1. Introduction
Most solid materials, especially metals, have atoms arranged in a regular, repeating three-dimensional pattern known as a crystal structure. This orderly arrangement determines many mechanical and physical properties such as:
- Strength
- Hardness
- Ductility
- Electrical and thermal conductivity
2. Crystalline and Non-Crystalline Materials
2.1 Crystalline Materials
- Atoms arranged in a regular, repeating pattern
- Example: Metals, salts
2.2 Amorphous (Non-Crystalline) Materials
- No long-range order
- Example: Glass, plastics
3. Space Lattice and Unit Cell
3.1 Space Lattice
A space lattice is a three-dimensional arrangement of points representing atomic positions.
3.2 Unit Cell
- The smallest repeating unit of a crystal lattice
- Repetition of unit cell forms the entire structure
Types of Unit Cells
- Primitive cell
- Body-centered cell
- Face-centered cell
4. Crystal Systems
There are seven crystal systems based on axial lengths and angles:
| System | Axes Relation |
|---|---|
| Cubic | a = b = c, ฮฑ = ฮฒ = ฮณ = 90ยฐ |
| Tetragonal | a = b โ c |
| Orthorhombic | a โ b โ c |
| Hexagonal | a = b โ c, ฮณ = 120ยฐ |
| Monoclinic | a โ b โ c, ฮฒ โ 90ยฐ |
| Triclinic | a โ b โ c, ฮฑ โ ฮฒ โ ฮณ |
| Rhombohedral | a = b = c, ฮฑ = ฮฒ = ฮณ โ 90ยฐ |
5. Common Crystal Structures of Metals
5.1 Body-Centered Cubic (BCC)
4
Characteristics
- Atoms at 8 corners + 1 atom at center
- Atoms per unit cell = 2
Examples
- Iron (ฮฑ-Fe)
- Chromium
- Tungsten
Properties
- Strong but less ductile
5.2 Face-Centered Cubic (FCC)
4
Characteristics
- Atoms at 8 corners + 6 face centers
- Atoms per unit cell = 4
Examples
- Aluminum
- Copper
- Gold
Properties
- Highly ductile
- Good formability
5.3 Hexagonal Close-Packed (HCP)
4
Characteristics
- Hexagonal arrangement
- Atoms per unit cell = 6
Examples
- Magnesium
- Zinc
- Titanium
Properties
- Less ductile than FCC
- Strong structure
6. Atomic Packing Factor (APF)
- Fraction of volume occupied by atoms
| Structure | APF |
|---|---|
| BCC | 0.68 |
| FCC | 0.74 |
| HCP | 0.74 |
7. Coordination Number
Number of nearest neighboring atoms:
| Structure | Coordination Number |
|---|---|
| BCC | 8 |
| FCC | 12 |
| HCP | 12 |
8. Crystal Defects
8.1 Point Defects
- Vacancy defect
- Interstitial defect
8.2 Line Defects
- Dislocations
8.3 Surface Defects
- Grain boundaries
9. Grain Structure
- Polycrystalline materials consist of many grains
- Grain size affects strength and hardness
10. Importance of Crystal Structure
- Influences deformation behavior
- Determines mechanical properties
- Affects electrical and thermal properties
11. Applications
- Material selection in engineering
- Heat treatment processes
- Alloy design
- Failure analysis