Qwestrum Engineering360 · Mechanical Engineering · Iron-Carbon Diagram
Invariant Reactions
The Fe-C diagram has three invariant reactions: eutectoid γ(0.76 %C) → α + Fe₃C at 727 °C, eutectic L(4.3 %C) → γ + Fe₃C at 1147 °C, and peritectic at 1493 °C. Each occurs at fixed T and composition, per physical-metallurgy texts.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.
Key formulas & points
Skim these first — then read the full notes below.
- Invariant = fixed T, fixed composition, three phases
- Eutectoid produces pearlite lamellae (α + Fe₃C plates)
- Cooling rate affects lamellar spacing in pearlite
Topic details
Introduction
Invariant reactions are the fixed-temperature, fixed-composition transformations that shape steel and cast-iron microstructures. This entry focuses on the three invariant points of the iron-carbon system.
Scope in B.Tech and GATE syllabus
The eutectoid reaction (solid → two solids) at 727 °C produces pearlite and governs all steel heat treatment. The eutectic (liquid → two solids) at 1147 °C produces ledeburite in cast irons. The peritectic (liquid + solid → new solid) at 1493 °C matters in low-carbon solidification.
Why this topic matters in practice
At an invariant point the phase rule gives zero degrees of freedom (three phases coexist at constant pressure), so temperature and compositions are all fixed. Identifying the reaction type, temperature, and composition is the exam demand.
Key relations & formulas
Formulas (Indian textbook notation)
Formulas (Indian textbook notation)
Formulas (Indian textbook notation)
Formulas (Indian textbook notation)
Notation and sign conventions
Relation 1 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Metallurgical Thermodynamics — Dekkar before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Metallurgical Thermodynamics — Dekkar before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Metallurgical Thermodynamics — Dekkar before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 4 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Metallurgical Thermodynamics — Dekkar before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Fundamentals and definitions
An invariant reaction involves three phases in equilibrium; by the phase rule (at constant pressure, F = C − P + 1 = 2 − 3 + 1 = 0) it has no degrees of freedom, so it occurs at a single temperature and fixed compositions.
Governing relations in practice
The eutectoid reaction γ (0.76 % C) → α (0.022 % C) + Fe₃C (6.67 % C) at 727 °C is the most important, converting austenite to pearlite on cooling — the basis of annealing, normalising, and the pearlite/martensite competition.
Design and analysis considerations
The eutectic reaction L (4.3 % C) → γ + Fe₃C at 1147 °C forms ledeburite, present in all cast irons and responsible for their castability and hardness.
Advanced theory and extensions
The peritectic reaction L + δ → γ at 1493 °C occurs in low-carbon steels during solidification and can cause casting defects. Recognising each reaction's type (eutectoid, eutectic, peritectic), its temperature, and the compositions of the participating phases is the core skill for interpreting the diagram.
Assumptions and validity limits
State assumptions explicitly before using any relation for invariant reactions — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Iron–Carbon Diagram viva and GATE descriptive questions, listing valid assumptions often earns separate marks.
Step-by-step problem approach
1. Read the question and list given data with SI units (common in Iron–Carbon Diagram papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to invariant reactions.
4. Use equation 1:
5. Use equation 2:
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to invariant reactions.
4. Use equation 1:
.
5. Use equation 2:
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
Applications & exam relevance
Invariant Reactions appears in heat treatment shop decisions. In Indian mechanical curricula this topic is tested because it connects theory to phases and transformations in steels.
GATE and semester exams often combine invariant reactions with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use invariant reactions?" — answer with a lab, mini-project, or plant visit example if possible.
Common mistakes in exams
• Confusing the eutectoid (solid→2 solids) with the eutectic (liquid→2 solids)
• Wrong invariant temperatures (727, 1147, 1493 °C) or compositions
• Claiming degrees of freedom exist at an invariant point (there are none)
• Applying the eutectoid composition (0.76 %) to the eutectic reaction
• Wrong invariant temperatures (727, 1147, 1493 °C) or compositions
• Claiming degrees of freedom exist at an invariant point (there are none)
• Applying the eutectoid composition (0.76 %) to the eutectic reaction
Quick revision checklist
Before attempting invariant reactions problems, confirm you can:
1. Invariant = fixed T, fixed composition, three phases
2. Eutectoid produces pearlite lamellae (α + Fe₃C plates)
3. Cooling rate affects lamellar spacing in pearlite
2. Eutectoid produces pearlite lamellae (α + Fe₃C plates)
3. Cooling rate affects lamellar spacing in pearlite
Revise the solved examples in Metallurgical Thermodynamics — Dekkar and one previous-year GATE or university paper for this unit.
Worked examples
Try the problem first — open the solution when you are ready to check.
Identify the reaction
Problem
Liquid of 4.3 % C transforms to austenite plus cementite at 1147 °C. Name the reaction and its product.
Solution
This is the eutectic reaction; its product is ledeburite (austenite + cementite), characteristic of cast irons.
Conceptual check — Invariant Reactions
Problem
In a Iron–Carbon Diagram semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of invariant reactions." What should a complete answer include?
Practice questions
Most-asked interview and GATE questions for this topic — expand any item for a model answer.
- 1What is Invariant Reactions, and why does it appear in B.Tech / GATE syllabi?
Model answer
The Fe-C diagram has three invariant reactions: eutectoid γ(0.76 %C) → α + Fe₃C at 727 °C, eutectic L(4.3 %C) → γ + Fe₃C at 1147 °C, and peritectic at 1493 °C. Each occurs at fixed T and composition, per physical-metallurgy texts. - 2State the relation Eutectoid: γ and name each symbol.
Model answer
The governing relation is . Write every symbol with SI units before substituting numbers. - 3State the relation Eutectic: L and name each symbol.
Model answer
The governing relation is . Write every symbol with SI units before substituting numbers. - 4State the relation Peritectic: L and name each symbol.
Model answer
The governing relation is . Write every symbol with SI units before substituting numbers. - 5State the relation Peritectoid: and name each symbol.
Model answer
The governing relation is . Write every symbol with SI units before substituting numbers. - 6Explain: Invariant = fixed T, fixed composition, three phases
Model answer
Invariant = fixed T, fixed composition, three phases — state the assumption range and one exam trap linked to this point. - 7Explain: Eutectoid produces pearlite lamellae (α + Fe₃C plates)
Model answer
Eutectoid produces pearlite lamellae (α + Fe₃C plates) — state the assumption range and one exam trap linked to this point. - 8Explain: Cooling rate affects lamellar spacing in pearlite
Model answer
Cooling rate affects lamellar spacing in pearlite — state the assumption range and one exam trap linked to this point. - 9How would you correct this error in a viva: Confusing the eutectoid (solid→2 solids) with the eutectic (liquid→2 solids)?
Model answer
Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check. - 10How would you correct this error in a viva: Wrong invariant temperatures (727, 1147, 1493 °C) or compositions?
Model answer
Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check. - 11How would you correct this error in a viva: Claiming degrees of freedom exist at an invariant point (there are none)?
Model answer
Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check. - 12How would you correct this error in a viva: Applying the eutectoid composition (0.76 %) to the eutectic reaction?
Model answer
Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
Exams & GATE
- 1State reaction, temperature, and composition for each invariant point.
- 2Avoid: Confusing the eutectoid (solid→2 solids) with the eutectic (liquid→2 solids)
- 3Avoid: Wrong invariant temperatures (727, 1147, 1493 °C) or compositions
- 4Avoid: Claiming degrees of freedom exist at an invariant point (there are none)
📖 Standard books (India)
Metallurgical Thermodynamics — Dekkar
Read: Syllabus unit
Iron-carbon, heat treatment, and alloys
Explore related topics
See real mechanical engineering careers
After exams and interviews, see how engineers actually built careers — milestones and decisions from people in the field.