Eutectic Point

The valley in the phase diagram

Mix two solids that don't form a compound — say tin and lead, or salt and ice — and something counter-intuitive happens. The mixture melts at a lower temperature than either pure ingredient. Pure tin melts at 232 °C, pure lead at 327 °C, yet a 63% tin / 37% lead blend turns to liquid at just 183 °C. Add more of either metal and the melting point climbs back up. There is exactly one composition that melts as low as it can possibly go. That composition, and the temperature it melts at, is the eutectic point.

On a temperature–composition phase diagram, this shows up as a distinctive V. Each pure component sits high on its own axis, and the temperature at which the solid first appears on cooling — the liquidus — slopes downward as you add the other component. Two liquidus lines descend from the two sides and meet at the bottom of a valley. That meeting point is the eutectic.

T
 │ Tₐ ●                                   ● T_b
 │     ╲          LIQUID                  ╱
 │      ╲                                ╱     ← liquidus lines
 │   α+L ╲                              ╱ β+L
 │        ╲                            ╱
 │ T_E ────●──────────────────────────●────   ← eutectic (solidus) line
 │         ▲ eutectic point (lowest melt T)
 │   α + β  (two-phase solid below this line)
 │
 └──────────────────────────────────────────→  composition
   pure A          X_E              pure B

The word comes from the Greek eútēktos — "easily melted" — coined by the physicist Frederick Guthrie in 1884, who noticed that certain salt-and-ice mixtures stayed liquid far below 0 °C. The defining feature is that V-shaped minimum: the one place on the whole diagram where the system is fully liquid at the lowest temperature.

Why the melting point drops: dueling freezing-point depressions

The physics is the same colligative effect that makes salt melt road ice. Whenever you dissolve a second component into a liquid, you lower that liquid's freezing point, because the dissolved particles dilute the liquid and reduce its chemical potential — making it harder for ordered crystals to form.

In a eutectic system this happens from both directions at once. Starting from pure A, dissolving B lowers A's freezing point, so the A-side liquidus slopes down. Starting from pure B, dissolving A lowers B's freezing point, so the B-side liquidus slopes down too. The two falling curves have to meet somewhere — and where they meet is the lowest temperature at which any liquid of that pair can survive. Below the eutectic temperature, no composition can stay liquid.

Each liquidus can be modeled from the freezing-point-depression / solubility relation. For an ideal solution, the liquidus for component A is set by the Schröder–van Laar equation:

ln(x_A) = −(ΔH_fus,A / R) · (1/T − 1/T_m,A)

where x_A is the mole fraction of A in the liquid, ΔH_fus,A is A's enthalpy of fusion, T_m,A its pure melting point, and R = 8.314 J/(mol·K). Write the analogous equation for B, and the eutectic is the (T, x) pair that satisfies both at the same time — the unique temperature and composition where liquid is simultaneously saturated with respect to solid A and solid B.

Freezing a eutectic: the lever rule and the invariant point

What makes the eutectic point genuinely special is how it freezes. At the eutectic composition the liquid transforms in a single step into two solids at once — the eutectic reaction:

cooling
  L  ──────────▶  α  +  β        (at fixed T = T_E)

This is an invariant reaction. By the Gibbs phase rule, F = C − P + 1 (at constant pressure, for a binary system C = 2). With three phases coexisting — liquid, solid α, solid β — the degrees of freedom are F = 2 − 3 + 1 = 0. Zero degrees of freedom means the temperature cannot change while all three phases are present. The whole liquid solidifies at one fixed temperature, just like a pure substance, producing a flat plateau ("eutectic arrest") on a cooling curve.

Off the eutectic composition, freezing is gradual. Cool a lead-rich liquid and proeutectic solid α (lead-rich) crystallizes first; this removes lead from the melt, so the remaining liquid drifts along the liquidus toward the eutectic composition. When it finally reaches the eutectic point, whatever liquid is left freezes all at once as the fine eutectic mixture. The amounts of each are set by the lever rule:

fraction of phase α = (X_overall − X_β) / (X_α − X_β)

Example, 50Sn/50Pb just above 183 °C:
  liquid is at eutectic X_E = 61.9% Sn, proeutectic α (Pb-rich) ≈ 19% Sn
  fraction liquid = (50 − 19)/(61.9 − 19) = 31/42.9 ≈ 0.72
  → ~72% of the mass freezes as fine eutectic, ~28% as primary Pb-rich grains

Common eutectic systems and their numbers

System	Eutectic composition	Eutectic T	Pure melting points
Tin–Lead (solder)	61.9% Sn / 38.1% Pb (≈63/37 by convention)	183 °C	Sn 232 °C, Pb 327 °C
Sn–Ag–Cu (SAC305, Pb-free)	96.5 Sn / 3.0 Ag / 0.5 Cu	≈217 °C	Sn 232 °C, Ag 962 °C, Cu 1085 °C
Water–NaCl (brine)	23.3% NaCl by mass	−21.1 °C	H₂O 0 °C, NaCl 801 °C
Water–CaCl₂	≈29.8% CaCl₂	−51 °C	H₂O 0 °C, CaCl₂ 772 °C
Aluminum–Silicon (cast alloy)	12.6% Si	577 °C	Al 660 °C, Si 1414 °C
Gold–Silicon (chip bonding)	2.85% Si (≈97 Au / 3 Si)	363 °C	Au 1064 °C, Si 1414 °C
Field's metal (Bi–In–Sn)	32.5 Bi / 51 In / 16.5 Sn	62 °C	Bi 271 °C, In 157 °C, Sn 232 °C

Notice how dramatic the depressions are. Gold melts at 1064 °C and silicon at 1414 °C, yet a few percent of silicon drops the Au–Si eutectic to 363 °C — a 700-degree plunge that lets microchip dies be bonded to gold-plated packages without cooking the silicon. Field's metal melts below the boiling point of water, which is why you can melt it in a hot cup of tea.

The fine-grained microstructure

Because both solids crystallize simultaneously and neither is allowed to run ahead, eutectic solids develop a characteristic fine, intimately interleaved two-phase texture — usually alternating lamellae (thin plates) or rods of α and β, spaced from a fraction of a micron up to a few microns apart. The spacing λ follows λ²·v ≈ constant, where v is the solidification rate: cool faster and you get finer lamellae.

Lamellar eutectic (cross-section):
  ▓░▓░▓░▓░▓░▓░▓░     ▓ = phase α (e.g. Pb-rich)
  ▓░▓░▓░▓░▓░▓░▓░     ░ = phase β (e.g. Sn-rich)
  ▓░▓░▓░▓░▓░▓░▓░     spacing λ ≈ 0.1–10 µm

This is a real microscopic difference, not bookkeeping. A coarse mixture would scatter light and crumble; the fine eutectic lamellae act like a natural composite — the soft phase absorbs strain, the hard phase carries load — which is why eutectic Al–Si is the workhorse alloy for cast engine blocks and pistons. The diffusion distance an atom must travel to sort itself into the right lamella is tiny, which is also why eutectic alloys solidify and reach equilibrium so much faster than off-eutectic ones.

Where eutectics show up

• Electronics soldering. The 183 °C tin–lead eutectic was the backbone of electronics for a century: a sharp melt with no pasty range means a joint that solidifies cleanly and instantly when the iron lifts, avoiding "cold joints" from movement during the mushy phase. RoHS pushed industry to near-eutectic SAC305 at ~217 °C.
• De-icing roads. Rock salt works because the H₂O–NaCl eutectic is −21 °C, so salted ice stays liquid down to that point. Below about −10 °C, salt loses its punch and crews switch to CaCl₂, whose eutectic reaches −51 °C.
• Casting and 3D-printed metal. Al–Si near-eutectic alloys (e.g. A356, ~7% Si) fill thin molds cleanly because the eutectic liquid stays fluid right up to solidification, giving castings with low porosity.
• Pharmaceuticals. Deliberately forming a eutectic between a poorly soluble drug and a co-former can lower the melting point and boost dissolution rate; "deep eutectic solvents" (e.g. choline chloride + urea, melting near 12 °C versus 302 °C and 133 °C for the pure salts) are a green-chemistry solvent class.
• Heat-sensitive safety devices. Fire-sprinkler links and fusible plugs use low-melting eutectics (Field's metal, Wood's metal) that liquefy at a precise, repeatable temperature.

Eutectic vs peritectic vs solid solution

	Eutectic	Peritectic	Isomorphous (full solid solution)
Reaction on cooling	L → α + β	L + α → β	L → single solid (no invariant point)
Degrees of freedom at the point	0 (invariant)	0 (invariant)	1 (freezes over a range)
Melting of that composition	Sharp, single T (lowest on diagram)	Sharp at the peritectic T	Over a temperature interval
Microstructure	Fine lamellae/rods of two phases	Cored grains, often non-equilibrium	Homogeneous single phase
Phase diagram shape	V-shaped valley, liquidus minimum	Step/ledge on the liquidus	Smooth lens (two curves, no minimum)
Classic example	Sn–Pb, Al–Si	Fe–C (δ-ferrite + L → austenite)	Cu–Ni, Au–Ag
Solidification speed	Fast (short diffusion distances)	Sluggish (must diffuse through solid)	Moderate

The complementary case is worth noting too: a eutectoid, where one solid transforms into two other solids (S → α + β) instead of liquid splitting. The iron–carbon eutectoid at 727 °C and 0.76% carbon produces pearlite — the lamellar ferrite-plus-cementite structure that underpins all of steel metallurgy. Same V-shaped logic, all-solid version.

Worked example: estimating a eutectic temperature

For an ideal binary system you can predict the eutectic by solving the two liquidus equations together. Take a simplified naphthalene–biphenyl-style organic pair, A and B:

A: T_m = 353 K,  ΔH_fus = 19.0 kJ/mol
B: T_m = 342 K,  ΔH_fus = 18.6 kJ/mol

Liquidus A:  ln(x_A)     = −(ΔH_A/R)(1/T − 1/T_mA)
Liquidus B:  ln(1 − x_A) = −(ΔH_B/R)(1/T − 1/T_mB)

Solve simultaneously (x_A + x_B = 1) for the T where both hold.
Iterating: T_E ≈ 314 K (41 °C), x_A ≈ 0.45.

The eutectic temperature, 41 °C, sits well below both pure melting points (80 °C and 69 °C) — which is exactly why mixed organic crystals are notoriously hard to purify by simple melting, and why melting-point depression of a "mixed melt" is a classic test for sample impurity in the organic teaching lab. A pure compound melts sharply; contaminate it and you slide down a liquidus toward some eutectic, lowering and broadening the melt.

Common misconceptions and pitfalls

• A eutectic is not a compound. The eutectic ratio (e.g. 61.9% Sn) is set by where two phase boundaries cross, not by chemical valence. Under the microscope you see two separate phases interleaved, not one homogeneous phase.
• The eutectic is the lowest melting point, not the lowest freezing point of one ingredient. It is a property of the system — the lowest temperature at which any liquid of that pair can exist — not a depressed melting point of A or B alone.
• "63/37 solder" is an approximation. The true Sn–Pb eutectic is 61.9% Sn by mass; the round 63/37 is shop convention. Both melt sharply near 183 °C, but 60/40 (a common general-purpose solder) is not eutectic and stays pasty from ~188 °C down to 183 °C.
• Only the eutectic composition has no mushy zone. Every other composition freezes over a range, with primary crystals forming first. Casting engineers exploit or fight this "freezing range" deliberately.
• Eutectic ≠ eutectoid. Eutectic splits a liquid into two solids; eutectoid splits a solid into two solids. Steel's pearlite is a eutectoid product, not a eutectic.
• The phase rule applies at constant pressure. The "invariant" zero-degrees-of-freedom statement uses the condensed phase rule F = C − P + 1. Change the pressure and the eutectic temperature shifts slightly; the usual diagrams assume 1 atm.