A phase diagram is a map of which solid and liquid phases a given alloy contains at each temperature and composition once it has had time to settle, and it tells you before you light the furnace what melts when, what dissolves what, and which structures can form. The lever rule converts a point on the map into the proportion of each phase present. For a slowly cooled steel with 0.40% carbon, the lever rule gives about 51% pearlite and 49% ferrite, which is why that steel is tougher but reaches a lower hardness than one with 0.76%.
Part of Crystal Structure
A phase diagram plots temperature against composition for an alloy system and marks the regions where each phase, such as liquid, austenite or ferrite, is stable at equilibrium.
Three Questions Read Most Of A Diagram
The vertical axis is temperature and the horizontal axis is composition. For any point you ask:
- What phases are present? The region the point lies in names them.
- What is each phase’s composition? In a two-phase region, draw a horizontal line (a tie line) through the point. Where it meets the region’s edges gives the composition of each phase.
- How much of each? The lever rule: the fraction of a phase is the length of the line segment on the opposite side of the point, divided by the whole line.
Three boundaries recur. The liquidus is the temperature above which the alloy is fully liquid. The solidus is the temperature below which it is fully solid. Between them is a mushy range. A eutectic is the composition that melts at the lowest temperature and freezes all at once, and a eutectoid is the same behaviour inside a solid.
The Iron-Carbon Diagram Explains Every Row In The Steel Table
The corpus classifies steel by carbon content in Steel Production, from wrought iron at 0.02-0.10% to cast iron above 2.0%. The diagram shows why those classes behave differently. The values below are the standard textbook ones and are the inputs to the arithmetic that follows.
- Below the eutectoid temperature of about 727 °C, steel is made of ferrite (almost pure iron, dissolving at most about 0.022% carbon) and cementite (the iron carbide, about 6.67% carbon).
- Above that temperature, steels turn into austenite, which dissolves up to about 2.1% carbon. The corpus puts the transformation at 725-850 °C in Heat Treatment; the range reflects carbon content.
- At about 0.76% carbon, steel is entirely pearlite when slowly cooled, a fine layered mixture of ferrite and cementite.
- Cast iron, above about 2% carbon, reaches a eutectic near 4.3% carbon that melts around 1,147 °C. That is why cast iron can be melted in a furnace that could not melt wrought iron, and why it can be poured into a mould.
The Lever Rule Gives The Pearlite Share Of A Slowly Cooled Steel
For steel below 0.76% carbon cooled slowly, the structure at room temperature is pearlite plus extra ferrite. The pearlite fraction runs from 0 at 0.022% carbon to 1 at 0.76%.
Worked example, 0.40% carbon: Fraction pearlite = (0.40 − 0.022) / (0.76 − 0.022) = 0.378 / 0.738 = 0.512. The rest, 1 − 0.512 = 0.488, is ferrite. So the steel is about 51% pearlite and 49% ferrite.
Worked example, 0.20% carbon: Fraction pearlite = (0.20 − 0.022) / 0.738 = 0.178 / 0.738 = 0.241, or about 24% pearlite.
The 0.40% steel has roughly twice the pearlite of the 0.20% steel, and pearlite is the harder, stronger constituent. That is the structural reason the corpus calls 0.30-0.50% steel “medium carbon” for axe heads and hammers while 0.05-0.15% is nails and wire, and why only steels with enough carbon harden at all: there must be enough carbon in the austenite to make martensite when it is quenched.
Alloys Beyond Iron Read The Same Way
The method transfers to any alloy. Bronze Making says bronze melts at a lower temperature than copper and that tin above about 14% makes it brittle. Those two observations are what a copper-tin diagram shows: tin pulls the liquidus down, and past a certain tin content a hard, brittle second phase appears. Precipitation Hardening depends on the solvus, a boundary showing that a solid dissolves less of the alloying element as it cools.
What A Phase Diagram Does Not Tell You
- Speed. A diagram describes equilibrium, the state reached after unlimited time. A quenched steel never reaches it. Martensite does not appear on the iron-carbon diagram at all, because it forms only when cooling is too fast for the equilibrium structure.
- Grain size and shape. Two samples with the same phases can differ greatly in strength.
- Impurities. The diagram assumes a pure binary system. Real scrap with sulfur, phosphorus or silicon moves the lines.
Making A Diagram Yourself: The Cooling Curve
Melt an alloy of known composition, let it cool slowly in the crucible, and record temperature against time. A pure metal or a eutectic freezes at one temperature and the curve goes flat while latent heat is released. An alloy that freezes over a range shows a change of slope at the liquidus and another at the solidus. Repeat for several compositions and plot the arrest temperatures. The method needs temperature readings that are accurate to a few degrees, which at the temperatures of copper or iron is beyond colour estimation. See Temperature Reading for the limits of colour.
Common Mistakes
- Using the diagram for a quenched part — the diagram predicts the slow-cooled structure only.
- Reading composition in the wrong units — diagrams are in weight percent unless stated.
- Forgetting the tie line is horizontal — reading the composition of a phase from a vertical line gives nonsense.
What’s Next
- Learn next: Precipitation Hardening — a heat treatment that follows directly from a solvus line
- Combine with: Metallography — checking which phases a real sample contains