Iron – Iron Carbide diagram and Heat Treatment of Steels

The Fe-Fe$_3$C diagram shows the phases of plain carbon steels and cast irons against carbon content (0 to 6.67 wt% C, where Fe$_3$C cementite forms) and temperature, under slow cooling.

 T(C)   (schematic)
 1538 +   Liquid (L)
 1495 +-- delta / peritectic (0.17%C)
 1147 +--- L + g ---- eutectic (4.3%C) -- L+Fe3C
      |  Austenite (g)   g+Fe3C   Ledeburite
  912 +-- a+g
  727 +--- eutectoid (0.76%C) ------------------
      |  Ferrite+pearlite | Pearlite+Fe3C | Cast
      +-----|-------|---------|-------|-----> %C
          0.022   0.76      2.14    4.3    6.67

Phases

• Ferrite ($\alpha$): interstitial solid solution of C in BCC iron, max 0.022% C at 727 °C. Soft, ductile.
• Austenite ($\gamma$): C in FCC iron, max 2.14% C at 1147 °C. Non-magnetic, ductile, stable above 727 °C.
• $\delta$-ferrite: C in BCC iron, up to 0.09% C at 1495 °C.
• Cementite (Fe$_3$C): hard, brittle compound with 6.67% C.
• Liquid (L).

Invariant reactions

Critical lines: A$_1$ (727 °C), A$_3$ (GOS line, ferrite starts to form), A$_{cm}$ (SE line, cementite starts to form from austenite).

Classification by carbon

• Steel: up to 2.14% C (hypoeutectoid below 0.76, hypereutectoid 0.76-2.14).
• Cast iron: 2.14-6.67% C (hypoeutectic below 4.3, hypereutectic above).

Applications

• Selecting austenitising temperatures for annealing, normalising, hardening.
• Predicting microstructure and phase fractions with the lever rule.
• Understanding properties of steels and cast irons, and welding behaviour.

Limitations

• It is an equilibrium diagram (very slow cooling); real heat treatment produces non-equilibrium phases such as martensite and bainite, which do not appear on it.
• Alloying elements (Cr, Ni, Mn) shift transformation temperatures and the eutectoid composition; the diagram is valid only for plain carbon steel.
• It gives no information about the rate of transformation (TTT/CCT diagrams are needed).
• Cementite is actually metastable; graphite is the stable phase (Fe-C diagram).

Notes

• Pearlite forms when austenite of 0.76% C cools slowly through 727 °C: $\gamma \rightarrow \alpha + \text{Fe}_3\text{C}$. Lamellar spacing decreases with faster cooling.
• Martensite forms by a diffusionless shear transformation when austenite is cooled faster than the critical cooling rate, below the $M_s$ temperature. Carbon is trapped, distorting the lattice into BCT, which gives hardness. It is tempered to improve toughness.
• Other constituent: bainite (fine ferrite + carbide formed between about 250 and 550 °C), ledeburite (eutectic of austenite and cementite in cast iron).

Cooling path

1. At 950 °C the structure is 100% austenite ($\gamma$) of 0.4% C.
2. On cooling to the A$_3$ line (about 790 °C), pro-eutectoid (primary) ferrite nucleates at austenite grain boundaries. The remaining austenite is enriched in carbon.
3. Between A$_3$ and 727 °C more ferrite forms; austenite composition follows the GOS line toward 0.76% C.
4. Just above 727 °C the austenite has 0.76% C. At 727 °C it transforms by the eutectoid reaction $\gamma \rightarrow \alpha + \text{Fe}_3\text{C}$ into pearlite.
5. Below 727 °C: pro-eutectoid ferrite + pearlite, little change on cooling to room temperature.

 950C: austenite     ->  790C: ferrite at grain boundaries
 +-----------+            +-----------+
 | gamma     |            |f gamma  f |
 +-----------+            +-----------+
 727C and below: ferrite (white) + pearlite (dark)

Phase fractions just below 727 °C

Pro-eutectoid ferrite (using tie line from 0.4 to 0.76 and 0.022):

$$W_{\alpha'} = \frac{0.76 - 0.40}{0.76 - 0.022} = \frac{0.36}{0.738} = 0.488$$

Pearlite (formed from the remaining austenite):

$$W_{P} = \frac{0.40 - 0.022}{0.76 - 0.022} = \frac{0.378}{0.738} = 0.512$$

Total ferrite and cementite (phases, including those inside pearlite):

$$W_{\alpha} = \frac{6.67 - 0.40}{6.67 - 0.022} = \frac{6.27}{6.648} = 0.943$$ $$W_{Fe_3C} = \frac{0.40 - 0.022}{6.67 - 0.022} = \frac{0.378}{6.648} = 0.057$$

Answer: 48.8% pro-eutectoid ferrite and 51.2% pearlite; total phases 94.3% ferrite and 5.7% cementite.

Microstructure development

1. At high temperature the alloy is austenite of 1.2% C.
2. On cooling to the A$_{cm}$ line (about 900 °C for 1.2% C), austenite becomes saturated with carbon and pro-eutectoid cementite precipitates, mostly as a network along the austenite grain boundaries.
3. The remaining austenite loses carbon and reaches 0.76% C at 727 °C.
4. At 727 °C it transforms to pearlite.
5. Room-temperature structure: cementite network + pearlite. The network makes the steel hard and brittle, which is why such steels are spheroidise-annealed.

Lever rule (just below 727 °C)

Pro-eutectoid cementite (tie line 0.76 to 6.67):

$$W_{Fe_3C'} = \frac{1.20 - 0.76}{6.67 - 0.76} = \frac{0.44}{5.91} = 0.0745$$

Pearlite:

$$W_{P} = \frac{6.67 - 1.20}{6.67 - 0.76} = \frac{5.47}{5.91} = 0.9255$$

(b) In 1 kg

Pro-eutectoid cementite = 0.0745 kg = 74.5 g; pearlite = 0.9255 kg = 925.5 g.

(c) Total phases

$$W_{Fe_3C} = \frac{1.20 - 0.022}{6.67 - 0.022} = \frac{1.178}{6.648} = 0.1772 \quad (177.2\ \text{g})$$ $$W_{\alpha} = 1 - 0.1772 = 0.8228 \quad (822.8\ \text{g})$$

Answer: pro-eutectoid cementite 7.45%, pearlite 92.55%; per kg: 74.5 g cementite network + 925.5 g pearlite; total ferrite 822.8 g and total cementite 177.2 g.

Cooling path

1. Above the liquidus, the alloy is liquid.
2. Between the liquidus and 1147 °C, primary austenite dendrites separate; the liquid becomes richer in carbon, reaching 4.3% C at 1147 °C.
3. At 1147 °C the remaining liquid undergoes the eutectic reaction $L \rightarrow \gamma + \text{Fe}_3\text{C}$, giving ledeburite.
4. Below 1147 °C, the austenite loses carbon as secondary cementite and at 727 °C reaches 0.76% C and transforms to pearlite.
5. At room temperature: pearlite (dendrites) + cementite + transformed ledeburite. The structure is hard and brittle white cast iron.

Fractions just above 1147 °C

Primary austenite (tie line 2.14 to 4.3):

$$W_{\gamma'} = \frac{4.3 - 3.0}{4.3 - 2.14} = \frac{1.3}{2.16} = 0.602$$

Liquid, which becomes ledeburite:

$$W_{L} = \frac{3.0 - 2.14}{4.3 - 2.14} = \frac{0.86}{2.16} = 0.398$$

Phases just below 1147 °C

Total cementite (tie line 2.14 to 6.67):

$$W_{Fe_3C} = \frac{3.0 - 2.14}{6.67 - 2.14} = \frac{0.86}{4.53} = 0.190$$ $$W_{\gamma} = 1 - 0.190 = 0.810$$

Answer: primary austenite 60.2% and ledeburite 39.8%; just below 1147 °C austenite 81.0% and cementite 19.0%.

Method: compare volume per atom in the two structures.

BCC has 2 atoms per cell and FCC has 4 atoms per cell.

Volume per atom

$$V_{BCC} = \frac{a^3}{2} = \frac{(0.2903)^3}{2} = \frac{0.02446}{2} = 0.012232\ \text{nm}^3$$ $$V_{FCC} = \frac{a^3}{4} = \frac{(0.3647)^3}{4} = \frac{0.04851}{4} = 0.012127\ \text{nm}^3$$

Volume change

$$\Delta V\% = \frac{V_{FCC} - V_{BCC}}{V_{BCC}}\times100 = \frac{0.012127 - 0.012232}{0.012232}\times 100 = -0.86\%$$

The negative sign means a contraction of about 0.86% on heating through 912 °C (and an expansion on cooling).

Atomic radius

$$R_{BCC} = \frac{\sqrt3\, a}{4} = \frac{1.732 \times 0.2903}{4} = 0.1257\ \text{nm}$$ $$R_{FCC} = \frac{\sqrt2\, a}{4} = \frac{1.414 \times 0.3647}{4} = 0.1289\ \text{nm}$$

The FCC structure is denser (APF 0.74 against 0.68) but the atom appears larger because of coordination 12 against 8; the net effect is a small contraction.

Practical effect

When steel cools through the $\gamma\rightarrow\alpha$ change, the volume change causes distortion and internal stresses, and in quenching can lead to cracking. Also, since FCC iron dissolves much more carbon (2.14% against 0.022%), steel is austenitised before hardening.

Answer: volume contraction of 0.86% on $\alpha\rightarrow\gamma$; $R_{BCC} = 0.1257$ nm, $R_{FCC} = 0.1289$ nm.

Heat treatment is controlled heating and cooling of a solid metal to obtain desired properties.

Notes

• Annealing gives the softest, most ductile state. Spheroidise annealing (just below $A_1$ for a long time) turns lamellar cementite into spheres in high-carbon steel.
• Normalised steel is stronger and harder than annealed, because air cooling is faster, giving finer pearlite.
• Hardening needs the cooling rate to exceed the critical cooling rate so that austenite transforms to martensite without diffusion. Hardenability depends on carbon and alloy content. Retained austenite and cracking can occur in high-carbon steels.
• Tempering allows carbon to precipitate as fine carbide. Low tempering (150-250 °C) keeps hardness for tools; medium (350-450 °C) gives spring steel; high (500-650 °C) gives tough, strong shafts and bolts (quench plus high temper is called hardening and tempering).

 T
 A3 ----- ---- hardening/annealing/normalising
 A1 ---------------------
         tempering (below A1)
 time -->