1. Crystal Structure and Crystallography of Materials
Chapter 2: Defect Structure in FCC, HCP, and BCC

2. A B C Structure Visualization in Projection: (110) Projection of FCC
[111]
[001]
[110]
{111} Planes A B C
 Stacking sequence of FCC ; A B C A B C A B C …..

3. Perfect Dislocation and Shockley Partial Dislocation in FCC:
Have to understand dislocation both perfect and partial
Perfect Dislocation
 1/2 [110] type
Shockley Partial Dislocation
 1/6 [112] type
[112]
a/2[112]
a/2[110]
a/6[112] C A B C A A B A

4. Shockley Partial Dislocation:
Moving atom from B → C position A B C

5. A B C A B C A B C A A B C A C A B C A B A B C A C B C A B C
Shockley Partial Dislocation:
A B C A B C A B C A
A B C A C A B C A B
Stacking fault (one layer missing)
→ intrinsic stacking fault
Locally HCP form
A B C A C B C A B C
Intrinsic stacking fault
Extrinsic stacking fault ▼ A B

6. Shockley Partial Dislocation:B C
B→C
C→A
A→B
[111]
[110] projection B

7. A B A B A B A B A B A B A B A B A A B A B C A C A C A C A C A C A C
Phase Transformation from HCP to FCC:
A B A B A B A B A B A B A B A B A
A B A B C A C A C A C A C A C A C
A B A B C A B C B C B C B C B C B
A B A B C A B C A B A B A B A B A
A B A B C A B C A B C A C A C A C
A B A B C A B C A B C A B C B C B

8. A B C A B C A B C A B C A B C A B C A B C
Twin Structure Formation:
A B C A B C A B C A B C A B C A B C A B C
A B C A B C A B C A C B A B C A B C A B C
A B C A B C A B C A C A B C A B C A B C A
A B C A B C A B C A C B C A B C A B C A B
A B C A B C A B C A C B A C A B C A B C A
A B C A B C A B C A C B A C B C A B C A B
A B C A B C A B C A C B A C B A B C A B C
Shockley partials on consecutive closed packed planes.

9. Twin Structure Formation:

10. Twin Structure Formation:

11. Twin Structure Formation:
Fig. 3 Image simulations of Si-{111}-twin structures: (a) relaxation using empirical MD with the TS potential and atoms according to Fig.2, (b) non-relaxed twin, (c) ab-initio relaxed twin (T), (d) C-layer outside the twin, (e) half layer C-occupation, (f) double layer C-occupation, (g) random C-substitution (R) from Fig. 1.

12. Grain Boundary Structure:

13. Grain Boundary Structure: Coincident Site Lattice (CSL)

14. Grain Boundary Structure: Coincident Site Lattice (CSL)
Shown is the calculated (0oK) energy for symmetric tilt boundaries in Al produced by rotating around a <100> axis (left) or a <110> axis (right). We see that the energies are lower, indeed, in low S orientations, but that it is hard to assign precise numbers or trends. Identical S values with different energies correspond to identical grain orientation relationships, but different habit planes of the grain boundary.

15. Grain Boundary Structure in Colloidal Particle Self-AssemblyV I D G

16. Grain Boundary Structure in Graphene:

17. Cation-Anion radius ratio
Interstitial Sites in Close-Packed Structure:
Geometry
Coordination #
Cation-Anion radius ratio 2 3 4 6 8
<

18. Interstitial Sites in FCC Structure:
Octahedral sites: 4
Tetrahedral sites: 8

19. Interstitial Sites in HCP Structure:
Tetrahedral sites ; 4
(0,0,3/8) (0,0,5/8) (1/3,2/3,1/8) (1/3,2/3,7/8)

20. (2/3,1/3,1/4) (2/3,1/3,3/4) Interstitial Sites in HCP Structure:
Octahedral sites ; 2
A site
B site
C site
(2/3,1/3,1/4) (2/3,1/3,3/4)

21. Interstitial Sites in BCC Structure:
3 octa octa = octa

22. 4/2 tetra x 6 = 12 tetra Interstitial Sites in BCC Structure: a r+ri

23. Phase Transformation (Allotropic Phase Transformation)