Chapter 12

1. Chapter 12 Additional Analytical Methods

2. Analytical Methods

3. Analytical Methods

4. Analytical Methods

5. Chapter 13 Mechanical properties and deformation

6. Stress-strain • Mechanical properties – expression of history of crystal • Definitions: • Stress (σ) • Force per surface area • Strain (ε) • Deformation resulting from the stress • Deformation • Elastic • When stress removed strain returns to original value • Plastic or ductile • Active dislocations cause permanent changes in structure and shape, but material stays in tact • Work-hardening • Stress needed for creating increasing strain increase rapidly as multiplying dislocations interfere with each other • Brittle (Failing) • Material has reach its ultimate strength and fractures completely

7. Deformation • Stress applied to crystal • Deforms crystal on crystallographic slip planes (hkl) with displacements along crystallographic slip directions [uvw] • Slip is not instantaneous but propagate along this slip plane, breaking one bond at a time but resulting in a complete displacement of the two parts of the crystal

8. Deformation • Fig 13.2; 13.3; 13.4

9. Dislocation microstructures • Present in most crystals even at ideal growth conditions • Number of dislocations generally increase with deformation • Development and propagation of dislocations are influenced by each other or other obstacles such as inclusions • Loops, diffusion of vacancies (climb)

10. Dislocation microstructures • Loops • Fig. 13.6, 13.7

11. Dislocation microstructures • Diffusion of vacancies (climb) • Fig. 13.8, 13.9

12. Mechanical twinning • A mechanical stress cause part of crystal to flip into new orientation about a plane • New orientation related to old orientation by mirror plane • Thus: Geometric twinning relationship • Fixed small sized deformation unlike slip which is a continuous arbitrary deformation and can be large

13. Mechanical twinning • Fig 13.10, 13.11