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7.2 Iron-Carbon Equilibrium Phase Diagram & Heat Treatment Processes

Key Takeaways

  • Gibbs Phase Rule at constant atmospheric pressure (condensed system) is $F = C - P + 1$, which dictates the number of independent thermodynamic degrees of freedom $F$ available in equilibrium phase mixtures.
  • The Iron-Iron Carbide ($Fe-Fe_3C$) system features three invariant reactions: Eutectic at $4.30\% C, 1148^\circ\text{C}$ ($L \rightleftharpoons \gamma + Fe_3C$), Eutectoid at $0.76\% C, 727^\circ\text{C}$ / $1341^\circ\text{F}$ ($\\gamma \rightleftharpoons \alpha + Fe_3C$), and Peritectic at $0.16\% C, 1493^\circ\text{C}$ ($\\delta + L \rightleftharpoons \gamma$).
  • Martensite forms via a diffusionless, athermal, shear transformation of austenite, resulting in a highly strained Body-Centered Tetragonal (BCT) lattice with extreme hardness and high brittleness.
  • Tempering consists of reheating as-quenched martensite strictly below the $A_1$ lower critical temperature ($150-650^\circ\text{C}$) to precipitate fine transition carbides, relieving internal residual stresses and restoring ductility and fracture toughness.
  • Hardenability (measured by the standard Jominy End-Quench test) represents the depth and profile to which a steel can transform to martensite upon quenching and depends on alloying elements (Cr, Mo, Ni, Mn, B), whereas maximum achievable surface hardness depends solely on carbon content.
Last updated: August 2026

Iron-Carbon Equilibrium Phase Diagram & Heat Treatment Processes

Thermal processing and heat treatment allow mechanical engineers to tailor the microstructure, tensile strength, ductility, and fracture toughness of steel components. The NCEES PE Mechanical exam regularly tests the thermodynamics of phase equilibrium (lever rule and Gibbs phase rule), invariant reactions on the iron-carbon phase diagram, continuous cooling transformation (CCT) diagrams, and case hardening methods.

1. Equilibrium Phase Diagrams & Gibbs Phase Rule

An equilibrium phase diagram graphically displays the thermodynamically stable phases present in an alloy system as a function of temperature, pressure, and chemical composition.

Gibbs Phase Rule (Condensed System at Constant 1 atm Pressure)

F=C−P+1F = C - P + 1

Where:

  • $F = \text{number of degrees of freedom (independent variables: temperature, composition)}$

  • $C = \text{number of chemical components (for binary alloys, } C = 2\text{)}$

  • $P = \text{number of phases coexisting at equilibrium}$

  • In a single-phase field ($P = 1$): $F = 2 - 1 + 1 = 2$ (both temperature and composition can vary independently).

  • In a two-phase field ($P = 2$): $F = 2 - 2 + 1 = 1$ (fixing temperature automatically fixes the compositions of both phases along the tie line).

  • At an invariant point ($P = 3$): $F = 2 - 3 + 1 = 0$ (three phases coexist at an exact fixed temperature and composition).

The Lever Rule for Phase Mass Fractions

In any two-phase region (e.g., $\alpha + L$ or $\alpha + Fe_3C$), constructing a horizontal isothermal tie line between the phase boundary limits ($w_\alpha$ and $w_L$) allows calculating the weight fraction of each phase:

+---------------------------------------------------------------------------------------------------------+
|                                      THE LEVER RULE TIE-LINE GEOMETRY                                   |
|                                                                                                         |
|   Temperature                                                                                           |
|        ^                                                                                                |
|        |        Liquidus Line                                                                           |
|        |       \                                                                                        |
|        |        \  (Tie line at T_0)                                                                    |
|   T_0  +---------[ w_alpha ]----------[ w_0 ]-------------------------[ w_L ]----                       |
|        |             |<--- (w_0 - w_alpha) --->|<------ (w_L - w_0) ----->|                             |
|        |             |<------------------- (w_L - w_alpha) -------------->|                             |
|        +-------------+-------------------------+----------------------+------------------> Weight % C   |
|                     w_alpha                   w_0                    w_L                                |
+---------------------------------------------------------------------------------------------------------+

Wα=wL−w0wL−wαandWL=w0−wαwL−wαW_\alpha = \frac{w_L - w_0}{w_L - w_\alpha} \quad \text{and} \quad W_L = \frac{w_0 - w_\alpha}{w_L - w_\alpha}

2. The Iron-Iron Carbide ($Fe-Fe_3C$) Phase Diagram

The iron-carbon system forms the metallurgical basis for all carbon and low-alloy steels ($<2.14% C$) and cast irons ($2.14% - 6.70% C$).

+---------------------------------------------------------------------------------------------------------+
|                              SIMPLIFIED Fe-Fe3C PHASE DIAGRAM (0 to 6.70% C)                            |
|                                                                                                         |
|   Temp (C)                                                                                              |
|     1600+                                                                                               |
|     1538|--\ Delta                                                                                      |
|     1493|   +-- Peritectic (0.16% C)   Liquid (L)                                                       |
|         |    \                                              /                                           |
|     1200|     \   Austenite (gamma)                       /                                             |
|     1148+------+------------------+---------------------+----------------------                         |
|         |      |                  |   gamma + Fe3C      | Eutectic (4.30% C): L -> gamma + Fe3C        |
|         |      | (Max sol: 2.14%) |                     | Ledeburite                                   |
|      912|--\   |                  |                     |                                              |
|         |   \  |                  |                     |                                              |
|      727+----+--+------------------+---------------------+---------------------- A1 (Lower Critical)    |
|         |alpha| alpha + Fe3C      | Eutectoid (0.76% C): gamma -> alpha + Fe3C (Pearlite)               |
|         |     | (Hypoeutectoid)   | (Hypereutectoid)    |                                              |
|        0+-----+-------------------+---------------------+----------------------+-----> Weight % Carbon |
|         0   0.022%              0.76%                 2.14%                  4.30%           6.70%      |
|             (Ferrite)          (Eutectoid)          (Steel / Cast Iron)     (Eutectic)    (Cementite)   |
+---------------------------------------------------------------------------------------------------------+

Primary Phases in the $Fe-Fe_3C$ System

Phase NameCrystal StructureMaximum Carbon SolubilityMechanical Characteristics
Ferrite ($\alpha$)Body-Centered Cubic (BCC)$0.022% C$ at $727^\circ\text{C}$ ($0.008% C$ at room temp)Soft, ductile, magnetic below Curie point ($770^\circ\text{C}$). Yield strength $\approx 150 \text{ MPa}$, elongation $\approx 30%$.
Austenite ($\gamma$)Face-Centered Cubic (FCC)$2.14% C$ at $1148^\circ\text{C}$Ductile, non-magnetic, dense interstitial packing. Stable only above $727^\circ\text{C}$ in plain carbon steels.
Cementite ($Fe_3C$)Orthorhombic IntermetallicFixed $6.70% C$ by weight ($25% C$ atomic)Extremely hard ($>60$ HRC, $>800$ HV) and brittle. High wear resistance.
Delta-Ferrite ($\delta$)Body-Centered Cubic (BCC)$0.09% C$ at $1493^\circ\text{C}$High-temperature solid solution ($1394^\circ\text{C} - 1538^\circ\text{C}$).

The Three Invariant Reactions

Reaction TypeTemperatureCompositionReaction Equation & Resulting Microstructure
Eutectoid$727^\circ\text{C}$ ($1341^\circ\text{F}$)$0.76% C$$\gamma (0.76% C) \rightleftharpoons \alpha (0.022% C) + Fe_3C (6.70% C)$<br/>Pearlite: Alternating lamellae (plates) of ferrite and cementite.
Eutectic$1148^\circ\text{C}$ ($2098^\circ\text{F}$)$4.30% C$$L (4.30% C) \rightleftharpoons \gamma (2.14% C) + Fe_3C (6.70% C)$<br/>Ledeburite: Solidified cast iron eutectic matrix.
Peritectic$1493^\circ\text{C}$ ($2719^\circ\text{F}$)$0.16% C$$\delta (0.09% C) + L (0.53% C) \rightleftharpoons \gamma (0.16% C)$

Critical Temperatures: $A_1$, $A_3$, $A_{cm}$

  • $A_1$ (Lower Critical Temperature): $727^\circ\text{C}$ ($1341^\circ\text{F}$) — Eutectoid line where austenite begins to transform to pearlite.
  • $A_3$ (Upper Critical Temperature for Hypoeutectoid Steels, $<0.76% C$): Boundary between $\gamma$ and $\alpha + \gamma$ regions.
  • $A_{cm}$ (Upper Critical Temperature for Hypereutectoid Steels, $>0.76% C$): Boundary between $\gamma$ and $\gamma + Fe_3C$ regions.

3. Microstructures: Pearlite, Bainite & Martensite

+---------------------------------------------------------------------------------------------------------+
|                                 TRANSFORMATION MICROSTRUCTURES SUMMARY                                  |
|                                                                                                         |
|   MICROSTRUCTURE        TRANSFORMATION TYPE      MORPHOLOGY                      HARDNESS & TOUGHNESS   |
|   -------------------   ---------------------    ----------------------------    --------------------   |
|   Coarse Pearlite       Diffusion (High T: 650C) Thick alternating alpha/Fe3C    Moderate (15-20 HRC)   |
|   Fine Pearlite         Diffusion (Med T: 550C)  Thin alternating alpha/Fe3C     Higher (25-30 HRC)     |
|   Upper Bainite         Diffusion (400-550C)     Feathery cementite in ferrite   Tough, 35-45 HRC       |
|   Lower Bainite         Diffusion (250-400C)     Fine acicular needles           Very tough, 45-55 HRC  |
|   Martensite            Diffusionless Athermal   Needle-like / Lath BCT          Extreme hardness, 65HRC|
|   Tempered Martensite   Diffusional Tempering    Submicroscopic carbide dots     High strength + tough  |
+---------------------------------------------------------------------------------------------------------+

The Martensitic Transformation

When austenite is rapidly cooled (quenched) below the Martensite Start ($M_s$) temperature, carbon atoms are trapped in solution because there is insufficient time for carbon diffusion. The FCC lattice undergoes an instantaneous shear deformation into a distorted Body-Centered Tetragonal (BCT) lattice.

  • Athermal Transformation: The extent of transformation depends only on the temperature reached below $M_s$, not on holding time.
  • Properties: Extremely high hardness and yield strength, but high residual stresses and severe brittleness ($0% EL$). As-quenched martensite cannot be put directly into engineering service without tempering.

4. Bulk Heat Treatment Processes for Steels

+---------------------------------------------------------------------------------------------------------+
|                                       BULK HEAT TREATMENT PROCESSES                                     |
|                                                                                                         |
|   [ AUSTENITIZING ] Reheat steel above critical line (A3 or A1) to form 100% gamma                     |
|           |                                                                                             |
|           +-------------------+-------------------+-------------------+                         |
|           |                   |                   |                   |                         |
|           v                   v                   v                   v                         |
|   [ FULL ANNEALING ]   [ NORMALIZING ]      [ QUENCHING ]      [ AUSTEMPERING ]                 |
|   - Furnace cool       - Still air cool     - Rapid water/oil  - Isothermal quench in           |
|   - Very slow cooling  - Moderate cooling   - 100% Martensite    molten salt (300-400C)         |
|   - Coarse pearlite    - Fine pearlite      - Hard & brittle   - 100% Lower Bainite             |
|   - Softest, machinable- Uniform grain size        |           - High strength + no distortion  |
|                                                    v                                            |
|                                              [ TEMPERING ]                                      |
|                                              - Reheat at 150-650C (below A1)                    |
|                                              - Tempered Martensite                              |
|                                              - Restores ductility & toughness                   |
+---------------------------------------------------------------------------------------------------------+

Comparison of Heat Treatment Regimes

Heat Treatment ProcessHeating TemperatureCooling MethodResulting Microstructure & Goal
Full Annealing$30-50^\circ\text{C}$ above $A_3$ (hypo) or above $A_1$ (hyper)Slow furnace cooling ($<10-30^\circ\text{C/hr}$)Coarse pearlite + proeutectoid ferrite/cementite. Minimum hardness, maximum ductility, relieves internal stress for heavy machining or forming.
Normalizing$50^\circ\text{C}$ above $A_3$ (hypo) or above $A_{cm}$ (hyper)Cooling in still airFine pearlite. Produces a uniform, refined equiaxed grain structure with higher yield strength than annealed steel.
Quenching$30-50^\circ\text{C}$ above $A_3$ (hypo) or $A_1$ (hyper)Rapid immersion in water, brine, or agitated oil100% Martensite. Maximum attainable hardness; requires immediate tempering.
Tempering$150^\circ\text{C} - 650^\circ\text{C}$ (strictly below $A_1$)Air cool after soakTempered martensite (ferrite matrix with uniformly dispersed nano-carbide precipitates). Restores fracture toughness and relieves quench stress.
AustemperingAbove $A_3$, then rapid quench into molten salt bath at $300-400^\circ\text{C}$, held until transformation finishesAir cool to room temp100% Bainite. Outstanding impact toughness and high strength without quench cracking.
Martempering (Marquenching)Above $A_3$, rapid quench to molten salt bath just above $M_s$, equalized in temperature, then air cooledSlow air cool through $M_s - M_f$ rangeUntempered martensite with minimal residual stress and near-zero dimensional distortion; followed by tempering.

5. Surface & Case Hardening Methods

For components requiring a wear-resistant surface combined with a tough, shock-absorbing core (such as gears, camshafts, and bearing races), case hardening processes are employed:

+---------------------------------------------------------------------------------------------------------+
|                                        CASE HARDENING TECHNIQUES                                        |
|                                                                                                         |
|   1. CARBURIZING           Low-carbon steel (0.15-0.25% C) heated in carbon-rich gas/pack at 900-950C.  |
|                            Carbon diffuses into surface (up to 1.0% C). Subsequent quench & temper      |
|                            yields hard high-carbon martensite case with tough low-carbon core.          |
|   2. NITRIDING             Alloy steel (containing Al, Cr, Mo, V) heated in ammonia gas at 500-550C     |
|                            (BELOW A1!). Nitrogen forms ultra-hard alloy nitrides (65-70 HRC). Zero      |
|                            quenching required -> virtually ZERO dimensional distortion!                 |
|   3. CARBONITRIDING        Simultaneous diffusion of carbon and nitrogen at 750-850C followed by quench.|
|   4. FLAME HARDENING       Oxy-acetylene flame heats surface of medium-carbon steel (0.4-0.6% C) above   |
|                            A3, followed immediately by water spray quench and temper.                   |
|   5. INDUCTION HARDENING   High-frequency eddy currents heat surface layer via induction coil, followed |
|                            by immediate water quench. Ideal for high-volume shafts and gear teeth.      |
+---------------------------------------------------------------------------------------------------------+

6. Hardenability & The Jominy End-Quench Test

It is vital to distinguish between hardness and hardenability:

  • Hardness: The maximum resistance to localized indentation. In steels, maximum surface hardness depends almost exclusively on Carbon content (e.g., $0.60% C$ can reach $\approx 65$ HRC regardless of alloy additions).
  • Hardenability: The capability of an alloy steel to transform to martensite at a given depth beneath the surface upon quenching. Hardenability depends on alloying additions (Manganese, Chromium, Molybdenum, Nickel, Boron), which retard the formation of pearlite and bainite, shifting the TTT nose to longer times.
+---------------------------------------------------------------------------------------------------------+
|                                 JOMINY END-QUENCH TEST SCHEMATIC & CURVES                               |
|                                                                                                         |
|   [ 1" Dia x 4" Specimen ]                               Hardness (HRC)                                 |
|   Austenitized at ~850C                                       ^                                         |
|           |                                                60 +=======------------ (4340 High Alloy)   |
|           v                                                50 |       \                                 |
|   [ WATER JET QUENCH ]                                     40 |        \                                |
|   (Chills bottom end only)                                 30 |         \--------- (4140 Med Alloy)     |
|   - End: Fastest cooling rate (Martensite)                 20 |          \                              |
|   - Top: Slowest cooling rate (Pearlite)                   10 |           \_______ (1045 Plain Carbon)  |
|                                                             0 +----+----+----+----> Distance from       |
|                                                               0    4    8   12     Quenched End (1/16") |
+---------------------------------------------------------------------------------------------------------+

7. Step-by-Step Worked Problem: Lever Rule & Phase Calculations

Problem Statement

A hypoeutectoid plain carbon steel containing $0.40\text{ wt% C}$ (AISI 1040) is cooled under equilibrium conditions from the austenite region ($900^\circ\text{C}$) to just below the eutectoid temperature ($727^\circ\text{C} - \Delta T$).

Given the phase boundary compositions at $727^\circ\text{C}$:

  • Eutectoid carbon composition: $w_{\text{eutectoid}} = 0.76% C$
  • Maximum ferrite solubility: $w_\alpha = 0.022% C$
  • Cementite stoichiometric composition: $w_{Fe_3C} = 6.70% C$

Calculate:

  1. The mass fraction of proeutectoid ferrite ($W_{\alpha,\text{pro}}$) and austenite ($W_\gamma$) just above $727^\circ\text{C}$.
  2. The mass fraction of total ferrite ($W_{\alpha,\text{total}}$) and total cementite ($W_{Fe_3C,\text{total}}$) just below $727^\circ\text{C}$.
  3. The mass fraction of pearlite ($W_{\text{pearlite}}$) in the final room temperature microstructure.
+---------------------------------------------------------------------------------------------------------+
|                                     STEP-BY-STEP SOLUTION PROCEDURE                                     |
|                                                                                                         |
|   STEP 1: Proeutectoid Ferrite & Austenite Fractions Just Above 727 deg C                               |
|           Apply the lever rule across the tie line from w_alpha (0.022%) to w_gamma (0.76%):            |
|           W_{alpha,pro} = (0.76 - 0.40) / (0.76 - 0.022) = 0.360 / 0.738 = 0.4878 (48.78%)             |
|           W_gamma       = (0.40 - 0.022) / (0.76 - 0.022) = 0.378 / 0.738 = 0.5122 (51.22%)             |
|                                                                                                         |
|   STEP 2: Total Ferrite & Total Cementite Fractions Just Below 727 deg C                                |
|           Apply the lever rule across the entire tie line from w_alpha (0.022%) to w_Fe3C (6.70%):      |
|           W_{alpha,total} = (6.70 - 0.40) / (6.70 - 0.022) = 6.300 / 6.678 = 0.9434 (94.34%)           |
|           W_{Fe3C,total}  = (0.40 - 0.022) / (6.70 - 0.022) = 0.378 / 6.678 = 0.0566 (5.66%)            |
|                                                                                                         |
|   STEP 3: Final Microstructural Constituents                                                            |
|           All austenite present at 727 deg C transforms into pearlite:                                  |
|           W_{pearlite} = W_gamma = 51.22%                                                               |
|           Total Microstructure = 48.78% Proeutectoid Ferrite + 51.22% Pearlite                          |
+---------------------------------------------------------------------------------------------------------+

8. Common Exam Traps & PE Pro-Tips

  • Trap 1 — Total Ferrite vs. Proeutectoid Ferrite: Proeutectoid ferrite is only the ferrite that nucleated above $727^\circ\text{C}$ along austenite grain boundaries. Total ferrite includes both proeutectoid ferrite and the eutectoid ferrite plates contained inside the pearlite colonies.
  • Trap 2 — Hardness vs. Hardenability Confusion: Adding molybdenum, chromium, or nickel to a $0.20% C$ steel will not increase its maximum achievable surface hardness (still $\approx 45$ HRC), but it will dramatically increase the depth of hardening (hardenability).
  • Trap 3 — Distortion in Case Hardening: Gas nitriding is performed below $A_1$ ($500-550^\circ\text{C}$) with no subsequent quench, producing negligible dimensional distortion. In contrast, carburizing requires austenitizing at $925^\circ\text{C}$ followed by severe liquid quenching, causing significant volumetric distortion.
Test Your Knowledge

Applying Gibbs phase rule for a condensed binary alloy system at constant atmospheric pressure (F = C - P + 1), how many thermodynamic degrees of freedom exist at an invariant eutectic reaction point where Liquid, Austenite, and Cementite coexist at equilibrium?

A
B
C
D
Test Your Knowledge

Which heat treatment process involves heating a hypoeutectoid carbon steel 30-50 deg C above the upper critical line (A3), soaking, and then allowing it to cool slowly inside the furnace to achieve maximum ductility and lowest hardness?

A
B
C
D
Test Your Knowledge

A gear manufacturer needs to surface-harden precision finished alloy steel transmission pinions without causing quench distortion or dimensional warping. Which case-hardening process is most appropriate?

A
B
C
D
Test Your Knowledge

Which alloying addition primarily enhances the hardenability of alloy steels by delaying the diffusional transformation of austenite to pearlite/bainite?

A
B
C
D
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