21-Mat-B6 Ceramic Materials · December 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Both transformations are ultimately driven by the same thermodynamic quantity — the Gibbs free-energy difference $\Delta G_v = G_{austenite}-G_{product}$, which becomes negative (favourable) as the steel is undercooled below a reference equilibrium temperature: $A_1$ (the eutectoid temperature) for pearlite, and $T_0$ (the temperature at which austenite and diffusionless martensite of the SAME composition have equal free energy) for martensite. The key DIFFERENCE is how much undercooling each needs, and why. Austenite→pearlite is a diffusional, nucleation-and-growth transformation that is overall composition-invariant (pearlite's average composition equals the parent austenite's) but requires long-range carbon partitioning between the forming ferrite and cementite lamellae; a comparatively small undercooling below $A_1$ (tens of degrees) already supplies enough driving force, because atomic mobility just below $A_1$ is still fast and does the rest of the work. Austenite→martensite is diffusionless (see part ii) and forms with NO change in composition at all, so it gets no assistance from a diffusion/partitioning contribution to the free energy; it must instead be driven by the chemical free-energy difference ALONE, which only becomes large enough to nucleate martensite — overcoming a substantial shear-strain and interfacial-energy barrier as well — at a much larger undercooling, i.e. cooling well below $T_0$, down to $M_s$, which lies far below $A_1$ for essentially every steel. In short: both are driven by undercooling-generated $\Delta G_v$, but pearlite needs only a small $\Delta G_v$ because diffusion assists it, while martensite needs a very large $\Delta G_v$ because it must unassisted supply both the chemical driving force and the extra non-chemical energy a diffusionless shear transformation demands.
Martensite forms by a diffusionless, cooperative SHEAR ("military," not "civilian") mechanism: on cooling below $M_s$, small regions of austenite transform almost instantaneously (an individual plate/lath forms in roughly $10^{-7}$ s, propagating near the speed of sound in the lattice) by a coordinated, homogeneous shear-plus-volume-change distortion of the parent FCC austenite lattice into the body-centred tetragonal (BCT) martensite lattice. This is classically described by the Bain distortion — a compression along one FCC axis and an expansion along the other two converts the FCC cell into the BCT cell — modified by additional, lattice-invariant shears (fine internal slip or twinning within the plate) that accommodate the overall shape change while keeping a coherent, unrotated HABIT PLANE with the surrounding parent austenite. Because there is no long-range diffusion, EVERY carbon atom that was in interstitial solution in the parent austenite is carried over, trapped, into the martensite's own octahedral interstitial sites — this supersaturation is what produces the tetragonal distortion and high hardness discussed in part (iii). The transformation is ATHERMAL: the fraction transformed depends only on how far below $M_s$ the steel has been cooled (each further increment of undercooling triggers a fresh burst of new plates), not on how long it is held at a given temperature — unlike the isothermal, diffusional pearlite/bainite reactions — and it proceeds only while temperature keeps falling, stopping at $M_f$ (or earlier, if remaining retained austenite becomes mechanically stabilized).
As in Question IV(iii): martensite is a diffusionless, supersaturated interstitial solid solution of carbon trapped in a body-centred tetragonal (BCT) iron lattice, rather than the cubic lattice a diffusional product would allow. Carbon that would ordinarily partition into cementite is instead frozen in octahedral interstitial sites, distorting the surrounding lattice anisotropically along the tetragonal $c$-axis (the $c/a$ ratio rises roughly linearly with wt% C). This distortion generates strong local strain fields that strongly resist dislocation motion — interstitial solid-solution strengthening — so a higher parent-austenite carbon content, carried over unchanged into the martensite, produces a larger $c/a$ distortion and correspondingly higher hardness, up to the point (roughly 0.6–0.8 wt% C) where the benefit saturates and increasing retained-austenite content begins to work against further hardness gain.
