Chemistry: Solids and Unit Cells

Solids

• A solid has a definite shape and volume because its particles are tightly packed.
• Solids can exist as crystals with regular lattices or as amorphous solids with irregular arrangements.

Unit Cells

• Unit cells are the fundamental building blocks of crystal structures.
• There are three main types of unit cells: simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC).

Simple Cubic (SC)

• The SC unit cell has atoms only at the corners of a cube.
• Polonium is the only element with a simple cubic structure.

Face-Centered Cubic (FCC)

• FCC unit cells have atoms at each corner and in the center of each face of the cube.
• Important characteristics of an FCC structure include a coordination number of 12 and an atomic packing factor of 0.74.
• The volume of an FCC unit cell can be calculated using the formula: VC = (4√2)R³
• Examples of FCC structures include copper, silver, and gold.

Atomic Packing Factor

• The atomic packing factor represents the proportion of space occupied by atoms in a unit cell.
• It is calculated by dividing the volume of atoms in the unit cell by the volume of the unit cell.
• A higher atomic packing factor indicates a more efficient packing of atoms.

Body-Centered Cubic (BCC)

• BCC unit cells have atoms at each corner and one atom at the center of the cube.
• Important characteristics of a BCC structure include a coordination number of 8 and an atomic packing factor of 0.68.
• The edge length (a) of a BCC unit cell is related to the atomic radius (R) by the equation: a = 4R/√3.
• Examples of BCC structures include iron, chromium, and tungsten.

Hexagonal Close-Packed (HCP)

• HCP unit cells have atoms at the corners of a hexagon, a single atom in the center of the hexagon, and three atoms between the top and bottom planes.
• Important characteristics of an HCP structure include a coordination number of 12 and an atomic packing factor of 0.74.
• The number of atoms per unit cell in an HCP structure can be calculated using the equation: N = (12 * 1/6) + 2 + 3 = 6.
• Examples of HCP structures include magnesium, zinc, and titanium.

Density Computations

• The theoretical density of a solid can be calculated using the equation: ρ = (n * A) / (VC * NA).
• Where:
  • n = number of atoms per unit cell
  • A = atomic weight
  • VC = volume of the unit cell
  • NA = Avogadro’s number (6.022 x 10^23 atoms/mol)

Types of Crystals

• Crystals are classified into four types based on the forces holding the particles together: ionic, covalent, molecular, and metallic.

Ionic Crystals

• Ionic crystals are composed of charged species (anions and cations).
• Anions and cations in ionic crystals are generally quite different in size, and their radii need to be considered for understanding the structure and stability of the compound.
• The edge length of an ionic crystal unit cell is often related to the sum of the ionic radii.
• Examples of ionic crystals include NaCl (sodium chloride), CaCl2 (calcium chloride), and MgO (magnesium oxide).

Conclusion

• Understanding the basic concepts of crystal structures, unit cells, density computations, and different crystal types is crucial in the study of engineering materials.
• These concepts provide insights into the properties and behaviors of materials used in various engineering applications.