Cake
Diffraction images are transformed to a different coordinate system or “caked”
One Ring χ Q χ
Transformation Q

13. Straining Iron
Strain Direction
The slopes of the lines give us the elastic modulus in a crystallographic direction
[200]: 152.3
Error: 6.05
[211]: 207.3
Error: 9.2
[110]: 177.5
Error: 10.9

14. The polycrystalline sample exhibits properties of the single crystal
How far can you stretch?
Single Crystal Values
110  210 GPa
200  125 GPa
211  210 GPa
Measured Values
110  177 ± 11 GPa
200  152 ± 6 GPa
211  207 ± 9 GPa ~ ~
The polycrystalline sample exhibits properties of the single crystal

15. So what Really Happens? 1 2 + = ?

16. Acknowledgements Department of Energy, SLAC, and SSRL Apurva Mehta
David Bronfenbrenner