This is the Fe–Fe₃C (metastable) phase diagram from 0 to 6.70 wt% C and from 400 to 1600 °C. Click or tap the diagram, or enter a carbon content and temperature, to see the phases at that point. In a two-phase region, a tie line is drawn and the compositions of the phases at its ends and their mass fractions by the lever rule are calculated. It also shows an estimate of the room-temperature microstructure when a steel or cast iron of that carbon content is cooled slowly from high temperature. The default is a 0.40 wt% C hypoeutectoid steel held at 750 °C (the α + γ two-phase region).
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Diagram and results
Phases at the point
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Class by carbon content
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Composition and mass fraction of the phases at the point
Room-temperature microstructure after slow cooling (estimate)
The key points (eutectoid 727 °C and 0.76 wt% C, eutectic 1147 °C and 4.30 wt% C, peritectic 1495 °C, and others) follow standard textbook values, and the lines are approximated by straight lines or smooth curves through them. They may differ from the real lines by a few to a few tens of degrees, and in commercial steels containing alloying elements the lines themselves shift.
See it as a graph
Other inputs stay at their current values while the chosen input varies from 1/4 to 4 times its current value. The red dot is the current value.
How to read the Fe–Fe₃C phase diagram
The vertical axis is temperature and the horizontal axis is carbon content (wt%); the right edge at 6.70 wt% C corresponds to the iron–carbon compound cementite (Fe₃C) itself. If a point lies in a single-phase region, only that phase is stable at equilibrium. If it lies in a two-phase region, draw a horizontal line (tie line) at that temperature: its ends, where it meets the region boundaries, give the carbon contents of the two coexisting phases. The amount of each phase follows from the lever rule Wα = (Cβ − C₀)/(Cβ − Cα). Three phases can coexist only on the three horizontal lines at 1495 °C, 1147 °C and 727 °C.
The three invariant reactions and the transformation points of pure iron
At 1495 °C the peritectic reaction δ (0.09 wt% C) + L (0.53 wt% C) → γ (0.17 wt% C) occurs, and at 1147 °C the eutectic reaction L (4.30 wt% C) → γ (2.14 wt% C) + Fe₃C; the eutectic structure is called ledeburite. At 727 °C the eutectoid reaction γ (0.76 wt% C) → α (0.022 wt% C) + Fe₃C forms lamellar pearlite. Pure iron with no carbon changes between α (BCC) and γ (FCC) at 912 °C and between γ and δ (BCC) at 1394 °C, and melts at 1538 °C. The maximum carbon solubility in γ, 2.14 wt%, is the usual dividing line between steel and cast iron.
What the A1, A3 and Acm lines mean
A1 is the horizontal line at the eutectoid temperature of 727 °C; below it, austenite does not exist at equilibrium. A3 is the temperature at which ferrite starts to form from austenite in a hypoeutectoid steel; it falls from 912 °C for pure iron to 727 °C at the eutectoid point as carbon increases. Acm is the temperature at which cementite starts to form from austenite in a hypereutectoid steel; it is the carbon solubility limit of austenite and rises from 727 °C at 0.76 wt% to 1147 °C at 2.14 wt%. Heating temperatures for annealing and hardening are chosen with reference to these lines. In real heating and cooling the transformations shift from the equilibrium temperatures, so the values on heating are written Ac and those on cooling Ar.
Microstructures of hypoeutectoid, eutectoid and hypereutectoid steels
On slow cooling from austenite, a hypoeutectoid steel with less than 0.76 wt% C forms proeutectoid ferrite between crossing the A3 line and reaching 727 °C, and the remaining austenite becomes pearlite at 727 °C. For 0.40 wt% C, the lever rule gives proeutectoid ferrite (0.76 − 0.40)/(0.76 − 0.022) ≈ 48.8 % and pearlite about 51.2 %. A eutectoid steel at 0.76 wt% C becomes all pearlite. In a hypereutectoid steel, proeutectoid cementite forms on grain boundaries from the Acm line; for 1.2 wt% C it is about 7.4 % proeutectoid cementite and about 92.6 % pearlite. Pearlite itself is about 89 % ferrite and 11 % cementite by mass.
The cast iron range and ledeburite
Above 2.14 wt% C, a eutectic reaction occurs at 1147 °C at the end of solidification. A eutectic cast iron at 4.30 wt% C becomes entirely ledeburite (a mixture of γ and Fe₃C), and since the γ in it changes to pearlite at 727 °C, the room-temperature structure is called transformed ledeburite. A hypoeutectic cast iron below 4.30 wt% consists of primary γ and ledeburite, and a hypereutectic one above 4.30 wt% of primary cementite and ledeburite. Cast iron that solidifies with all its carbon as cementite in this way is white cast iron, with a white fracture surface, hard and brittle.
Metastable versus stable (graphite) systems
Strictly, cementite is a metastable phase, and the true equilibrium of iron and carbon is between Fe and graphite. In the stable Fe–graphite system, the eutectic is at about 1153 °C and about 4.2 wt% C and the eutectoid at about 738–740 °C and about 0.65–0.69 wt% C (the values differ slightly between sources), slightly higher in temperature and lower in carbon than in the metastable system. Graphite forms more easily with more Si and slower cooling, giving gray cast iron and others that contain graphite. Conversely, fast cooling or much of a carbide-forming element such as Cr or Mo favors cementite. In steels graphite usually forms with difficulty, so the Fe–Fe₃C system is used.
With fast cooling this diagram does not apply
A phase diagram shows the phases reached at equilibrium with sufficiently slow heating and cooling, and contains no information on the time transformations take. With fast cooling, as in quenching, transformations shift to temperatures below equilibrium and, with diffusion unable to keep up, nonequilibrium structures such as martensite and bainite form. These do not appear on the phase diagram, so to know which structure results you need a TTT diagram, for transformations during isothermal holding, or a CCT diagram, for transformations during continuous cooling. Treat the structures and fractions found with this diagram and the lever rule as estimates for slow cooling (annealing).
About the approximations in this diagram
The values of the key points follow those commonly used in textbooks, and the lines join these points with straight lines. Only the A3 line is a smooth curve from 912 °C to 727 °C, T = 912 − 185·(C/0.76)^0.7. This formula was chosen to pass through the two end points, and the temperatures in between (for example about 794 °C at 0.40 wt% C) are an approximation fitted to the shape of the diagram. They may differ from the real A3 by ten or more degrees, so check a published diagram when you need an exact value. The carbon solubility of α below 727 °C is a schematic showing it falling from 0.022 wt% to nearly zero. The liquidus to the right of 4.30 wt% differs widely between sources and is shown as a dashed guide. The carbon content of Fe₃C is taken as 6.70 wt% to match the other explanations and questions on this site. Sources give 6.67–6.70 wt% (about 6.69 wt% from the stoichiometry of Fe₃C), and some sources also give the eutectic as 1148 °C and the peritectic as 1493 °C. These differences change the calculated fractions only in the decimal places.
AAt about 0.76 wt% C and 727 °C, γ → α + Fe₃C occurs and pearlite forms
BAt about 4.3 wt% C and 1147 °C, L → γ + Fe₃C occurs and lamellar pearlite forms
CAt about 0.022 wt% C and 912 °C, γ → α occurs and bainite forms
Show answer and explanation
Answer: A. At about 0.76 wt% C and 727 °C, γ → α + Fe₃C occurs and pearlite forms
The eutectoid point of the Fe-Fe₃C system is at about 0.76 wt% C and 727 °C, where austenite (γ) transforms into pearlite, a lamellar structure of ferrite (α) and cementite (Fe₃C). The reaction at about 4.3 wt% C and 1147 °C is the eutectic reaction involving the liquid, and the structure it produces is ledeburite, not pearlite. 0.022 wt% C is the maximum solubility of carbon in α at 727 °C, and 912 °C is the γ → α transformation temperature of pure iron. Bainite does not appear on the equilibrium phase diagram; it is a nonequilibrium structure that forms from undercooled austenite in an intermediate temperature range. Steels with less carbon than the eutectoid composition are called hypoeutectoid, and those with more are called hypereutectoid.
Proeutectoid ferrite is the ferrite already formed in the α + γ region just above 727 °C, and all the remaining γ becomes pearlite. From the lever rule, W_proeutectoid α = (0.76 − 0.40)/(0.76 − 0.022) = 0.36/0.738 ≈ 0.49. About 0.51 is the fraction of the remaining pearlite, the mistake of taking the opposite distance. About 0.94 is the fraction of all ferrite treating the steel as the two phases α + Fe₃C, (6.70 − 0.40)/(6.70 − 0.022), which includes the ferrite inside the pearlite as well. The area ratio of proeutectoid ferrite to pearlite in a micrograph is a clue for estimating the carbon content of a hypoeutectoid steel.
In a hypereutectoid steel, with more carbon than the eutectoid composition of 0.76 wt% C, crossing the Acm line during cooling first precipitates proeutectoid cementite as a network along the austenite grain boundaries. On reaching 727 °C, the remaining austenite (about 0.76 wt% C) becomes pearlite through the eutectoid reaction, so the room-temperature microstructure is proeutectoid cementite and pearlite. Proeutectoid ferrite and pearlite is the microstructure of a hypoeutectoid steel, and pearlite alone forms in a eutectoid steel. Because a grain-boundary cementite network causes brittleness, tool steels and similar grades are given a spheroidizing anneal to make the cementite globular.
FAQ
Why can the room-temperature fractions be calculated with the values just below 727 °C?
Because below 727 °C the carbon solubility of the α phase falls only slightly even at equilibrium, so the amounts of proeutectoid ferrite and pearlite hardly change. Textbook calculations also usually use the compositions just below 727 °C.
How does the fraction of proeutectoid ferrite differ from the fraction of all ferrite phase?
Proeutectoid ferrite is the fraction of a microstructural constituent (a part distinguishable under the microscope), about 48.8 % for 0.40 wt% C. All ferrite phase is the phase fraction including the ferrite inside pearlite; with the ends at 0.022 wt% and 6.70 wt% C it is about 94 %. Which ends of the tie line you use depends on which fraction you want.
Can this diagram tell me the structure of a quenched steel?
No. Martensite is a nonequilibrium structure formed by a diffusionless transformation and does not appear on the phase diagram. The structure after quenching is considered with TTT or CCT diagrams and the cooling rate. What you can read from this diagram's A3 and Acm lines is how high to heat before quenching to make the steel austenite.
At what wt% C is the boundary between steel and cast iron?
In the Fe–Fe₃C system, the maximum carbon solubility of austenite, 2.14 wt%, is the usual guide. Below it the whole alloy can be made austenite in the solid state; above it a eutectic reaction occurs at the end of solidification. Some sources use 2.0–2.11 wt%.