2.1 — (i) Experimental construction of a TTT curve
A TTT (time–temperature–transformation) curve is built from a large batch of small, identical specimens of the steel, all austenitized together (same temperature above A3/Acm, same soak time) so every specimen starts from the same fully austenitic, uniform-composition state. The procedure is then, for one chosen hold temperature $T_1$ (below A1, above room temperature) at a time:
Rapidly transfer a specimen from the austenitizing furnace into an isothermal bath (molten salt or lead) held precisely at $T_1$ — the transfer must be fast enough that no transformation occurs on the way down, so the specimen effectively starts the clock already at $T_1$.
Hold at $T_1$ for a chosen time $t$, then withdraw and immediately water-quench that specimen to room temperature — this freezes whatever fraction had transformed isothermally at $T_1$ and converts any UNTRANSFORMED remaining austenite to fresh martensite (readily told apart microscopically/by hardness from the isothermal product).
Repeat step 2 with a fresh specimen at many different hold times $t$ at the SAME $T_1$, from very short (little/no transformation) to long enough that no further untransformed austenite remains.
Determine, for each specimen, the transformed fraction — by quantitative metallography (point count of isothermal product vs. quenched martensite), or non-destructively by dilatometry (transformation is accompanied by a volume change) or magnetic permeability (austenite is paramagnetic, the transformation products are ferromagnetic), tracked continuously on a single specimen if a non-destructive method is used.
Plot transformed fraction vs. log(time) at $T_1$; read off the time at which transformation is first detectable (conventionally ∼1%, the "start" point) and the time at which it is essentially complete (∼99%, the "finish" point) for that temperature.
Repeat the whole procedure (steps 1–5) at a series of other hold temperatures, spanning from just below A1 down to just above $M_s$.
Cross-plot all the start points as one curve and all the finish points as a second curve on temperature (vertical axis) vs. log(time) (horizontal axis) — these are the TTT diagram's "start" and "finish" curves. $M_s$ and $M_f$ (determined separately, e.g. by dilatometry on a continuously cooled specimen, since martensite formation is athermal and not part of the isothermal-hold experiment) are added as horizontal lines, since they depend only on temperature, not time.
2.2 — (ii) Why the curve has a "C" shape
Fig. 2.1 — Schematic isothermal-transformation (TTT) diagram for a eutectoid steel: the "start" and "finish" curves are both C-shaped, with a single time-minimum (the "nose") near 550 °C, between the pearlite field (upper shelf, near A1) and the bainite field (lower shelf, near Ms). Ms/Mf are horizontal (athermal, time-independent).
The transformation time at any hold temperature is set by two competing, temperature-dependent effects acting on the SAME (nucleation-and-growth, diffusion-controlled) pearlite/bainite reaction:
Thermodynamic driving force ($\Delta G_v$, set by the undercooling below A1) is small just below A1 and grows steadily as the hold temperature drops further — a larger driving force favours faster nucleation and a shorter transformation time.
Atomic (carbon) diffusivity falls off exponentially (Arrhenius behaviour) as temperature drops — slower diffusion favours slower growth and a LONGER transformation time.
Near A1, diffusion is fast but the driving force is almost zero, so nucleation is rare and transformation is slow (long times, upper-left "shelf" of the C). Near $M_s$, the driving force is huge but diffusion has become sluggish, so growth is slow and transformation is again slow (long times, lower-left "shelf"). Somewhere in between — the "nose" of the curve, typically around 550 °C for a eutectoid steel — the product of a still-substantial driving force and a still-reasonable diffusivity is maximized, giving the FASTEST possible transformation and the shortest time on the diagram. Plotting time (which is minimized at the nose and rises on both sides of it) against temperature therefore traces out exactly the two-branched "C" (or "nose") shape common to every diffusional transformation curve.
