Crystallography for 2nd Year Students

Crystallography

• Crystallography is a branch of chemistry for second-year students.
• Interstitial sites are locations in a crystal where atoms or ions different from the "normal" atoms can be placed.

Interstitial Sites

• Cubic site: An interstitial site with a coordination number of eight. An atom/ion in this site touches eight other atoms/ions.
• Octahedral site: An interstitial site with a coordination number of six. An atom/ion in this site touches six other atoms/ions.
• Tetrahedral site: An interstitial site with a coordination number of four. An atom/ion in this site touches four other atoms/ions.

Crystals Having Filled Interstitial Sites

• FCC lattices have:
  • 3 octahedral (Oh) sites at edge centers and 1 at body center.
  • 8 tetrahedral (Th) sites at 1/2, 1/4, 1/4 positions.
• Interstitial sites are important because they allow for the derivation of various crystal structures (FCC, BCC, HCP) with slightly different arrangements.

Density Calculations

• Density (ρ) of a crystalline material is calculated as:
  • ρ = (number of atoms in the unit cell, n) × (mass of atom, m) / (volume of unit cell, v)
• Number of atoms in unit cells:
  • BCC: 2
  • FCC: 4
  • HCP: 6
• Mass of atom (m) is the atomic weight (a) in g/mol or amu.
• To convert from amu to grams: (atomic weight in amu) / (Avogadro's number).
• Avogadro's number (NA): 6.023 × 10²³ atoms/mol
• Volume of the unit cell (Vc):
  • SC: a³
  • BCC: a³√3/4
  • FCC: a³√2/4

Density Calculation Example (Copper)

• Radius (Rcu) of copper = 0.128 nm
• Crystal structure of copper = FCC
• Atomic weight (Acu) of copper = 63.5 g/mol
• Number of atoms per unit cell (n) = 4
• Volume of unit cell (Vc) = a³ = (2R√2)³ = 16√2R³
• Calculate Density (ρ) using the formula above
• Results in density of approximately 8.89 g/cm³.

Planar Density

• Planar Density (PD) represents the density of atomic packing on a particular crystal plane.
• PD = (Number of atoms on a plane) / (Area of the plane)
• Example: In an FCC lattice, the {110} planes have 2 atoms per unit area.

Linear Density

• Linear Density (LD) refers to the number of atoms per unit length along a specific direction.
• LD = (Number of atoms along the direction) / (Length of the direction)
• Example: The <110> directions in an FCC lattice have a linear density of 2 atoms/√2a.

Lattice Constants and Atomic Radii

• Table provided that gives lattice constant (a,c) and atomic radius (R) for various metals with different crystal structures (BCC, FCC, HCP).

X-Ray Diffraction

• Bragg's law:
  • 2d sin θ = mλ
  • m: order of diffraction
  • d: spacing between crystal planes
  • θ: diffraction angle
  • λ: wavelength of X-rays
• Diffraction patterns help identify the crystal structure of a material.

This quiz explores the fundamental concepts of crystallography, focusing on interstitial sites in crystalline structures. Students will learn about cubic, octahedral, and tetrahedral sites, as well as their significance in various crystal lattices. Perfect for second-year chemistry students looking to solidify their understanding of crystal structures.