Module I: Introduction to Material Science and Crystallography

Definition: Studies composition (chemical make-up) and structure (atomic arrangement across length scales) to control properties through synthesis and processing.
Classification of Materials: - Metals and alloys: High strength, ductility, and conductivity (e.g., Aluminum, Titanium, Steel). - Ceramics, glasses, and glass-ceramics: Inorganic, nonmetallic, high compression strength, brittle (e.g., Silica, Zerodur™). - Polymers: Organic materials produced via polymerization; high strength-to-weight ratio (e.g., Rubber, CD, LCD). - Semiconductors: Intermediate conductivity; essential for electronics (e.g., Silicon, Germanium, Gallium Arsenide). - Composite materials: Combined materials for unique properties (e.g., Concrete, Plywood, Fiberglass, Boeing 787 carbon fiber-reinforced plastics).

Metallic Bonds: Delocalized "sea" of electrons around ion cores; nondirectional, providing high ductility and conductivity.
Covalent Bonds: Shared valence electrons; very strong and directional; high melting points but limited ductility (e.g., Diamond, $SiC$ , $Si_3N_4$ , $BN$ ).
Ionic Bonds: Electrostatic attraction between cations and anions via electron transfer; stronger than covalent (e.g., $NaCl$ ).
Van der Waals Bonds: Weak secondary bonds from dipole interactions (London, Debye, and Keesom forces). Hydrogen bonding is a specialized Keesom force.

Lattice Parameters: Defined by interatomic spacing ( $a, b, c$ ) and inter-axial angles ( $\alpha, \beta, ext{γ}$ ).
Standard Systems: 7 crystal systems and 14 Bravais lattices.
Cubic Unit Cell Properties: - Simple Cubic (SC): $1$ atom per cell; Coordination Number = $6$ ; $APF = 0.52$ . - Body-Centered Cubic (BCC): $2$ atoms per cell; Coordination Number = $8$ ; $APF = 0.68$ . - Face-Centered Cubic (FCC): $4$ atoms per cell; Coordination Number = $12$ ; $APF = 0.74$ .
Hexagonal Closed Packed (HCP): $6$ atoms per cell; Coordination Number = $12$ ; $APF = 0.74$ .
Theoretical Density ( ho): Calculated as $\rho = \frac{n \times A}{V_c \times N_A}$ , where $n$ is atoms per cell, $A$ is atomic weight, and $N_A = 6.023 \times 10^{23}$ .

Crystalline vs. Amorphous: Crystalline has long-range order and a definite melting point; Amorphous (e.g., Glass) has short-range order and a melting temperature range.
Polymorphism (Allotropy): Capability of a material to exist in multiple crystal structures (e.g., Carbon as Graphite/Diamond; Pure Iron changing from BCC to FCC at $912\,^{\circ}C$ ).
Miller Indices: - Directions: Represented as $[u v w]$ . - Planes: Represented as $(h k l)$ based on the reciprocals of axis intercepts.

Plastic Deformation: Permanent atomic movement to new equilibrium positions.
Modes: - Slip: Sliding of atomic planes; orientation remains the same; occurs on densest planes and directions. - Twinning: Lattice divided into two symmetric parts with different orientations; common in HCP structures.
Schmid's Law: Relates applied stress ( $\sigma$ ) to critical resolved shear stress ( $\tau_{cr}$ ): $\tau_{cr} = \sigma \cos(\alpha) \cos(β)$ .
Structure and Ductility: - FCC: $12$ slip systems; highly ductile ( $Cu$ , $Al$ , $Au$ ). - BCC: $12$ slip systems but lower atomic density; less ductile ( $Fe$ , $W$ , $V$ ). - HCP: $3$ slip systems; brittle ( $Zn$ , $Graphite$ ).
Hall-Petch Equation: $\sigma_y = \sigma_0 + k D^{-1/2}$ , establishing that yield strength increases as grain diameter ( $D$ ) decreases.