Measuring Strain Using X-Ray Diffraction

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. d0 d0 d2* Strained Sample d1* The Value of X-Ray Diffraction Normal Space Diffraction Space d0 d0 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. One Ring χ Transformation Q To Have Cake • Diffraction images are transformed to a different coordinate system or “caked” χ Q

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

14. 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