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

2. Content Introduction Unit Cell Metallic Crystal Structure
Crystallographic Directions and Planes
Interstitial Position and Coordination Number
Ceramic Structure
Polymer Structure
Structure Determination (X-Ray)

3. Crystallographic Directions, and Planes
Crystallographic Coordinates
Position: fractional multiples of the unit cell edge lengths
ex) P: q, r, s

4. Crystallographic Directions, and Planes
a line between two points or a vector
[uvw] square bracket, smallest integer
families of directions: <uvw> angle bracket

5. Crystallographic Directions, and Planes
Crystallographic Planes
Miller Indices: Reciprocals of the three axial intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller indices.
(hkl)
Algorithm 
Read off intercepts of plane with axes in terms of a, b, c
Take reciprocals of intercepts
Reduce to smallest integer values
Enclose in parentheses, no commas i.e., (hkl) .
Example
let m=2, n=1, p=∞
reciprocals are 1/2, 1, 0
then, h=1, k=2, l=0
Miller index is (120)

6. Crystallographic Directions, and Planes
Crystallographic Planes A B C D E F

7. Crystallographic Directions, and Planes
Crystallographic Planes

8. Crystallographic Directions, and Planes
Crystallographic Planes Family : ex. {110}

9. Crystallographic Directions, and Planes
Crystallographic Planes Family : ex. {110}

10. Crystallographic Directions, and Planes
Hexagonal Crystal System
Miller-Bravais Scheme

11. Crystallographic Directions, and Planes
Hexagonal Crystal System
example a2 a3 a1 z
a a a c
Intercepts  -1 1
Reciprocals / -1 1
Reduction -1 1
Miller-Bravais Indices
(1011)

12. Crystallographic Directions, and Planes
Directions, Planes, and Family
line, direction
[111] square bracket
<111> angular bracket - family
Plane
(111) round bracket (Parentheses)
{111} braces - family

13. 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 …..

14. 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

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

16. 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

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

18. 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

19. 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.

20. Twin Structure Formation:

21. Twin Structure Formation:

22. 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.

23. Grain Boundary Structure:

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

25. 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.

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

27. Grain Boundary Structure in Graphene:

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

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

30. 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)

31. (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)

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

33. 4/2 tetra x 6 = 12 tetra Interstitial Sites in BCC Structure: a r+ri

34. Phase Transformation (Allotropic Phase Transformation)