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

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

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

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

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)

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

Crystallographic Directions, and Planes Crystallographic Planes

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

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

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

Crystallographic Directions, and Planes Hexagonal Crystal System example a2 a3 a1 z a1 a2 a3 c 1. Intercepts 1  -1 1 2. Reciprocals 1 1/ 1 0 -1 1 3. Reduction 1 0 -1 1 4. Miller-Bravais Indices (1011)

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

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 …..

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

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

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

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

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

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.

Twin Structure Formation:

Twin Structure Formation:

Twin Structure Formation: Fig. 3 Image simulations of Si-{111}-twin structures: (a) relaxation using empirical MD with the TS potential and 54000 atoms according to Fig.2, (b) non-relaxed twin, (c) ab-initio relaxed twin (T), (d) C-layer outside the twin, (e) half (C@T) layer C-occupation, (f) double (2C@T) layer C-occupation, (g) random C-substitution (R) from Fig. 1.

Grain Boundary Structure:

Grain Boundary Structure: Coincident Site Lattice (CSL)

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.

Grain Boundary Structure in Colloidal Particle Self-Assembly V I D G

Grain Boundary Structure in Graphene:

Cation-Anion radius ratio Interstitial Sites in Close-Packed Structure: Geometry Coordination # Cation-Anion radius ratio 2 3 4 6 8 < 0.155 0.155 - 0. 225 0. 225 - 0.414 0. 414 - 0. 732 0. 732 - 1. 0

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

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)

(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)

Interstitial Sites in BCC Structure: 3 octa + 3 octa = 6 octa

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

Phase Transformation (Allotropic Phase Transformation)