Engineering Materials: Crystal Structure

Crystal Structure

• Solids can be classified into two broad categories: crystalline and non-crystalline (amorphous)
• Crystalline solids have an ordered geometric array of atoms that stretches endlessly in all directions in a repetitive fashion
• Amorphous solids, such as silica glass and most hydrocarbon polymers, do not have predictably ordered arrays of atoms

Bravais Point Lattices

• There are only 14 ways to arrange points in space having identical neighbors, known as Bravais point lattices
• These 14 point lattices can be further classified into one of seven crystal systems
• The unit cell dimensions, a, b, and c, are known as lattice parameters or constants, and can be measured with high precision by X-ray diffraction (XRD) techniques

Crystalline vs Amorphous Solids

• Crystalline solids have:
  • Atoms arranged in regular 3D arrays
  • Sharp melting points
  • Anisotropic properties
  • True solid structure
  • Symmetrical structure
  • More rigid structure
  • Long-range order
• Amorphous solids have:
  • No regular arrangement of atoms
  • No particular melting point
  • Isotropic properties
  • Pseudo-solid structure
  • Unsymmetrical structure
  • Less rigid structure
  • Short-range order

Crystalline vs Polycrystalline Solids

• Polycrystalline solids are composed of many crystalline solids
• Crystalline solids have ordered structures and symmetry, but polycrystalline solids have disrupted long-range order
• Crystalline structure is uniform and has no boundaries, but polycrystalline structure has boundaries between grains

Number of Atoms per Unit Cell

• The number of atoms per unit cell, N, can be computed using the formula: N = Ni + Nf/2 + Nc/8
• Where Ni is the number of interior atoms, Nf is the number of face atoms, and Nc is the number of corner atoms

Crystal Structure Characteristics

• Coordination number: the number of nearest-neighbor or touching atoms
• Atomic packing factor (APF): the sum of the sphere volumes of all atoms within a unit cell divided by the unit cell volume

Simple Cubic (SC) Structure

• No additional information provided

Body-Centered Cubic (BCC) Structure

• Atomic packing factor (APF) = 0.68

Face-Centered Cubic (FCC) Structure

• Atomic packing factor (APF) = 0.74

Hexagonal Close-Packed (HCP) Structure

• Corner atoms are shared by 6 cells (3 from below and 3 from above)
• Face atoms are shared by adjacent 2 cells
• Atoms in the interior are shared by only one cell
• Nav = (Nc/6) + (Nf/2) + (Ni/1)
• For HCP structure, Nav = 6