γ austenite
α ferrite
Fe3C cementite
pearlite (α + Fe3C)
Schematic. Pearlite lamellae are drawn far thicker than real (≈ 0.1–1 µm spacing).
This simulation shows how the equilibrium microstructure of a plain-carbon steel develops as it is slowly cooled from the austenite region of the iron–iron carbide (Fe–Fe3C) phase diagram.
Set the carbon content with the slider, or select a hypoeutectoid, eutectoid, or hypereutectoid preset. Press Play to remove heat from the steel at a constant rate, or move the add/remove heat slider (left removes heat, right adds heat). Removing heat lowers the temperature except at 727 °C, where the temperature stays constant while the heat removed goes into transforming the remaining austenite to pearlite; the temperature drops again only after that transformation is complete. You can also drag the red point on the diagram to change both the temperature and the carbon content.
In a two-phase region, the tie line (black) connects the compositions of the two phases in equilibrium. The tables give the lever-rule mass fractions of the phases (α, γ, Fe3C) and of the microconstituents (proeutectoid ferrite or cementite, pearlite, and untransformed austenite). The bars show the same fractions graphically.
The carbon axis is broken between 2.2 and 6.4 wt% C so that the steel region keeps a readable scale while the cementite boundary is still drawn at its true composition, 6.70 wt% C.
The microstructure panel is a schematic of the grains at the current temperature. The area fraction of each constituent equals its mass fraction.
α-ferrite (BCC) dissolves at most 0.022 wt% C (at 727 °C); γ-austenite (FCC) dissolves up to 2.14 wt% C (at 1147 °C); cementite, Fe3C, contains 6.70 wt% C. The eutectoid point is at 0.76 wt% C and 727 °C:
\[ \gamma\,(0.76\ \text{wt}\%\text{ C}) \;\longrightarrow\; \alpha\,(0.022\ \text{wt}\%\text{ C}) + \text{Fe}_3\text{C}\,(6.70\ \text{wt}\%\text{ C}) \]For an alloy of overall composition \(C_0\) in a two-phase region, the tie line at temperature \(T\) ends at the phase compositions \(C_1\) and \(C_2\) (\(C_1 < C_2\)). The mass fractions are
\[ W_1 = \frac{C_2 - C_0}{C_2 - C_1}, \qquad W_2 = \frac{C_0 - C_1}{C_2 - C_1} \]Between A3 and 727 °C (hypoeutectoid), \(C_1 = C_\alpha\) on the α/(α + γ) boundary and \(C_2 = C_\gamma\) on the A3 line. Between Acm and 727 °C (hypereutectoid), \(C_1 = C_\gamma\) on the Acm line and \(C_2 = 6.70\). Below 727 °C, \(C_1 = C_\alpha\) on the ferrite solvus and \(C_2 = 6.70\).
Just above 727 °C, the remaining austenite has the eutectoid composition and becomes pearlite. For a hypoeutectoid steel (\(0.022 < C_0 < 0.76\)):
\[ W_{\alpha'} = \frac{0.76 - C_0}{0.76 - 0.022}, \qquad W_p = \frac{C_0 - 0.022}{0.76 - 0.022} \]For a hypereutectoid steel (\(0.76 < C_0 < 2.14\)):
\[ W_{\text{Fe}_3\text{C}'} = \frac{C_0 - 0.76}{6.70 - 0.76}, \qquad W_p = \frac{6.70 - C_0}{6.70 - 0.76} \]Pearlite itself is ferrite and cementite in the ratio
\[ W_{\alpha,\,p} = \frac{6.70 - 0.76}{6.70 - 0.022} = 0.889, \qquad W_{\text{Fe}_3\text{C},\,p} = 0.111 \]which sets the relative thickness of the lamellae in the microstructure panel.
The boundaries are smooth fits to the standard Fe–Fe3C diagram (\(C\) in wt%, \(T\) in °C):
\[ \text{A}_3:\;\; T = 912 - 320.6\,C + 101.6\,C^2 \] \[ \text{A}_{cm}:\;\; T = 727 + 359.6\,(C - 0.76) - 40\,(C - 0.76)^2 \]The carbon axis is broken between 2.2 and 6.4 wt% C so that the steel region keeps a readable scale while the cementite boundary is still drawn at its true composition, 6.70 wt% C.
The α/(α + γ) boundary is taken as a straight line from 0 wt% C at 912 °C to 0.022 wt% C at 727 °C. Below 727 °C the ferrite solvus is approximated by \(C_\alpha = 0.022\,[(T - 400)/327]^{1.5}\).
The add/remove heat slider sets the heat content of the steel, not its temperature. Removing heat \(\delta Q\) per unit mass either lowers the temperature or transforms austenite:
\[ \delta Q = -c_p\,\delta T + \Delta H_t\,\delta W_{\text{tr}} \]where \(W_{\text{tr}}\) is the mass fraction of the steel that has transformed from austenite (proeutectoid constituent plus pearlite). In the single-phase austenite region and below 727 °C, nothing transforms, so all the heat removed lowers the temperature. Between A3 (or Acm) and 727 °C, part of the heat removed is released by the growing proeutectoid ferrite (or cementite), so the temperature drops more slowly for the same heat removal. At 727 °C the eutectoid reaction occurs at constant temperature (\(\delta T = 0\)), so the heat that must be removed before the temperature can drop again is
\[ Q_e = \Delta H_t\,W_p \]The temperature arrest at 727 °C is therefore longest for the eutectoid steel (\(W_p = 1\)) and shorter for steels that form more proeutectoid ferrite or cementite. The simulation uses a constant \(c_p\) and \(\Delta H_t / c_p = 120\) °C (an approximate value), with the same \(\Delta H_t\) for the proeutectoid and eutectoid transformations.
Austenite grains are Voronoi cells. Proeutectoid ferrite or cementite forms at the austenite grain boundaries and grows inward, and pearlite then grows from the interfaces into the remaining austenite. The area of each constituent is set equal to its mass fraction; the densities of ferrite (7.87 g/cm³) and cementite (7.69 g/cm³) are close enough that area and mass fractions nearly coincide. The lamellar spacing is drawn much larger than in real pearlite (about 0.1 to 1 µm). Cooling is assumed slow enough to maintain equilibrium, so bainite and martensite do not form.
| \(C\) | carbon content (wt% C) |
| \(C_0\) | overall carbon content of the steel (wt% C) |
| \(C_1,\ C_2\) | compositions at the left and right ends of a tie line (wt% C) |
| \(C_\alpha\) | carbon content of ferrite in equilibrium (wt% C) |
| \(C_\gamma\) | carbon content of austenite in equilibrium (wt% C) |
| \(T\) | temperature (°C) |
| \(Q\) | heat removed per unit mass of steel |
| \(Q_e\) | heat removed at 727 °C during the eutectoid reaction |
| \(c_p\) | heat capacity per unit mass |
| \(\Delta H_t\) | latent heat released per unit mass of austenite transformed |
| \(W_{\text{tr}}\) | mass fraction transformed from austenite |
| \(W_1,\ W_2\) | mass fractions of the phases at the two ends of a tie line |
| \(W_{\alpha'}\) | mass fraction of proeutectoid ferrite |
| \(W_{\text{Fe}_3\text{C}'}\) | mass fraction of proeutectoid cementite |
| \(W_p\) | mass fraction of pearlite |
| \(W_{\alpha,\,p},\ W_{\text{Fe}_3\text{C},\,p}\) | mass fractions of ferrite and cementite within pearlite |
| \(\alpha\) | ferrite (BCC iron) |
| \(\gamma\) | austenite (FCC iron) |
| Fe3C | cementite (iron carbide, 6.70 wt% C) |
| L | liquid (molten iron–carbon solution); present only above 1147 °C in this carbon range |
| A1 | eutectoid temperature line (727 °C) |
| A3 | upper boundary of the α + γ region |
| Acm | upper boundary of the γ + Fe3C region |
This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.
Schematic. Pearlite lamellae are drawn far thicker than real (≈ 0.1–1 µm spacing).