Materials Science
Materials science in the EPE exam tests structure–property links: which crystal structure, defect or strengthening mechanism explains the observed strength, ductility, conductivity or thermal behaviour.
Crystal structures
- FCC: 4 atoms per cell, APF 0.74, coordination 12, 12 slip systems of {111}<110> - hence high ductility in copper, aluminium and austenite.
- BCC: 2 atoms per cell, APF 0.68, coordination 8; slip is not on truly close-packed planes, giving temperature-sensitive yield in ferritic steel.
- HCP: 6 atoms per cell, APF 0.74, coordination 12, only about 3 easy slip systems, so magnesium, zinc and alpha-titanium are less ductile.
Defects and strengthening
- Point defects (vacancies, interstitials), line defects (edge and screw dislocations, Frank–Read sources), planar defects (stacking faults, grain boundaries, twin boundaries), volume defects (pores, inclusions).
- Strengthening: solid solution, grain refinement via Hall–Petch, precipitation hardening (particle cutting at small sizes, Orowan bypass when larger), work hardening, and martensitic transformation.
- Ceramics are stiff and brittle with ionic or covalent bonding; polymers show glass transition and viscoelastic creep; composites follow a rule of mixtures, with the isostrain upper bound and isostress lower bound.
Worked example
Density of FCC copper with a = 0.3615 nm and M = 63.55 g/mol: ρ = n·M/(NA·a³) = 4 × 63.55/(6.022 × 10²³ × (0.3615 × 10⁻⁷ cm)³) = 254.2/(6.022 × 10²³ × 4.726 × 10⁻²³) = 8.93 g/cm³, matching the handbook value.
Traps that cost marks
Assuming FCC and BCC have equal packing factor; both FCC and HCP are 0.74 while BCC is 0.68. Using the wrong number of atoms per cell in a density calculation. Treating the rule of mixtures as exact for all loading directions.