Phase diagrams

Why it matters

Alloys are mixtures, and a mixture can exist as one phase or several, depending on composition and temperature. A phase diagram is a map that tells you, for any alloy composition and temperature at equilibrium, which phases are present, what each contains, and how much of each there is. Metallurgists use phase diagrams to choose casting and heat-treating temperatures, to predict microstructures, and to understand why, for example, solder melts at a low temperature or why steel can be hardened.

Phases and components

A component is a pure substance (copper, nickel, iron, carbon). A phase is a region of uniform structure and composition: a liquid, or a solid solution with one crystal structure, or a compound. A binary phase diagram plots temperature (vertical) against composition of two components (horizontal, usually in weight percent).

The isomorphous diagram: copper-nickel

Copper and nickel are both FCC with similar atom sizes, so they dissolve in each other completely in the solid state. Their diagram has just three regions:

• liquid (L) at the top;
• solid solution (α) at the bottom, for every composition;
• a lens-shaped L + α region between them, bounded by the liquidus (above it, all liquid) and the solidus (below it, all solid).

Unlike a pure metal, an alloy melts over a range of temperatures.

Reading a two-phase point: tie line and lever rule

Take a Cu-Ni alloy with C0 = 35 wt% Ni held at 1,250 °C. That point falls in the L + α region.

Step 1: compositions (tie line). Draw a horizontal line through the point to the liquidus and solidus. Where it meets the liquidus gives the liquid's composition, CL ≈ 31.5 wt% Ni; where it meets the solidus gives the solid's composition, Cα ≈ 42.5 wt% Ni.

Step 2: amounts (lever rule). The fraction of each phase is the length of the opposite arm of the tie line divided by the whole tie line:

W_L = (Cα − C0) / (Cα − CL) = (42.5 − 35) / (42.5 − 31.5) = 7.5 / 11 = 0.68
W_α = (C0 − CL) / (Cα − CL) = (35 − 31.5) / 11 = 0.32

So at 1,250 °C the alloy is 68 % liquid (containing 31.5 % Ni) and 32 % solid (containing 42.5 % Ni) by weight. In a single-phase region there is no lever rule: one phase, with the alloy's own composition.

The eutectic diagram: lead-tin

When two components have limited solubility in each other, the diagram has two solid phases (α on one side, β on the other) and a special eutectic point where liquid transforms directly into both solids at one temperature:

L  →  α + β        (Pb-Sn: 61.9 wt% Sn, 183 °C)

The eutectic alloy melts at a single, lowest temperature, which is why traditional tin-lead solder used compositions near 60-40. (Lead-free solders are now required in much electronics; they use other eutectic-like systems such as tin-silver-copper.) Cooling a eutectic alloy gives a fine layered mixture of α and β called the eutectic microstructure.

The iron-carbon diagram

The most important phase diagram in engineering covers iron with up to 6.70 wt% carbon (the compound cementite, Fe₃C). Key phases:

• ferrite (α): BCC iron, which dissolves at most 0.022 wt% C;
• austenite (γ): FCC iron, which dissolves up to 2.14 wt% C;
• cementite (Fe₃C): hard, brittle iron carbide.

The key reaction for steels is the eutectoid, at 0.76 wt% C and 727 °C:

γ (austenite)  →  α (ferrite) + Fe₃C (cementite)

Slowly cooled, eutectoid steel forms pearlite, fine alternating layers of ferrite and cementite. Steels with less carbon (hypoeutectoid) form some ferrite first, then pearlite; those with more (hypereutectoid) form cementite first. There is also a eutectic at 4.30 wt% C and 1,147 °C, relevant to cast irons. Steels are iron-carbon alloys up to about 2.14 wt% C; above that are cast irons.

Worked example. A 0.40 wt% C steel cooled slowly to just below 727 °C contains pearlite and the ferrite that formed earlier. The lever rule between 0.022 and 0.76 wt% C gives the fraction of pearlite:

W_pearlite = (0.40 − 0.022) / (0.76 − 0.022) = 0.378 / 0.738 ≈ 0.51

About half pearlite and half ferrite: that mix of soft ferrite and harder pearlite is typical of medium-carbon structural and machine steels.

Limits of phase diagrams

Phase diagrams show equilibrium, which needs slow cooling. Fast cooling can produce phases not on the diagram at all, most importantly martensite in quenched steel. That is the subject of the next lesson.

Common mistakes

• Using the near arm in the lever rule. The fraction of a phase uses the arm on the opposite side.
• Confusing wt% with at%. Most engineering diagrams use weight percent.
• Expecting equilibrium phases after rapid cooling.

Recap

• Phase diagrams map phases against temperature and composition at equilibrium.
• Tie lines give phase compositions; the lever rule gives phase amounts.
• Eutectic: L → α + β at one temperature (Pb-Sn at 61.9 % Sn, 183 °C).
• Fe-C eutectoid: γ → α + Fe₃C at 0.76 % C, 727 °C, forming pearlite.