5.1 — (i) Cementite fraction just above the eutectoid temperature
Given. SAE 1090 steel, $C_0=0.90$ wt% C (hypereutectoid, above the eutectoid composition $C_{eu}=0.77$ wt% C); held for a long time at a temperature just above 727 °C; ferrite solubility limit $C_\alpha=0.022$ wt% C (irrelevant here, no ferrite present); cementite composition $C_{\text{Fe}_3\text{C}}=6.67$ wt% C.
Find. The total weight fraction of cementite present at that holding temperature.
Approach. A 0.90 wt% C steel is hypereutectoid: cooling from full austenite, it enters the γ+Fe3C two-phase field on crossing the Acm boundary and precipitates PROEUTECTOID cementite continuously until it reaches 727 °C, by which point the remaining austenite has been depleted down to exactly the eutectoid composition. "Just above the eutectoid temperature, held for a long time" is therefore the equilibrium end-point of that proeutectoid-cementite formation, immediately before any pearlite has formed — apply the lever rule on the $\gamma$/Fe3C tie line at that point.
Set up the tie line just above 727°C. The two phases present are austenite at the eutectoid composition ($C_\gamma=0.77$ wt%C, since the long hold lets it fully equilibrate) and cementite ($C_{\text{Fe}_3\text{C}}=6.67$ wt%C).
Apply the lever rule for the cementite fraction:
$$W_{\text{Fe}_3\text{C}}=\dfrac{C_0-C_\gamma}{C_{\text{Fe}_3\text{C}}-C_\gamma}=\dfrac{0.90-0.77}{6.67-0.77}=\dfrac{0.13}{5.90}$$
Evaluate: $$\boxed{W_{\text{Fe}_3\text{C}}\approx0.0220=2.2\%\text{ by weight}}$$ — all of it proeutectoid (no pearlite exists yet at a temperature above 727 °C).
Final results — Question V(i)
Quantity
Value
Austenite composition on the tie line
0.77 wt% C (eutectoid)
Cementite composition
6.67 wt% C
Weight fraction cementite (just above 727 °C)
2.2%
5.2 — (ii) Microstructure after the slow cool and lengthy sub-eutectoid hold
Fig. 5.1 — Schematic microstructure after the very slow cool: a thin, continuous proeutectoid-cementite network (white) decorating the prior-austenite grain boundaries, enclosing coarse pearlite grains (dark, widely spaced lamellae, sketched as the fine parallel lines) — not fine pearlite, because the eutectoid reaction here runs to completion at a temperature only marginally below 727 °C, held for a very long time.
Cooling further and holding JUST BELOW 727 °C for a very long time lets the remaining eutectoid-composition austenite transform by the eutectoid reaction $\gamma\rightarrow\alpha+\text{Fe}_3\text{C}$ essentially at zero effective undercooling. Because the driving force is minimal that close to A1, both nucleation and growth are slow and the lamellae that do form have time to grow thick and widely spaced — the transformation produces coarse pearlite rather than the fine pearlite typical of a faster, larger-undercooling transformation. The subsequent slow cool to room temperature changes essentially nothing further (equilibrium phase amounts and the already-formed pearlite morphology are preserved). The proeutectoid cementite that had already formed above 727 °C (2.2 wt%, part (i)) does not redissolve on further cooling; it persists as a thin but continuous white network decorating the prior-austenite grain boundaries, since cementite that has already precipitated preferentially at boundaries stays there. The resulting room-temperature microstructure is therefore a thin, continuous proeutectoid-cementite grain-boundary network enclosing coarse pearlite — despite being only 2.2% of the total weight, the cementite is visually prominent because it is concentrated into a continuous boundary film rather than spread through the grain interior.
