Crystallography for Second-Year Students

Crystallography

• Crystallography is a branch of chemistry for second-year students.
• The majority of 92 stable elements are metallic.
• 68 of the stable metallic elements have one of three fundamental structures: body-centered cubic (BCC), face-centered cubic (FCC), or hexagonal close-packed (HCP).

Structures of Common Materials

• BCC Structure:
  • Described by a non-primitive cubic unit cell.
  • Contains one lattice point at each corner and one at the center of the unit cell.
  • 21 metallic elements have this structure, mostly rare-earths.
  • Characteristics:
    • Ductile at high temperatures.
    • Resistant to crack propagation.
    • Brittle at low temperatures.
    • Strength influenced by temperature.
    • Hardened by interstitial solutes.
• FCC Structure:
  • Described by a non-primitive cubic unit cell.
  • Contains one lattice point at each corner and one at the center of each face.
  • 17 metallic elements have this structure.
  • Characteristics:
    • Highly ductile when pure.
    • Resistant to crack propagation.
    • Retains ductility and toughness to absolute zero (unique among structures).
• HCP Structure:
  • Described by layers of spheres, where spheres in alternating layers overlie one another.
  • A close-packed structure with a slip system
  • Common in elements like Beryllium, Cadmium, Magnesium, Titanium, Zinc, and Zirconium.
  • Elastic nature.

Lattice Constant and Atomic Radius

• A table provides lattice constant (a and c, in nm) and atomic radius (in nm) for various metals categorized by structure (BCC, FCC, HCP).

Coordination Number

• Defined as the number of nearest neighbors of a central atom or ion within a solid.
• Examples show coordination numbers: 3, 4, 6, and 8, with corresponding shapes like triangles, tetrahedrons, octahedrons, and cubes.
• BCC coordination number is 8.
• FCC coordination number is 12.
• HCP coordination number is 12.

The number of lattice points per cell

• Atoms inside the cell are considered as 1 atom within the cell.
• Atoms on faces are sharing with 1/2 atom within the cell.
• Atoms on edges are sharing 1/4 atom within the cell.
• Atoms in corners are sharing with 1/8 atom within the cell.

Atomic Packing Factor

• Atomic packing factor (APF) is a ratio of the volume of atoms in a unit cell to the volume of the unit cell itself.
  • APF reflects how closely atoms are packed.
• APF for different structures (BCC, FCC, Simple cubic, and HCP) is calculated based on the relevant formulae.

Structure-Property Correlation

• Ductility of aluminum is explained by its FCC crystal structure.
• Steel's (iron) properties are discussed compared to its BCC structure.
• Slip systems in metals are discussed as a way for plastic deformation to occur.
• Slip systems are closely related to the close-packed nature of the planes.