Physical Metallurgy
Physical Metallurgy tests structure-property relationships: crystallography, defects, solidification, phase diagrams, phase transformations, heat treatment, and strengthening mechanisms. Expect questions that move from a crystal structure or phase diagram to an observed property.
Core rules
- Miller indices (hkl) for planes and [uvw] for directions; in cubic crystals, [hkl] is normal to (hkl) only for cubic symmetry.
- FCC has 4 atoms/cell and APF 0.74; BCC has 2 atoms/cell and APF 0.68; HCP has 6 atoms/cell and APF 0.74.
- Point, line, and planar defects control diffusion and strength. Grain boundaries strengthen via Hall-Petch: σy=σ0+k d^(−1/2).
- Phase rule F=C−P+2 for pressure and temperature variables. Lever rule uses tie-line endpoints at the same temperature.
- Solidification: nucleation and growth; constitutional undercooling can cause dendritic or cellular growth.
- TTT diagrams describe isothermal transformations; CCT diagrams describe continuous cooling. They are not interchangeable.
Worked example
A tensile stress of 100 MPa is applied to a crystal. The slip plane normal is at 45° to the stress axis and the slip direction is also at 45° in the plane. Schmid factor m=cosφ cosλ=cos45° cos45°=0.5. Resolved shear stress τ=σm=100×0.5=50 MPa. If the critical resolved shear stress is 50 MPa, slip begins at this applied stress; if it is 60 MPa, slip does not begin.
Traps
- Interchanging Miller indices and direction indices.
- Using the wrong tie-line endpoints for the lever rule.
- Applying equilibrium phase fractions to a rapidly cooled non-equilibrium microstructure.
- Confusing TTT and CCT curves.
- Forgetting that Hall-Petch is valid only above a lower grain-size limit.