Materials Science and Engineering: Structure–Property Links
What this section tests
The Materials Science and Engineering section tests structure–property relationships: crystal structures and Miller indices, defects, diffusion, phase diagrams, and the mechanical behaviour of metals, ceramics and polymers.
Core rules
- BCC: 2 atoms/cell, coordination number 8, APF 0.68. FCC: 4 atoms/cell, CN 12, APF 0.74. HCP: 6 atoms/cell, CN 12, APF 0.74, c/a ≈ 1.633.
- FCC packs along the face diagonal: 4r = a√2, so a = 2√2 r.
- BCC packs along the body diagonal: 4r = a√3.
- Density ρ = nA/(V_c N_A), with n atoms per cell and V_c the cell volume.
- Miller indices: reciprocals of intercepts, cleared of fractions, in ( ) for planes and [ ] for directions.
- Engineering stress uses original area; true stress uses instantaneous area. Necking begins at the ultimate tensile strength.
- Hall–Petch: yield strength rises as grain size falls.
Worked example
Copper is FCC with atomic radius 0.128 nm. Find its lattice parameter. Face diagonal = 4r = 0.512 nm = a√2, so a = 0.512/1.414 = 0.362 nm. The measured value is 0.361 nm; the agreement confirms FCC rather than BCC is the right structural model.
Traps
Swapping BCC and FCC coordination numbers (8 versus 12); applying 4r = a√2 to a BCC metal; reporting engineering stress where true stress was requested; confusing a eutectic (lowest melting point, fixed composition) with a eutectoid (the same idea in the solid state); forgetting ceramics are strong in compression but weak in tension.