Lecture Notes on Crystal Structures & Material Science

Announcements

• Quiz 1: Available only today until midnight. Five questions; seven-minute time limit. Resembles homework. Full credit for attempts.
• Homework 2: To be posted today, due next Wednesday at noon. Consists of 20 questions.
• TA Update: New TA, Sid, will manage quiz section next week.
• Midterm: First midterm in two weeks, conducted during quiz section.
• Reading: Stay ahead as the summer quarter is fast-paced.
• Office Hours: Mondays after class.

Lecture Topics

Crystallography

• Study of atomic arrangement in solids.
• Crystalline Solids: Exhibit long-range order.
• Amorphous Solids: Exhibit short-range order; no long-range order (e.g., glass).
• Examples: Quartz (crystalline) vs. Silica (amorphous).

Crystal Structures

• Corundum, Ruby, Sapphire: All have the same base material, aluminum oxide.
  • Doping: Adding impurities (chromium for ruby; titanium and iron for sapphire) to alter color.
• Polycrystals: Consist of many smaller crystals. Grain boundaries separate these crystals.

Real-life Crystal Examples

• Metals and Crystals: Most metals, like graphite, contain crystals.
• Polymers: Semi-crystalline with arranged polymer chains.

Crystalware

• A type of glass called "lead glass" or "crystal glass."
  • Contains lead oxide to increase refractive index and machinability.

Galvanization

• Zinc galvanized materials (e.g., guard rails) exhibit crystal structures called "spangles."

Common Crystal Structures

• Face-Centered Cubic (FCC): Nickel, Copper, Silver, Gold, Aluminum.
• Body-Centered Cubic (BCC): Iron, Alkali metals.
• Hexagonal Close Packed (HCP): Titanium.

Unit Cells and Calculations

Simple Cubic

• Number of Atoms: 1 atom per unit cell.
• Coordination Number: 6 neighbors.
• Lattice Parameter: a = 2r.
• Atomic Packing Factor (APF): 50%.

Face-Centered Cubic (FCC)

• Number of Atoms: 4 atoms per unit cell.
• Coordination Number: 12 neighbors.
• Lattice Parameter: a = 2r√2.
• APF: 0.74.

Body-Centered Cubic (BCC)

• Number of Atoms: 2 atoms per unit cell.
• Coordination Number: 8 neighbors.
• Lattice Parameter: a = 4r/√3.
• APF: 0.68.

Hexagonal Close Packed (HCP)

• APF: 0.74 (similar to FCC).
• Slip Systems: FCC has 12 slip systems making it more malleable.

Crystal Structures and Lattices

• Bravais Lattices: 14 distinct arrangements.
• Motif/Basis: The group of atoms placed at lattice points.
• Examples:
  • Sodium Chloride: FCC lattice with NaCl basis.
  • Cesium Chloride: Simple cubic lattice.

Interstitial Sites in Ionic Solids

• Coordination Numbers: Based on cation to anion radius ratios.
• Example: Magnesium oxide uses octahedral sites for magnesium.

Miller Indices

• Used to describe crystallographic directions and planes.
• Notation: Directions use brackets, planes use parentheses.
• Reciprocal Space: For plane indices.

Diffraction and Crystal Properties

• To be covered in future lectures.

Conclusion

• The lecture covered crystallography basics, common crystal structures, and unit cell calculations, providing a foundational understanding for students in material science.