Basic Materials Engineering
Basic Materials Engineering Lecture Notes
1. Structure of Crystalline Solids
Types of Order in Materials:
Short-Range Order (SRO): Preferred arrangement of atoms reaches only to nearest neighbors.
Example: Monoatomic gases, ionized gases in fluorescent tubes (random arrangement).
Amorphous Materials: Materials that lack a clear structure; examples include liquid crystals.
Long-Range Order (LRO): Arrangement forms a repetitive, grid-like structure extending over dimensions greater than 100 nm.
Example: Most metals, alloys, ceramic materials, semiconductors, and some polymers.
2. Single Crystal vs. Polycrystalline Materials
Single Crystal: Composed of one crystal, properties depend on chemical composition and crystallographic direction.
Polycrystalline Material: Consists of multiple crystals (grains) with varied orientations.
Grain Boundaries: Interfaces between misaligned crystals; properties influenced by both grains and boundaries.
3. Amorphous Materials
Defined as materials exhibiting only short-range atomic order; shake out orderly arrangements due to processing kinetics.
Examples: Glasses in ceramics and polymers, certain polymeric gels.
Offer unique blending properties since atoms are not in periodic arrangements.
4. Basic Terms in Crystallography
Lattice: Periodic collection of points or lattice points, which can be 1D, 2D, or 3D.
Motif/Basis: Group of atoms at each lattice point forming the crystal structure, acquired by combining lattice and basis.
Unit Cell: The smallest repeating unit of a lattice; a compact representation retains overall properties of the full lattice.
5. Bravais Lattices
Seven Crystal Systems:
Cubic, Tetragonal, Orthorhombic, Rhombohedral (Trigonal), Hexagonal, Monoclinic, Triclinic.
14 Unique Bravais Lattices: Arrangement of points used to describe 3D space filling.
6. Lattice Parameters
Define unit cell's size and shape, comprising dimensions and angles between sides.
7. Metallic Crystal Structures
Common Structures: Face-Centered Cubic (FCC), Body-Centered Cubic (BCC), Hexagonal Close-Packed (HCP).
Atomic Radius Data:
Aluminum (FCC): 0.1431 nm
Molybdenum (BCC): 0.1363 nm
Cadmium (HCP): 0.1490 nm
Others include Nickel (FCC), Chromium (BCC), Platinum (FCC), etc.
8. Number of Atoms per Unit Cell
Defined by lattice points: corners, face-centered, and body-centered positions.
Lattice point sharing: e.g., corner atoms shared by neighboring unit cells.
Formula: N = Ni + \frac{Nf}{2} + \frac{N_c}{8}
Where:
$N_i$ = number of interior atoms,
$N_f$ = number of face atoms,
$N_c$ = number of corner atoms.
Constant $X$ is 8 for cubic and 6 for hexagonal structures.
9. Allotropic and Polymorphic Transformations
Definitions:
Allotropic: Materials that can exist in more than one crystal structure.
Applies to pure elements and compounds.
10. Isotropic and Anisotropic Behavior
Isotropic: Properties are the same in all directions.
Anisotropic: Properties vary based on the crystallographic direction; typical in single crystals or materials with grains oriented in specific directions.
Most polycrystalline materials show isotropic properties.
11. Imperfections in Atomic and Ionic Arrangements
Types of Defects:
Point Defects
Line Defects (Dislocations)
Surface Defects
12. Point Defects
Localized disruptions in atomic/ionic arrangements:
Impurities: Unintentional constituents from raw materials or processing.
Dopants: Elements added purposefully to alter material properties.
Types include:
Vacancies
Interstitial atoms
Substitutional atoms (small or large)
Frenkel and Schottky Defects.
13. Vacancies
Occur when atoms or ions are missing from their standard sites, increasing randomness and thermodynamic stability.
Introduced during solidification, high temperatures, or radiation.
Crucial for atom movement and diffusion rates in metals.
14. Interstitial Defects
Additional atoms/ions placed in normally unoccupied positions, resistant to dislocation movement, enhancing metallic strength.
Remain constant with temperature changes, distinct from vacancies.
15. Substitutional Defects
One atom/ion replaced by another type, affecting interatomic distances and often increasing metallic strength.
16. Dislocations
Line imperfections, pivotal during material solidification or permanent deformation.
Types include:
Edge Dislocation: Creates an extra plane of atoms, characterized by the Burgers vector perpendicular to the dislocation line.
Screw Dislocation: Skewed crystal structure resulting in connections along cut planes; Burgers vector is parallel.
Mixed Dislocations: Combination of edge and screw character, with Burgers vector neither perpendicular nor parallel.
17. Surface Defects
Two-dimensional boundaries separating different crystal structures or orientations.
Types include:
Interfacial defects
External surfaces
Grain boundaries
Phase boundaries
18. Dislocations and Strengthening Mechanisms
Understanding dislocation behavior is essential for tailoring mechanical properties like strength in metals and alloys.
19. Plastic Deformation vs. Dislocation Motion
Plastic deformation results from large-scale dislocation movement, known as slipping along specific crystallographic planes called slip planes.
20. Analogy: Caterpillar in MatSci Lecture
An analogy comparing dislocation motion to a caterpillar's movement.
21. Formation of Steps on Crystal Surfaces
Movement of edge and screw dislocations results in step formations:
Edge Dislocation: Moves in shear stress direction.
Screw Dislocation: Moves perpendicular to stress direction.
22. Dislocation Density
Quantity of dislocations expressed in total dislocation length per volume. It varies by material type:
Examples:
Carefully solidified metals: approx. 10^3 dislocations/mm²
Heavily deformed metals: 10^9 – 10^{10} dislocations/mm².
23. Case Study: Dislocation Annihilation
Process where dislocations meet, demonstrating perfect crystalline behavior post-annihilation.
24. Slip Systems
Not all dislocations move easily across every crystallographic plane; specific planes (slip planes) and directions (slip directions) exist where motion occurs with preferred ease.
25. Conclusion: Motion of Dislocations
On a microscopic level, plastic deformation corresponds to the motion of dislocations in response to applied shear stress.