Materials Science Short Notes

Materials Science / Solid State Physics
Short Notes for Quick Understanding & Revision

1. Introduction to Materials: Historical Perspective and Importance

Historical Perspective

Early civilization → Stone Age → Bronze Age → Iron Age
19th century: Steel, aluminum, polymers → Industrial Revolution
20th century: Semiconductors (Si, Ge), ceramics, composites, nanomaterials → Electronics, aerospace, biomedical revolutions
Today: Smart materials, metamaterials, 2D materials (graphene), quantum materials → Driving Industry 4.0

Importance of Materials

Performance of any device/structure is limited by the properties of materials used.
Materials Science & Engineering = Interdisciplinary field combining Physics + Chemistry + Engineering to design materials with desired mechanical, electrical, thermal, optical & magnetic properties.

2. Modern & Atomic Concepts in Physics and Chemistry

Atomic Structure (Modern View)

Dalton → Thomson → Rutherford → Bohr → Quantum Mechanical Model (Schrödinger, Heisenberg)
Key features:
- Electrons occupy orbitals (s, p, d, f) with definite energy & probability distribution.
- Pauli exclusion principle, Hund’s rule, Aufbau principle govern electron filling.
- Valence electrons decide chemical bonding and properties.

Periodic Table

Modern periodic law: Properties are periodic function of atomic number.
Blocks (s, p, d, f) → Predict metallic, non-metallic, metalloid nature, electronegativity, ionization energy trends.

Types of Chemical Bonding

Ionic → Electron transfer (e.g., NaCl) → Strong electrostatic force.
Covalent → Electron sharing (e.g., diamond, Si) → Directional bonds.
Metallic → Delocalized electrons (“electron sea”) → Good conductivity, ductility.
Van der Waals → Weak intermolecular forces (important in polymers, molecular solids).

These bonding types decide whether a material is metal, ceramic, polymer or semiconductor.

3. Crystallography and Crystal Structures

Space Lattice & Unit Cell

Crystal = Periodic arrangement of atoms in 3D.
Space lattice: Infinite array of points with identical environment.
Unit cell: Smallest repeating unit showing full symmetry.
Parameters: a, b, c (lattice constants), α, β, γ (angles).

14 Bravais Lattices

7 crystal systems → 14 possible lattices (P, I, F, C)

Common Crystal Structures

Simple Cubic (SC) → Po; CN = 6
Body-Centered Cubic (BCC) → Fe, Cr, W; CN = 8
Face-Centered Cubic (FCC) → Cu, Al, Au, Ni; CN = 12
Hexagonal Close-Packed (HCP) → Mg, Zn, Ti; CN = 12
Diamond Cubic → Si, Ge (tetrahedral); CN = 4

Atomic Packing Factor (APF)

SC → 52%
BCC → 68%
FCC & HCP → 74% (highest, close-packed)

Theoretical Density

ρ = (Z × M) / (N_A × a³)
Z = atoms/unit cell, M = atomic mass, N_A = Avogadro’s number, a³ = volume of unit cell

Miller Indices

Plane (hkl): Reciprocals of intercepts → smallest integers
Direction [uvw]: Vector components → smallest integers
Family {hkl}, ⟨uvw⟩

X-Ray Crystallography – Bragg’s Law

2d sinθ = nλ
Used to determine crystal structure, lattice parameter, phase identification.

4. Imperfections in Crystals

No crystal is perfect. Defects control most properties!

Types of Defects

Point Defects (0D)
- Vacancy, Interstitial
- Schottky, Frenkel
- Substitutional & Interstitial impurity
Line Defects (1D) → Dislocations
- Edge dislocation → Extra half-plane
- Screw dislocation → Spiral ramp
- Burger’s vector b defines slip
Planar Defects (2D): Grain boundaries, Twin boundaries, Stacking faults
Volume Defects (3D): Voids, precipitates, inclusions

Role of Defects

Vacancies → Diffusion
Dislocations → Plastic deformation
Grain boundaries → Strengthening (Hall-Petch)
Point defects & impurities → Doping in semiconductors

Summary Table (Quick Revision)

Structure	Z (atoms/unit cell)	Coordination No.	APF	Examples
Simple Cubic	1	6	0.52	Po
BCC	2	8	0.68	α-Fe, Cr, W
FCC	4	12	0.74	Cu, Al, Ni, Au
HCP	6 (2-unit height)	12	0.74	Mg, Zn, Ti
Diamond Cubic	8	4	0.34	Si, Ge

Study crystal structures and defect diagrams along with this note for best understanding!
All the best for your exams!